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•
ASPECTS OF INSTITUTIONAL MOBILITY PATTERNS
OF CHEMISTS IN HIGHER EDUCATION
by
Ii:un Su1 Lee
Institute of StatisticsMimeograph Series No. 616li'ebruary 1910
I
"
)e.ABSTRACT
LEE, EON Sut. Aspects of Institutional Mobility Patterns of Chemists
in Higher Education. (Under the direction of CHARLES HORACE HAMILTON
and CHARLES HARRY PROCTOR).
This study is concerned with mobility of scholars among colleges
and universities in the academic training phase as well as in the
postdoctoral phase of professional careers. Patterns of mobility are
examined in terms of horizontal and vertical dimensions of academic
stratification system: geographic location and prestige structure of
institutions. The necessary data for the study are obtained from the
American Chemical Society's Directory of Graduate Research.
Mobility patterns of chemists among the 86 major institutions of
higher education is analized based on a random sample of 1,128 scholars
from seven successive directories covering the 1955-1967 period. Three
types of mobility are identified by linking such points of career
development as baccalaureate graduation, doctorate graduation, and
employment status. Inferences about patterns of these types of mobil
ity are made by examining the departures of the observed from the
expected frequencies of movements. The expected frequencies are de-
rived from the f1 quasi-perfect mobilityfl model presented by Goodman.
This model assigns zero frequencies along the main diagonal of the
mobility matrix and, subject to this constraint, calculates expected
values on the assam.Ption of no assooia.tion between the institution of
origin and the institution of destination.
The mobility from the bacoalaureate to the doctorate training is
oharacterized by stronger tendenoies toward regionalism than toward
prestige level homoge~eity. The regionalistio tendenoies appear to be
stronger for the institutions at the lower prestige level. The mobil
ity from the doctoral institution to the institution of employment is
also oriented toward stronger regionalistic tendencies than selective
prestige level tendencies. Thus, the academic stratification system
can be said to be a set of regional hierarchies rather than a rigid
prestige hierarchy. It is noted that downward mobility is more common,
especially at earlier stages of postdoctoral careers. Institutions at
the lower prestige level appear to have a relatively higher rate of
inbreeding and a stronger regionalistic orientation. Although patterns
are less distinctive than the tio'O previous types of mobility due in
part to insufficient number of cases, the postdoctoral job mobility
patterns are characterized by about equally strong tendencies toward
regionalism and prestige level homogeneity. The regionalistic tenden
cies are relatively stronger for institutions at the lower prestige
level and the tendencies toward homogeneous prestige were more operative
for institutions at the higher prestige level.
Implications of these mobility patterns for regional inequalities
in the quality of higher education and interregional cultural differ
ences are suggested. Regional tendencies would impose restrictions on
the development of institutions at the lower spectrum of quality and
newly emerging universities. Regions where higher education is compar
atively less effective are likely to remain so if mobility is allowed
to remain the primary equilibrium force.
A regression analysis using pair variables (mobility indicator and
distance between institutions) and point variables (institutional
characteristics) is performed to study the implied relationships and to
examine implications for mathematicaJ. model building. An examination
•-.
~.
of the residuals reveals a need for modifying extreme outliers or for
disaggregating the mobility into logical components for separate
analyses.
It is found that there is a high positive intraclass co=elation
among the residuals, which appears to be the reflection of structural
effects of the mobility system. Therefore models such as gravity models
~Ihich assume the independence among the pairwise interchanges of mobil
ity seems to.be inappropriate. An applica~ion of the systems theory
approach seems to offer some help in this line of further investiga
tion.
•
~.
ASPECTS OF INSTITUTIONAL MOBILITY PATTERNS OF CHEMISTS
IN HIGHER EDUCATION
by
EUN SUL LEE
".
A thesis submitted to the Graduate Faculty ofNorth Carolina State University at Raleigh
in partial fulfillment of therequirements for the Degree of
Doctor of Philosophy
DEPARTMENT OF SOCIOLOGY AND ANTHROPOLOGY
and
DEPARTMENT OF EXPERIMENTAL STATISTICS
RALEIGH
1 9 1 0
)
APPROVED BY:
Co-chairman of Advisory Committee Co-chairman of Advisory Committee
ii
:BIOGRAPHY·
The author was born September 19, 1934, in Kongju, South Choong-
chong, Korea. He reoeived his elementary and middle sohool eduoation
in Kongju and graduated from Chongju High Sohool, Chongju, Korea. In
1957, he reoeived the :Bachelor of Arts degree in Sooiologyfrom Seoul
National University, Korea. He was employed by the Christian Children's
Fund, Ino. until he oame to the United States for graduate study in
1962.
While studying at the University of Kentuoky, the author was
granted a graduate research assistantship. He reoeived the Master of
Arts degree in Sooiology from the University of Kentuoky in 1964. He,
transferred to North Carolina State University at Raleigh for further
graduate stUdy in the oo-major program in Sociology (Demography) and
Experimental Statistics. He was employed by the North Oarolina :Board
of Higher Eduoation as Research Assooiate and Direotor of Statistioal
Services from June 1966 to August 1969. He aocepted a position as
Researoh Demographer with The University of Texas, School of Publio
Health at Houston effeotive September 1, 1969.
The author married Chong :Mahn Lee in 1964, and they have one
daughter, Margaret Juhae, who was born April 26, 1966 in Raleigh,
North Oarolina.
iii
ACKNOWLEDGMENTS
The author wishes to express his sincere appreciation to
Professors C. Horace Hamilton and Charles H. Proctor for their skillful
guidance throughout the period of the graduate study, espeoia.lly in the
preparation of this dissertation. Appreoiation is also extended to the
other members ot the advisory' oommittee, Drs. Glenn C. McCann and F. E.
McVay, for reading the manuscript and making helpful suggestions.
Speoial gratitude is expressed to Dr. B. Ro Stanerson, exeoutive
seoretary, American Chemical Sooiety, for making available the old
direotories of the Society and to Professor O. D. Dunoan and J. Michael
Coble of Population Studies Center, University ot Miohigan, for prOVid
ing computer programs used in this study.
The author is grateful to the members of North Carolina Board of
Higher Eduoation staff (former Director, Dr. Howard R. Boozer, and
present Director, Dr. Cameron P. West) who inspired the present study
and gave him oontinued enoouragement in the completion ot this study.
Finally, the author expresses his thanks to his wite and daughter
tor their patience and sacrifice during the oourse ot this study.
iv
TABLE OF CONTENTS
Page
LIST OF TABLES. • • • • • • • • • • • • • • • • • • • • • • • • vi
LIST OF FIGURES • • • • • • • • • • • • 0 • • • • 0 • • • • • • viii
INTRODUCTION •• • • • • • • • • • • • • • • • • • • • • • • .. .. 1
The Problem • • • • • • • • • • • • • • • • • • • • • • •The Purpose .Signifioanoe of the Study ............... ••••The Data • • • .. • .. • • .. • • • • • • • • • .. • • • • ....Organization of the Thesis • • • .. .. .. • • .. .. .. • .. .. .. •
• •.. ... .· ..· ..
12345
REVIEW' OF LITERATURE .... • • • • • • • • • • • • • 0 • • • 7
Migration Theory • .. .. .. .. .. .. .. .. • • • .. .. • • .. • .. .. • .. .. 7Migration Models .. • .. .. .. .. .. • • .. .. .. .. .. .. .. • .. .. .. .. .. • 10Studies ot College Faoulty Mobility .. .. .. .. .. • • • .. • .. • .. 17
STu.DY PERSPECTIVE • 0 • • • • • • • • • • • • • • • • • • • • • 23
Frame of Referenoe • .. • .. .. • • .. .. .. • .. .. .. • .. .. • .. • • ..Hypotheses .. .. .. • .. .. .. • • .. .. .. • .. • .. .. .. • .. .. .. .. .. .. ..Definition of Mobility .. .. .. • • .. .. • .. .. • .. .. .. • • .. .. .. ..Sampling Prooedures • .. .. .. .. .. .. .. • .. .. ..Methods of Analysis • .. • • .. .. .. • • .. .. .. .. .. .. ..
2326272830
General Desoription of Data .. .. .. .. .. • .. • .. .. • .. .. • .. • ..Baooalaureate to Dootorate MObility .. • .. .. • , .. .. .. .. .. .. ..Dootorate to Employment Mobility.. • .. • • .. .. .. .. .. .. • • .. •Postdootoral Job Mobility .. .. .. .. .. .. • .. , .. • .. .. .. • .. .. ..
ANALYSIS OF MOBILITY' PATTERNS • • • • • • • • • • • •• • • • • • 35
35384755
REGRESSION ANALYSIS .. .. . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .. 61
Effeots of Distanoe 62Effeots of Prestige and Compensation .. .. .. .. .. .. .. • .. .. .. .. .. 66Examination of Residuals .. .. .. • .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 69Implioations for MathematiQal Model Building .. .. .. .. .. • • • .. 77
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . .. .sm-1MARY AND CONCLUSIONS
• • • • •
• • • • •
79
85
91.. ... .. .
.. .. ..
. ..
.. ..
.. ..... ... ..
. .. .. .... .... ..
.. .... .. .. ..
LIST OF B.EFERENCES •
APPENDICES • .. • •
v
TABLE OF CONTENTS (continued)
Page
APPENDIX A. Institutions Included in the Study • • • • • • • 91APPENDIX B. Regiona.l and Prestige Groupings of Institutions. 94APPENDIX C. A Note on the Method Used in Ca.lculating
Expected Frequencies in MObility Matrix • • • • 96APPENDIX D. Statistioal Tables ••••••••••••••• 100
vi
LIST OF TABLES
Page
Study population and selection of sample • • • • • • • • • 29
2. General characteristics of chemists sampled from doctoraldegree granting institutions, 1955-1967 • • • • • • • • • 36
3. Baccalaureate to doc'torate mobility patterns of chemistsamong the 86 major institutions of higher education. • • 39
4. Analysis of regional differences in baccalaureate todoctorate mobility patterns among the 86 majorinstitutions of higher education ••••••••• • • 0 42
5. Analysis of prestige level differences in bacoalaureate todoctorate mobility patterns of chemists among the 86major institutions· of higher eduoation •• • • • • • • • 44
6. Analysis of trends in baocalaureate to dootorate mobilitypatterns of ohemists among the 86 major institutions ofhigher education • • • • • • • • • • • • • • • • • • • • 46
7. Dootorate to employment mobility patterns of chemists amongthe 86 major institutions of higher eduoation • • • • • • 48
8. Analysis of regional differences in dootorate to employmentmobility patterns of chemists among the 86 major .institutions of higher eduoation • • • • • 0 • • • • • • 50
9. Analysis of prestige level differenoes in dootorate toemployment mobility patterns of ohemists among the 86major institutions of higher education • • • • • • • • • 52
100 Analysis of trends in doctorate to employment mobilitypatterns of chemists among the 86 major institutionsof higher education • • • • • • • • • • • • 0 • • • • • • 54
11. Postdoctoral job mobility patterns of chemists among the86 major institutions of higher education • • • • • • • • 56
12. Analysis of regional differenoes in postdoctoral jobmobility patterns of chemists among the 86 majorinstitutions of higher education ••••••••••
Analysis of prestige level differences in postdoctoraljob mobility patterns of chemists among the 86 majorinstitutions of higher education • • 0 • • • • • • •
• •
• •
58
59
vii
LIST OF TABLES (continued)
Page
14. Analysis of trends in postdootoral job mobility patternsof ohemists among the 86 major institutions of highereduoation .. • • • • It • • • .. • • • • .. .. • • • • • .. ... 59
15. Regression analysis for baooalaureate to dootoratemobility of chemists among the 86 major institutions ofhigher eduoation .. .. .. .. .. .. It • .. • It • • • .. • • • .... 6;
16. Regression analysis for dootorate to employment mobilityof chemists among the 86 major institutions of highereduoation .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. • • .. • • • .. • 64
18.
Regression analysis for postdootoral job mobility ofchemists among the 86 major institutions of highereduoation .. .. .. .. .. .. .. .. .. .. .. .. • .. .. • • • • .. .. ..
Differenoes of residuals and estimation of oorrelationfor the unordered pair regression .. .. • .. .. • • • .. ..
Differenoes of residuals and estimation of correlationfor the ordered pair regression .. .. .. .. .. • • .. • .. ..
.. ..
.. ..
• •
65
75
76
viii
LIST OF FIGURES
1. A typology of interinstitutional mobility components • . ., .Page
37
2. Distributions of residuals based on the standard errorof estimate for two types of regression analyses •••• 70
_e
Scatter diagrams of residuals against the fitted valuesfor regression analyses of baccalaureate to doctoratemobility • • • • • • • • • • • • • 0 • • 0 • • • • • • • 72
INTRODUCTION
The Problem
Institutional mobility of college and university professors is
rather high. Some eleven percent of teaching faculties in degree-grant
ing institutions were newly arrived from another educational institu
tion in the 1962-63 academic year (Dunham.ll~., 1966). There was
another ten percent newly employed in these institutions in that year.
This high rate of mobility is undoubtedly related to the well-documented
faculty shortage (McGrath, 1961; Porter, 1965; Brown, 1967, Pl'. 10-22;
Rogers, J. F., 1967). The increasing demand for faculty results from
rapidly increasing college enrollments which are a response to the
greatly increased demand for higher education and the increasing
societal requirement for research. Increasing faculty mobility has be
come a serious problem for educational planners and administrators in
assessing the supply of the faculty work force. Enrollment projections
placing the total at nine million in 1975, an increase of nearly four
million from 1965 (American Council on Education, 1968) lead us to
expect the demand, and hence faculty mobility, to continue at a high
rate in the foreseeable future.
Information about the supply of the faculty work force, as in any
demographic studies, could be reduced to three basic processes: births,
deaths, and migration. Although a reasonable amount of information
about ~aculty births," such as new degrees conferred, and about "faculty
deaths," such as retirement and actual mortality, is usually aVailable,
information about mobility is grossly inadequate. To describe, and
more importantly, to project the supply and location of the faculty work
2
force, information about its mobility is essential, increasingly so in
an increasingly mobile aoademic oommunity.
The Purpose
The movement of scholars from one institution to another can be
seen as the outcome of a complex individual deoision making prooess
under social constraints. Attraction and retention of an individual
in an institution beoomes a funotion of the oompatibility between indi
vidual conditioning and expeotations on the one hand and the charaoter
istios of the sooial system of the institution on the other. Inter
institutional mobility oan be studied from several different perspeo
tives. The foous of study oan be plaoed on the individual in a
oolleotivity. The problem may be formulated to understand motivations
for a move. The mobility oan also be studied in terms of institutional
attraotiveness~ The problem may be posed to understand how institutions·
of higher eduoation are attraoting scholars and how they are retaining
them. The institutional mobility oan also be studied from the stand
point of the total eduoational system.
The foous of the present study is on the total educational system.
There is a need to understand how institutions of higher education are
interaoting with one another in the exchange of scholars. The purpose
of this study is to desoribe and analyze patterns of migratory movements
of soholars among oolleges and universities with the ultimate aim of
developing a mathematioal model whioh oan satisfaotorily prediot inter
institutional mobility.
3
Significance of the Study
Mobility of professionals among colleges and universities is of
special interest and significance not only to students of population but
also to college administrators, educational planners and policy makers.
Development of all aspects of a modern society is intimately bound up
with the education of adequately trained manpower and the efficient and
effective use of their talents. College administrators are always con
cerned with the effectiveness of the institution. Does faculty mobility
improve the effectiveness of the educational institution in performing
its function of preserving, disseminating, and increasing knowledge?
Educational planners and policy makers are concerned with the effective
ness of the total educational system. Does interinstitutional mobility
improve the effectiveness of the total higher educational system in
fulfilling its mission? While maximizing institutional effectiveness
will tend to maximize the effectiveness of the total system, there may
be larger considerations which require examination from the standpoint
of the totality alone. While the present study is not addressed to such
broad questions, knowledge of significant trends and patterns in the
distribution of professionals among colleges and universities can be of
assistance to educational planners and policy makers in allocating
functions among institutions and in determining the strategy of geo
graphic realignment with respect to educational and socioeconomic
development of regions ..
Comparatively little is known, of a quantitative nature, regarding
the mobility of professionals among colleges and universities. Even in
general population research the migration component remains a source of
great uncertainty, especially in population estimates and forecasts.
4
This uncertainty is founded in part on conceptual difficulties. The
events of migration are difficult to cast in the same frame of reference
as vital events. While thepopulation-at-risk in vital events is rela
tively easy to define, migration as an event involves at least two
populations, one at the o:I,'igin and one at the destination of movement.
It is not at all clear which population is at risk, or how the migration
rate should be calculated. l These conceptual difficulties are coupled
with the lack of satisfactory data in the United States, although the
decennial census, supplemented by sample surveys, permits reasonable
estimates of migration. These circumstances challenge students of
population to search for new perspectives in migration research,.
The Data
Because as a rule it takes less research funds and time, secondary
analysis, as contrasted to interviewing a newly drawn sample, has become
increasingly prevalent in contemporary social science research. Of
course, the secondary analyst has no control over the questions which
were asked or not asked, and he must sometimes be frustrated by the
absence of a question or the classification of data in ways which in
hibit their usefulness to him. However, the advantages of secondary
analysis often far outweigh its limitation. For this reason an attempt
was made to utilize existing data which would allow the analysis of
institutional mobility.
The massive data collected by the National Science Foundation for
the National Register of Scientific and Technical Personnel looked
~ut practical suggestions were made by Hamilton (1965).
5
promising for the present study. The data have been collected every two
years for the past fourteen years and some recent data. have been formed
into a longitudinal file covering such subjects as geographic mobility,
mobility among types of employers, and career patterns in terms of train
ing and employment. Unfortunately, it was discovered that the identifi
cation of college or university with which a scientist was affiliated
was not included in the longitudinal file, although such information
was collected on the original questionnaire.
Since no other satisfactory data were available, it was decided to
obtain a random sample from the directories of professional societies.
TWo criteria were used in selecting professional societies: (l) the
availability of old directories covering at leas·t the past te~n years
and (2) the inclusion of a sufficient number of d,ata items in ·the
directory. One of the-key data items ""Tas this institutional affilia
tion of scientists. Most directories examin€.~d simply list the mailing
address for which the residential address is frequently given. Only
the American Chemical SocietJrt s Directory of Graduate Research met
these two criteria. The directory has been published every two years
since 1955. All the directories were availabll~ at the Society's
national office in Washington. A 25 percent remdom sample was obtained
from these directories. The sampling and recording of the data required
about 20 man-days. The detailed sampling proced~ures will be described
later.
Organization of the Thesis
This thesis is prese~ted under six major headings. The present
introduction is followed b:!y an extensive review o£. ~elated literature
6
in "three areas of interest: major migration researches, migration models
and methodology, and studies of oollege faoulty mobility. The study
perspective is presented to describe a frame of referenoe, hypotheses,
definition of mobility, sampling prooedures, and methods of analyses.
The next seotion describes analyses of mobility patterns by utilyzing
regional and prestige groupings of institutions. Three different types
of mobility are discussed: baccalaureate to doctorate, doctorate to
employment, and postdoctorate job mobility. A regression analysis is
performed to detect any relationships between interinstitutional
mobility and some independent variables, and to see whether suoh
relationships could be used in developing a model to forecast future
mobility. This is followed by a section oontaining the summary and
conclusions.
7
REVIEW OF LITERATURE
Migration Theory
Migration is oonsidered to be one of three major population
prooesses, but it differs fundamentally from the other two: mortality
and fertility. Lacking a biological basis, migration is neither in
evitable like death nor essential for the survival of a society like
reproduction. It is a more distinctively human activity occuring in
a social and cultural context. "The motives for which men migrate are
far more heterogeneous than their attitudes toward death or childbear
ing" (Wrong, 1962, p. 82). Due to its oomplexity, migration remains to
be least understood of the three major population processes, and it is
often the major unknown component of population estimates and forecasts.
The field of migration study is divided into two branches: inter
national migration and internal migration - movements of people within
national boundaries. Internal migration poses more of a theoretical
problem than international migration due to the fact that the latter
has been inspired by political and religious conflicts, while the former
takes place freely within national boundaries.
The first systematic study of migration was made by Ravenstein in
England in the late 19th oentury. He was concerned with producing
counter-evidence to a remark that migration appeared to go on without
any definite law. His two celebrated papers on "the laws of migration"
(Ravenstein, 1885 and 1889) can be summarized under the following head
ings: (1) migration and distance; (2) migration by stages; (3) migra
tion stream and counterstream; (4) urban-rural differences in propensity
to migrate; (5) predominance of females among short-distance migrants;
..
8
(6) technology m1d migration; and (7) dominance of economic motive. He
noted that the title of papers "ras ambitiously headed and warned that
"laws of population, and economic laws generally, have not the rigidity
of physical lavlS."
Ravensteinfs laws of migration provided the starting point for
work in migration theory. "In the three-quarters of a century "1hich
have passed, Ravenstein has been much quoted and occasionally challeng
ed. Eut, while there have been literally thousands of migration studies
in the meantime, few additional generalizations have been advance~'(Lee,
1966, p. 48).
A review of classic research literature since Ravenstein seems to
lead to the following three points: (1) there is a marked difference
in the various characteristics of migration streah1S between diffe~ent
types of areas or groups - migration differentials or selectivity;
(2) the volume of migration between pairs of areas is positively re
lated to the populations of the t\vO areas and negatively to the distance
between them; and (3) mi[,Tation can be interpreted as an effort to
maximize socioeconomic opportunities. These three classical points are
ordinarily presented by summary descriptions of migration data with
little attempts to generalize and relate the findings to a larger body of
social theory.
Most studies on differential migration focused upon the character
istics of migrants with little reference to the volume of migration,
and few studies have considered the reasons for migration. The tradi
tion of differential migration research reached its zenith in the study
by Eogue and Hagood (1953). I~y studies, however ended with a plea
for more data and more statistical ingenuity applied to existing data.
9
Most articles in migration theory have dealt with migration ro1d
distance and developed mathematioal formulations of the relationship.
The basic formulation was that the volume of migration between pairs of
cities stands .insome direct relation to the populations of the two
cities and in some inverse relation to the distance between the cities.
Perhaps the best known of recent theories of migration is Stouffer's
theory of intervening opportunities (1940 and 1960)0
Migration has been most frequently related to job-related variables.
Job opportunities were considered to be the driving mechanism ofmigra
tiona A simple theory is that economic opportunities are ca.used by
differences in the marginal produotivity of labor force that, in turn,
are caused by differential fertility and technical development of some
areas. Non-economic opportunities were also considered in some studies.
But measurement of opportunities hampered studies in this line. The
measurement has been complicated especially by its social-psychological
details.
At least two recent essays made effo~ts to provide a theoretical
frame of reference for migration ~tudies. Lee (1966) attempted to
develop a general schema of migration and to formulate certain hypo
theses in regard to the volume of migration, the establishment of stream
and counterstream, and the characteristics of migrants. :Beshera (1967)
attempted to interpret the past migration research literature from a
theoretical framework: household decision-making process within socio
cultural oonstraints. :But, neither Lee's conceptual schema nor :Beshers'
theoretical perspective seems to suggest a new direction of migration
researoh.
10
Perhaps migration "is hardly a subject of rapid advance in popula
tion study," as Davis (1959, p. 314) pu't it, due to the complexity of
migration phenomena and the heterogeneity of migration statistics.
This problem in migration study seems to be met by the following practi
cal suggestions; (1) the limitation of research projects to a small
number of important hypotheses, or to selected types of areas and
streams of migration; (2) limitation of studies to specific population
categories; and (3) concentrating research on specific factors (Hamilton,
1961, p. 300).
Migration Models
A variety of mathematical models have been developed to describe
and analyze patterns of internal migration. In most models of migration,
one or more of the following general principles were considered: (1)
distance between the origin and destination is an obstacle to migration;
(2) the volume of migration depends on the size of populations involved;
(3) the differential attractiveness of the origin and alternative des
tinations determine the volume of migration. The substance of these
principles finds its expression in the so-oalled gravity model, various
forms of which have been widely used to study social as well as physi
oal prooesses (See Carrouthers, 1956).
Perhaps the first of all migration models was Zipf's well known
P1P2/D hypothesis (1946a and 1946b; Dodd, 1950). It is based on the
first two principles above and states that gross migration is directly
proportional to the product of the populations of the two regions
involved, and inversely proportional to the distance between the
regions. This model reads in formula:
M..... kP.P .(Do .)-a~J ~ J ~J
(1)
11
where M.. indicates gross migration between regions i and j, P stands~J
for the size of population, Dij is the distance between i and j, and k
and a are positive variables. This gravity formulation does not specify
the directional flows of migration and defines distance in a purely
geographic sense.
In his "intervening opportunities" model, Stouffer (1940) consid-
ered the directional flow of migration and redefined distance in terms
of the cumulated "sizes" of intervening destinations. In other words,
his model states that the number of persons going to a given distance
is directly proportional to the number of opportunities at that distance
and inversely proportional to the number of intervening opportunities.
StoufferOs model can be represented:
(2)
•
where Mi~j total migration from i to j.
Mi. total out-migration from i to all other places.
M.j
total in':'migration to.j from all other places.
MI total in-migration to places located inside the circle
whose diameter connects i and j.
Later, Stouffer (1960) took the logical step of recognizing inter-
vening "competing migrants." In other words, the attractiveness of
place j for migrants from place i depends on how many potential migrants
are closed to j than are the potential migrants in i. For this effect
a new term is introduced in the denominator of equation (2):
,:
"
12
where MO represents total migration from all places in the circle
centered on j with radius Dij~
Stouffer's model has been tested with generally supportive results
by a number of people (Bright and Thomas, 1941; Isbell, 1944;
Strodtbeck. 1949; Folger. 1953; Galle and Taeuber. 1966). But the main
difficulty with this model is the appearance of l!non~competitive oppor-
tunities." That is to say. different types of opporlunites are relevant
for different migrants and they can not be represented by one indicator.
Besides, the usefullness of Stouffer's model seems to be limited in
explaining migration. since it does not include any variables other
than concurrent migration flows.
A model which takes into consideration the attractiveness of each
place is developed in the Netherlands by Somermeijer (ter Heide. 1963).
He takes advantage of the Zipf's hypothesis and introduces the relative
attractiveness of places i and j. Attractiveness indices were formu-
lated from such variables as per capita income, percent unemployed,
degree of urbanization, recreational resources, and quality of dwell-
ings. The following two formulas describe migration streams in opposite
directions:
M. . = [!k + c(F. - F.)] P.P .(D. ')-a~-J J ~ ~ J ~J
M. . = r!k + c(F. - F.) ] P. P . (D .. )-aJ~~ L ~ J ~ J ~J
where F represents average combined value of attractiveness factors.
The sum of these two formulas gives gross migration which takes the
same form as Zipf's model in equation (1). Somermeijer tested his
model with good results on migration between Dutch provinces and
13
obtained correlation coefficients for the effeots of the attractiveness
factors on net migratio~ in the neighborhood of 0.9 by fitting the con-
stants by iteration.
In an effort to explain migratory flows in the United States,
Lowry (1966, pp. 11-22) introduces a model that incorporates economic
as well as "gravity" variables. As Lowry (1966, p. 11) stated, her
model is "closest in spirit to Somermeijer's." Lowry's model takes the
following form:
(6)
•
\'J'here Li,Lj • =number of persons in the nonagricultural labor force at
i and j, respectively.
Ui ' Uj = unemployment as a percentage of the civilian nonagri
cultural labor force in i and j respectively.
Wi'Wj = hourly manufacturing wage, in dollars, in i and j
respectively•
.Lowry*s model is exceedingly convenient because it becomes linear
Ul1der logarithmic transformation as follows:
and this e:l>.']?ression is easy to use in a multiple linear regresElion. In
this model, attractiveness is proportional to the relative influences
of employment and of wages. Thus, it offers a very neat format for
data analysis and accessible interpretation as well. This model has
been tested bYLO\~ for national data and retested by Rogers (1968,
pp. 74-82) in California with minor modification, using "proxy" variables.
(8)
•
14
In her monograph, Lowry (i966, pp. 35-59) introduces another model
that is more useful as a tool for forecasting the migration component of
population change but less useful for scientific explanation. While the
first model considers the directional flows among various pairs of
metropolitan areas, the second model is addressed to the net effect of
migration upon metropolitan population growth. Lowry's second model is
patterned directly after the basic model developed by Blanco (1964).
The Lo~~'s version of Blanco model reads:
d11i = aO + aldPi + a2dQi + a3dAi
+ a4dEi + a5dI i + u
where dPi = net ohange in the number of residents 15-64 years of age in
the absence of migration ("natural inorease").
dQi = net ohange in oivilian nonagricultural employment.
dAi = net ohange in the number of Armed Foroes Personnel.
dEi = net ohange in the number of school enrollment 14-29 years
of age.
dIi = ohange (in percentage) in median inoome for "families and
unrelated indivieJ.uals."
By fitting this regression model, Lowry obtained an impressive value of
R2 = .9744, indicating that 97 peroent of the variance in migration
rates among Standard Metropolitan Statistical Areas could be accounted
for by regression on these independent variables.
Lowry's first model assumes that the interchange within eaoh pair
of places is independent of that within each other pair. This assump
tion greatly simplifies calculation and helps to achieve certain practi
cal objectives. But, the point of criticism stems from this assumption.
•
15
In this model, system effeots are disoarded so that any pair of oities
may be viewed as a oomplete system without regard to the migration flows
to and from the oities disoarded. In other words, a family of models
whioh use gravity prinoiples assumes a standard formula for pairwise
interaotions and the formula remains the same regardless of the struo
ture of the partioular system, or even of the nature of the phenomenon
itself. Certainly one formula does not work for everything and inter
aotion really is not invariant with structure and nature of the phenome
non. The systems theory approaoh seems to offer a new direction in
model-building efforts in migration researoh. A model based on a
connected graph with network concepts will remedy the weakness of
gravity formulas. The systems theory models prove to be promising in
various fields (Ellis and Van Doren, 1966).
Some other models have also been developed in migration studies.
Additive models suoh as those of Price (1959) and Tarver (1961) calcu
late migration probabilities by adding various attraotiveness factors
to form an attraotiveness index for eaoh region. In these models, the
"opportunities" faotors are introduoed only at the expense of losing
the distance and communication faotor. Thomlinson's model (1961)
provides a technique to control seven spatial variables including
distance, somewhat similar to standardization techniques in fertility
and mortality analyses. Thomlinson's model explains very little about
opportunities and its practical usefulness seems to be limited.
Paralleling the growing interest in quantitative analysis of migra
tion phenomena has been the emergence of Markov chain theory as a
methodological tool for investigating social, industrial, and geographic
mobility. Mobility in this conception is represented by quantities
•
16
governing the time until movement and by others governing the choice of
a destination, the transition probabilities. With its great variety
and flexibility as uncovered by extensive mathematical development,
Markov chains seem to have a great potential in studying various tempor-
al changes of social phenomena. Markov chain models have been used to
examine intergenerational social mobility (Prais, 1955; Kemeny and
Snell, 1960, pp. 191-200), to study the movement of workers between
industries (Blumen, ~~., 1955) and to project future population
totals for Census Divisions in the United States (Tarver and Gurley,
1965). The mover-stayer model, a generalization of the Markov chain
model, was elaborated by Goodman (1961) to present consistent estimators
and some statistical methods of testing hypotheses concerning the model.
Although not fully tested, some further modification has been attempted
to use the Markov chain model in sociological and demographic research
(Coleman, 1964; MYers,~~., 1967; McGinnis, 1968).
By and large, Markov chain models are more useful in analyses of
past migration flows and of less practical use in efforts to forecast
future place-to-place movements. This may be because the .transition
__~ probabilities themselves are changing in time in ways that need to be,_~ji~'
better understood. However, Markovian concepts do provide a useful
description of the observed differential behavior of migrant cohorts at
a given point in time (See Rogers, 1968, pp. 86-104).
The flcl''' of any kind of quantifiable transactions, including migra-
tion, usually requ1rel'l some preliminary gross analysis to eliminate the
primary effects of the "size variable" before introducing other possible
explanatory variables. For this purpose a statistical "null model" was
17
developed by Savage and Deutsch (1960). The method develops a matrix
of expected or baseline data from assumptions of complete indifference
among the actors and measures the plus or minus differences between
this baseline value and the actual amount of transactions in each direc
tion for every pair of actors. It thus removes gross size effects and
permits tentative inferences about the distribution of preferences
among pairs of larger groups of actors; about degree of clustering or
integration among actors; and about changes over time, if several
matrices are used. It thus locates interesting pairs or groups for
further study. This method was called a "null model" in the sense that
the departures from it are of primary interest. Savage and Deutsch
developed this model to analyze import-export data among North Atlantic
nations.
Subsequently Goodman (1963, 1964 and 1965) found that the methods
given by Savage and Deutsch require certain modifications and suggested
alternative methods that are preferable in some respects to the Savage
Deutsch method. Goodman further presented a generalization of the model
appropriate when transactions between certain actors may be restricted.
This model appears to be the most appropriate method for the preliminary
analysis of migratory flow data.
Studies of College Faculty Mobilit~
Sociologists have studied various aspects of the academic community
from a sociological perspective (Wilson, 1942; Lazarsfeld and Thielens,
1958; Caplow and McGee, 1958; Donovan, 1964; Hagstrom, 1965). A recent
study adds the perspective of an economist (Brown, 1965 and 1967). In
addition to these major studies, many studies on college faculty have
•
18
been conducted by institutions of higher education (Stecklein and
Lathrop, 1960), by states (Wilson, !i~., 1961)~ and by national organ
izations (Harmon, 1965; National Academy of Sciences, 1968), in order to
meet specific information needs. Some studies have dealt intensively
with faculty mobility, while others have provided insightful informa-
tion about problems related to mobility.
An earlier study made by Sorokin (1947, pp. 417-420) dealt with
patterns of faculty recruitment in four major universities. Another
earlier study by Hollingshead (1940) was concerned with progression
through faculty ranks and other aspects of the mobility patterns.
WilsonQs classical study, The Academic Man, can not be omitted from any
review of literature in this field. Though not systematic research,
his book provides a sensitive and insightful description of the careers
and problems of college faculty.
An intensive study of faculty mobility within and between ten major
universities was conducted more than ten years ago by Caplow and McGee
(1958). This study carried out the most extensive investigation of
faculty mobility in the academic stratification system. It was observed
that the possession of appropriate "contacts" in the discipline was an
important factor in recruitment to positions in academic institutions.
Caplow and McGee state:
A distinction must be made between the two kinds ofrecruitment in general use, "open" or competitive hiringand "closed," or preferential hiring. In theory, academicrecruitment is mostly open. In practice, it is mostlyclosed (Caplow and McGee, 1958, p. 109).
Deviations from the universalistic-achievement pattern in the
academic community are also observed in other studies. Marshall (1964,
pp. 85-90) reports some evidence of this in the academic market for
•
19
economists. Hargens and Hagstrom (1967) show that the prestige of the
institution where a scientist received his doctorate is related to the
prestige of his present affiliation even when the effects of his
productivity are controlled.
Hargens and Hagstrom related their findings to Turner's (1960) con-
cept of "contest" and "sponsored" mobility. Turneros two ideal-type
modes of social mobility might serve fruitfully as sensitizing concepts
in further research in this line. These two ideal-types of mobility
were designed to clarify observed differences in the predominantly
similar English and American systems of stratification and education.
Turner distinguishes these two types as follows:
Contest mobility is like a sporting event in which manycompete for a few recognized prizes. The contest isjudged to be fair only if all the players compete on ane~ual footing. Victory must be won solely by one's ovmefforts. The most satisfactory outcome is not necessarilya victory of the most able, but of the most deserving. • •Sponsored mobility, in contrast, rejects the pattern ofthe contest and favors a controlled selection process. Inthis process the elite or their agents, deemed to be best~ualified to judge merit, choose individuals for elitestatus who have the appropriate ~ualities. Individuals donot win or seize elite status; mobility is rather a processof sponsored induction into the elite (Turner, 1960, p.855).
In their investigations of academio stratification system, socio-
logists have emphasized the importanoe of a prestige faotor that leads
to deviations from the contest mobility. From an eoonomist's viev~oint,
Brown (1967, p. 62) desoribes the academic market place as a series of
submarkets partially isolated from each other by geography, subject
matter, research interest, demographic characteristios, purpose, and
stature. BrOi~ observes:
When viewed against olassical wage theories conoerningmobility in an economic utopia, the academic labor
20
market appears to be a maverick. Entry into and exit fromthe market are not unrestricted. Because of such practicesas inbreeding, promotion from within~ anti-pirating pacts,tenure, and fringe benefits, along with adherence to thecode of ethics, movement within the market is not free.Nor is movement costless; it involves both monetary andemotional costs. Decisions to relocate are seldom madewithin the confines of economic rationality or profit maximization (Brown, 1961, p. 61).
Some studies have been directed toward the causes of faculty flow
to and from a particular institution. These studies have direct impli~
cations for college and university administrators who are interested in
maximizing their institution's power to attract and retain staff.
Caplow and MoGee (1958) studied the job vacancy, the factors that had
led to the vacancy, and procedures followed in filling it. Their study
provided the following generalizations:
In summary, these findings lend support to the view thatthe "push" of academic migration is stronger than the"pull." The majority of vacancies cannot be attributed tothe lure of opportunities elsewhere but to dissatisfaction either the failure of the incumbent to please his associatesor their failure to please him, or both (Caplow and McGee,1958, p. 80).
and
In general we may say that an institution!s attractivenessto a candidate is determined by what it can offer him inthe way of prestige, security, or authorit~. The specificattraction is a function of the candidate 9s OylIl situation,so that, for example, prestige is usually the strongerlure for men on the way up, whereas security and authoritybecome more attractive to men on the way down (Caplow andMoGee, 1958, p. 147).
The University of Minnesota conducted the most intensive ,stUdy to
determine factors that were affecting faculty mobility at that institu
tion (Stecklein and Lathrop, 1960). The factors found to be influential
in this study mayor may not be typical of oonditions at other large
institutions. In fact, such faotors may change continuously at the same
21
institution. This study had led Stecklein to make the following remarks:
It should be clear by now that the factors that influ=ence faculty members to change jobs ~'e many and varied.They are different for individuals teaching in the sameand in different disciplines; they differ for differentage groups; they are different for single and marriedfaculty members and for married faculty members withand without children; they are determined by where aperson was born, went to school, or lived, they changefrom year to year or even from week to week and theyare influenced by sets of circumstances that no one eWl
predict or control (Stecklein, 1961, p. 31).
Despite the complexity and unpredictability of individual cases,
Ferriss (1966) maintains that faculty mobility ~ masse may present a
more predictable profile. After reviewing some fragmented mobility
studies, Ferriss hypothesizes that faculty mobility follows more "the
endogamous pattern" than flIthe stepladder pattern." He cites six factors
which influence faculty to move more readily between institutions of
similar character than between institutions of different type. The six
factors are (1) kinship among "sister" institutions, (2) informal
communication, (3) role performance and role rewards, (4) teaching or
research specialtyp (5) faculty-institutional organization, and (6) re-
muneration. In his discussion Ferriss implied that various colleges
and universities can be ranked in a hierarchical fashion.
The basis of this stratification of institutions has been usually
expressed in terms of institutional prestige. Veblen (1957, pp. 98-107)
suggested that academic prestige might be viewed as a type of institu-
tiona1 "good will" which attracted money from potential benefactors and
which could be unrelated to scholarly quality or achievement. He saw
American institutions of higher education as business enterprises which
acquired prestige by improving and expanding their physical facilities.
e
e
~e
•22
More recent discussions have portrayed academic prestige in terms of
the quality of scholars employed and trained at various institutions
(Caplow and McGee, 1958; Reisman, 1957; Berelson, 1960). It is clear
that the hierarchy of institutions consists of more than existing social
evaluations. Caplow and McGee (1958, p. 193) employ a "major league
minor league- bush league" metaphor in their discussion of the hierarchy,
and suggest that scholars are often enabled or condemned to spend their
entire careers in the "league" in which they obtain their doctorates.
Thus, the academic community is portrayed as a set of vertically
arranged strata, with little mobility between strata and hence the
dominance of horizontal mobility within the stratum. However, few
studies have attempted to summarize systematically the implications of
such inquiries for more general theories of stratification and to
examine these phenomena in the light of other pertinent factors that
are usually considered in migration researches, such as distance between
institutions, 1. £,., ,the dimension of regionalism.
•23
STUDY PERSPECTIVE
Frame of Reference
Institutional mobility of scientists is to be viewed as the result
of their individual decisions in the context of the social structure
and interpersonal relationships in the educational system. The recog
nition of individual decisions has been insufficient in traditional
demographic studies. In recent years, the possibilities of micro
demography, of building up demographic trends from individual decisions,
has become stronger as more individual control can be exerted over the
demographic events (Baok, 1967). T'ne most insightful discussion of the
effects of individual decisions upon demographic consequenoes was given
by Beshers (1967).
A move by an individual from one institution to another is a result
of the selection of alternatives by him. The individual selects alter
natives in terms of the consequences that he ascribes to them. Thus,
the occurrence of mobility in a given time period is viewed as the out
come of a process of decision making under sooial constraints.
Classic decision theory assumes that a complete set of his action
alternatives is known to the decision maker along with the set of
possible states of the world facing him, and that he is able to assign
a pair of numbers to each outcome. An outcome is a particular action
applied to a particular state of affairs. One number is the probability
of the occurrence of the state of affairs and the other number indexes
the desirability of the outcome, the utility of the result of aoting in
a certain way when the world is in a certain state. The individual
deoision maker takes the product of the pair of numbers associated with
•.
24
each outcome and adds these over all states of affairs, compares the
resulting expected utilities for all alternatives, and then selects
that alternative that will maximize his expected utility (Chernoff and
Moses, 1959). However, the actual deoision making is a process of
continuous reassessment of the probabilities and utilities using con-
stantly received new information, and accommodating to shifting values.
Characteristic patterns of decision making may differ between
traditional and modern society and among various groups of people in
modern society. :By slightly modifying Max Weber's concepts, :Beshers
(1961, p. 85) distinguishes three modes of orientation: traditional,
short-run hedonistic, and purposive-rational. In the traditional mode,
a decision is made according to custom with no recourse to new informa-
tion. The shorl-run hedonistic mode is oriented to a very brief future
time perspective. The individual acting in the purposive-rational mode
has an elaborate time perspective with sensitive recourse to new infor-
mation.
The events of institutional mobility of scientists could be
represented as the outcome of decision processes that are constrained
by the modes of orientation, social variables, and social psyohological
decision making prooesses. The job-ohange decision usually takes the
form of joint deoision in the family. The main constraints stem from
oharacteristics of the husband's job and from characteristics of the
household. When the mobility does not involve change of residence, the
job characteristios alone constitute the constraint.
The factors which enter into the deoision to move from one institu-
tion to another may be summarized under the following four controls of
mobility process:
•25
(1) The geographic extension of the academic job opportunities.
(2) The dispersion of knowledge about possible destinations.
(3) The differential attractiveness of the origin and possible
destinations.
(4) Personal and household characteristics a
The first and second variables are olosely interrelated and cannot be
studied separately. The fact that information itself may become less
available as distance increases makes it difficult to separate these
two. The third factor is most often expressed in terms of notions of
institutional "quality" or "prestige." It has been known that there is
a high positive correlation between institutional quality and other
indicants of attractiveness, such as average salary (Carter, 1966, pp.
111-112), formal honorary awards and recognitions (Crane, 1965; Cole
and Cole, 1967), and other social-cultural benefits. The fourth factor
includes the nuniber and spacing of children, the life cycle, the hous
ing requirements, and personal preferences. It is also known that
additional personal characteristics may offset the other factors cited
a.bove. For instance, the influence of distance is contingent upon the
skills of individuals. In general, the higher the skills of the indi
vidual, the more geographically extended the job market. High quality
scientists tend to be exposed to a national market and lower quality
scientists tend to form a local or regional market. Brown (1965, p.
132) has observed that top-quality institutions comprise a separate
labor market.
•,
26
Hnotheses
The foregoing observations se~m to suggest that the geographio
distrib~tion of institutions and the quality or prestige struoture of
institutions oomprise the major oonstraints on movement of persons
amongoolleges and universities. Studies (Marshall, 1964, pp. 71-90;
Brown, 1965, pp. 86-125) have shown that informal oontacts are a
primary means by which scholars obtain new positions. NeWly trained
doctorates are especially dependent upon their teaohers who already
have some sort of established communication ohannel. In such oiroum-
stanoes, geographic proximity provides an opportunity for the develop-
ment of regionalistio tendenoies in oommunioation and henoe mobility.
On the other hand, sooial-cultural proximity provides an opportunity
for the development of a stratification system within the academio
community. Thus, previous investigations (Caplow and McGee, 1957, p.
193; Hargens and Hagstrom, 1967, pp. 31-32) have asserted that posses-
sion of a degree from a top university is almost a necessary oondition
for recruitment to a position in a top university regardless of one's
competenoe.
From this line of notions the following hypotheses are derived:
(1) Institutions in the sa.Jlle region tend to exohange professionals
more among themselves than with institutions in other regions•
. MOre speoifically, ins~itutional mobility is negatively
assooiated with the distance involved between institutions
when the effect of institutional size is controlled.
(2) Institutions in the same prestige level tend to exchange
•r
27
mobility is negatively associated with the difference in the
prestige rankings of institutions when the effect of institu-
tional size is controlled.
(3) The tendencies and relationships specified in (1) and (2) are
• more distinctive for young scholars than for their elders.
Definition of Mobility
}~bility is defined in this study as a change of institutional
affiliation. No restriction is placed upon the distance of the move or
upon the voluntary or involuntary nature of the act. Thus, a move from
one institution to another in the same city constitutes mobility, re-
gardless of the involvement of geographic migration. .Any move from one
school or department to another within the same institution is not con-
sidered as mobility. In most cases there is no problem in choosing the
boundaries of institutions, but in a few cases of recently merged insti-
tutions it was decided to treat the merger as retroactive for the entire
period of the study.
Three types of mobility emerge ').'I.pon linking such points of career
development as baccalaureate graduatton, doctorate graduation, and
employment. The following three types of mobility are treated in this
study:
(1) Baccalaureate-to-doctorate mobility refers to the change of
educational institution between baccalaureate graduation and doctorate
graduation.
(2) Doctorate-to-ernwloyme~tmobility is the change of educational
institution between doctorate graduation and employment in institutions
of higher education.
e"
•
28
(3) Postdoctoral job mobility is the job change from one institu-
tion to another following the doctorate.
SamPling Procedures
The population to be studied consists of all faoulty members
affiliated with chemistry departments offering graduate degree programs
in institutions of higher education in the United States. The American
Chemioal Society (ACS) publishes directories of graduate programs every
two years, which contain such Wormation as degree origins and dates
and listing of pUblications for each scholar. The ACS Directory of
Graduate Research also inoludes as a separate seotion the departments
of biochemistry, medioal-phE;l.rlllaceutical ohemistry and chemical engineer
ing, but these related fields are excluded from the present. stUdy.
Canadian institutions are also-excluded from the stUdy.
The study sample was selected from seven successive editions of
direotories (1955, 1957, 1959, 1961, 1963, 1965 and 1967), using a
single-stage cluster sampling procedure. The main portion of the
directory is arranged by institution, with an alphabetical listing of
individual names at the end. The alphabetical listing of the latest
directory (1967) was first subdivided into 80 clusters of adjacent
listed names and a random sample of 20 clusters were selected. The
starting point of eaoh oluster in the alphabetical sequenoe plays an
important role in identifying the selected sample olusters in each cf
previous editions of the direotory. For example, suppose oluster 3 was
seleoted from the 1967 directory, then the corresponding cluster in the
1965 directory can be identified by taking a block of names in the
alphabetical listing inoluding the starting point of cluster 3 and not
29
including the starting point of cluster 4. The sample, then, consists
of all chemists included in these 20 clusters in at least one edition
of the directory. Thus, included in the sample are those who left the
profession as well as those who newly joined the profession during the
1955-1967 period.
A total of 1,128 unduplicated individual names were selected from
the 20 selected clusters following through the seven successive edi-
tions of the directory. The recording of names and necessary informa-
tion was done starting from the latest directory and working back to
earlier directories. From each of the earlier directories new names
were added. The recording of data from earlier editions of the direc-
tory was less time-consuming than the initial recording, since the main
task was to record the institutional affiliation to the names already
in the record. The sizes of the study population and sample are shown
in Table 1. Of the 1,128 names 244 appear in all seven successive
directories and 215 appear only one time.
Table 1. Study Population and Selection of Sample
Number of Estimated Number of Number ofYear institutions number of names new names
listed total names selected added
1967 165 3,572 881 881
1965 153 3,127 801 81
1963 140 2,686 653 461961 125 2,190 555 41
1959 122 2,087 504 31
1957 110 1,731 450 28
- 1955 98 1,556 376 20
Total • • • • • 1,128
.,
30
For eaoh listed name the following information was recorded; full
name, sex, year of birth, speoialty in chemistry, year and institution
of baohelor's degree, year and institution of master#s degree, year and
institution of doctorts degree, and institutions of employment with
academic rank for the seven directories. All the records were coded
and punched for IBM machine-processing - one card for each name. In
addition to careful checking of codes and verification of punched cards,
cheoking by machine was performed to detect and eliminate certain resi-
dual errors, such as impossible codes.
Methods of Analysis
The first task in the analysis of the data was to select a manage-
able number of institutions among whioh the flow of scholars could be
analyzed. The criteria employed in selecting institutions were (1) the
institution is included in the Directory since 1955 and (2) it employed
at least 15 faculty members and produced 5 or more doctorates in 1966
1967 in the chemistry department. After the screening process 86 insti
tutions were selected (See Appendix A).
In order to record the information about the flow of scholars
among these 86 institutions, sociometric-type matrices of the order of
86 x 86 were formed for various types of mobility. These matrices show-
ing observed numbers of movements were analyzed by using a method
presented by Goodman (1963 and 1964) in order to obtain expected fre-
quencies of movements. As reviewed earlier, this method assigns zero
frequencies along the main diagonal of the mobility matrix and, subject
to this constraint, calCUlates expected values on the assumption of no
association between the institution of origin and the institution of
,>
•
31
destination (See Appendix C). Then, a comparison of the observed and
expected frequenoies of movement would indicate the exoess or deficit
of mobility between institutions.
Inferences about patterns of mobility were made by utilizing a
combination of regional and prestige level groupings of institutions.
Regional groupings were formed basically on the census regions of the
United States (See Appendix B). The following five regions were used:
New England, Middle Atlantic, Midwest (East North Central and West
North Central), South (South Atlantic, East South Central, and West
South Central), and West (Mountain a.'1d Pacific). Any regional classi...
fication, including the one used here, is more or less arbitrary and
might be interpreted best as a crude method of measuring distance.
Prestige groupings were based on the American Council on Education
(ACE) study on quality rating of graduate faoulty as reported by Carter
(1966). Four levels of prestige groupings are used in this study (See
Appendix B). Although there is folklore in abundance regarding pres-
tige d..ifferentials among colleges and universities, there are no common-
ly acoepted indexes available analogous to the occupational and other
prestige scales routinely used in stratification research. While many
sociological studies of prestige have emphasized persons and categories
of persons as the unit of analysis, systematioally conducted research
of prestige as it relates to complex orgarli~ations is relatively rare.
The ACE study reported by Carter represents one of the rare pieces of re-
search in assessing quality or prestige of academic institutions.
The Carter study is essentially a subjective assessment of institu-
tional prestige based on responses from departmental chairmen, senior
scholars, and junior scholars. In order to avoid the shortcomings of
, ,
32
earlier studies (Keniston, 1959; Hughes, 1928), Carter made an attempt
to obtain well-balanced representation of judges. He provided separate
ratings for 29 different fields of study. Ninety six chemistry depart-
menta that awarded one or more q.octorates from July 1952 through June
1962 were rated by 218 chairmen, senior scholars and junior scholars.
These judges were asked to rate each institution on a six-point scale
concerning two quality aspects of graduate programs in chemistry: the
quality of graduate faculty and the effectiveness of doctoral program.
Results of the two sets of ratings are similar. The rating based on
the quality of graduate faculty was used in this study.
The analysis by the use of regional and prestige level groupings
was followed by a regression analysis. An index of mobility for each
ordered pair of institutions was oomputed from the signed difference
between the observed and expected frequencies of movements desoribed
earlier. The index of mobility is thus not symmetric. In other words,
the index from institution A to institution B is different from the
index from institution B to institution A. There are 7,310 (86 x 85)
ordered pairs to be analyzed in the 86 x 86 mobility matrix.
While the index of mobility is a "pair" variable, derived for each
of the 7,310 ordered pairs of institutions, some independent variables
such as prestige and average compensation are "point" variables which
are scored for each of t4e 86 institutions. As a third kind of vari-
able, another "pair" but symmetrical variable, the distance between
institutions, is measured for each of the 3,655 unordered pairs. ~le
"point" variables need to be converted into "pair" variables on ordered
pairs in order to carry out regre~sion analyses of the index of mobility.
..
33
Also, the index of mobility needs to be "symmetrical" in order to in-
elude distance as an independent variable. It was thus decided to
perform two types of regression analyses, one using the 3,655 unordered
pairs and the other using the 7,310 ordered pairs as the units of
analysis.
The regression analysis of unordered pairs was done using the
average of the two directional indices of mobility between each pair of
institutions as the symmetrical variable and the distance, absolute
differences of prestige scores and average compensation and average of
prestige scores and average compensation for each pair as the indepen-
dent variables. The distance was measured by highway mileage between
the locations of institutions. Prestige scores were taken from the 1964
American Council on Educ~tion study reported by Carter. The average
compensation (salary plus other benefits) figures were the mean of 1962-
63, 1963-64, and 1964-65 figures reported in the American Association
of University Professors (AAUP) Eulletin (1963, 1964 and 1965).
In the regression analysis of ordered pairs, the index of mobility
does not need any adjustment. The adjustment of prestige scores and
average compensation was done by taking the signed difference for each
ordered pair of institutions. Since the distance is symmetric, it was
necessary to consider the ~irection of distance. The adjustment of
distance was accomplished by designating as positive the south-to-north
direction and as negative the north-to-south direction; similarly,
west-to-east was designated positive and east-to-west negative. Thus
two sets of distance figures were entered in the regression analysis.
The computations of regression analyses were performed by using
the multiple regression comput~r program written by Goodnight (1967).
.'
•
34
This program provides more options to obtain various statistios associ-
ated with the regression analysis than other available oomputer programs.
These options, among other things, include simple statistios for eaoh
variable, bi-variate statistios, all statistics in the Doolittle prooe-
dure, and expected values. The input subroutine of the program also
allows transformations and other data manipulation before entering into
the main regression program.
•
35
ANALYSIS OF NOBILITY PATTERNS
General Description of Data
Some general characteristics of the data sampled for this study
are summarized in Table 2. It is to be noted that 97 percent of all
chemists in this study are men and only 3 percent are women. Due to
the small number of women in the sample, no attempt can be made to
analyze mobility patterns by sex. Of the total sample, 97 percent hold
the doctorate and the small number of non-doctorate chemists does not
allow any separate analyses.
The academic rank held in 1967 were divided as follows: professor,
42 percent; associate professor, 24 percent; assistant professor, 32
percent; and instructor and research associate, 2 percent. Since the
sample was obtained from the graduate school faculty in the institu
tions offering doctorate programs, the percentage of professors in the
sample is somewhat higher than it is in the total faculty in colleges
and universities.
The regional distribution of doctorate origins indicates that more
than one-third of the chemists in the sample obtained their doctorate
from the Midwest, whose doctorate-producing institutions constitute
principally the "Big Ten." iJ;'his J;'egion seems to provide dootorate
graduates in large numbers for other regions. This is apparent when
one compares the distribution of doctorate origins with the distribu
tion of postdoctoral employment. Whi~e producing 37 percent of the
doctorate in the sample, the Midwest employed only 24 percent of the
total in 1967. On the other hand, the South employed 22 percent of the
total doctorate in 1967 but produced only 10 percent. Many research and
-.Table 2. General Charaoteristios of Chemists Sampled from
Doctoral Deb~ee Granting Institutions, 1955-1967
36
Characteristios Number Percent
~
:Hale 1,094 97 .Ol~Female 34 Z·O
Total 1,128 100.0
Highest DeSFee Held
Dootor 1,099 97.4I'Taster 24 2.1Baohelor 5 0.5
Total 1,128 100.0
Speoialty
Analytioal chemistry 120 10.6Orgffi1io chemistry 308 27.3Inorganio chemistry 150 13.3Physioal oh~mistry 387 34.3Bioohemistry 71 6.3Other specialties 92 8.2
Total 1,128 100.0Regional Distributiop of Doctorate Orie;in
Nevi England 166 15.1I'riddle Atlantio 189 17.2NidVlest 401 36.5South 104 9.5"i'lest 165 15.0Foreign oountries 74 6.7
Total 1,099 100.0
Academio Rank in 1967
Professor 368 41.8Assooiate professor 210 23.8Assistant professor 286 32.5Instruotor &researoh assooiate 17 1.9
Total 881 100.0
Regional Distribution of Employrrlent in 1961New England 105 11.9Middle Atlantio 182 20.7Mid"lest 215 24.4South 196 22.2\I/est 183 20.8
- Tota~ 881 100.0
..
•
37
policy concerns have been fooused on suoh an imbalanoe in the quantita-
tive distribution and redistributj.on of doctoral manpovler. However, the
sheer quantitative consideration seems to be insufficient in assessing
regional equality. An understanding of the qualitative aspect and the
exchange mechanisms of scholars among institutions would add a new
perspective in studying the distribution and redistribution of educated
manpower.
The analysis of mobility patterns will be divided into three
general sections. The first section will focus upon patterns of the
baccalaureate-to-doctorate mooility among the 86 institutions; the
second section upon patterns of the doctorate-to-employment mobility;
and the final section upon patterns of po~tdoctoral job mobility. For
each section an origin-destination matrix describing the flow of
scholB.;l:.'s among the 86 institutions is analyzed to reveal mobility
patterns. As described earlier, the expected mobility is computed by
using Goodman's method (See Appendix C). These observed and expeoted
mobility matrices are condensed by using regional and prestige group-
ings of institutions. The following oomponents of mobility will be "
used in presenting the data:
Prestige groupingRegionalgrouping Same level Different level
Same region (I) Intraregional, (II) Intraregional,horizo~tal mobility vertical mobility
Different region (III) Interregional, (IV) Interregional,horizontal mobility vertical mobility
Figure 1. A Typology of Interinstitutional Mobility Components
e.
38
In addition to the above four components, there is another compo-
nent to be considered, namely, the non-movers or those who stayed at the
same institution. In the first two sections the stayer component w~ll
be considered as the fifth component g but it should be separated from
the other four, as far as the computation of expected values is con-
cerned. While the stayer component is calculated on the basis of the
total cases (movers plUS stayers), the other four components are calcu
lated on the basis of the total movers (total cases minus stayers).
The expected frequency for the stayer component is computed from the
observed frequencies along the main diagonal of the institutional
mobility matrix (diagonal cells not blocked) in the manner used in
ordinary contingency table analysis testing for independence (See Appen
dix C). For example, in the doctorate-to-employment mObility matrix,
if a given institution produced one-fifth of all the doctorates (total
including diagonal cells) during the study· period and employed one-
te~th of the total doctorates, one would expect that institution to
employ 2 percent (.20 x .10) of Us own doctorates. Summing expected
probabilities for all diagonal cells, one obtains the expected percent-
age for the stayer component. On the other hand, the other four compo-
nents are calculated from non-diagonal cells of the institutional
mobility matrix (diagonal cells blocked) according to a method presented
by Goodman (See Appendix C).
Bacca1aureate-to-Doctorate Mobility
Table 3 presents data on the baccalaureate-to-doctorate mobility
among the 86 major institutions of higher education. The table is
divided into five components and each component is further divided into
39
Table 3. Baccalaureate to Doctorate Mobility Patterns of ChemistsAmong the 86 Major Institutions of Higher Education
Component of Observed Expeoted DifferenceMobility Percentage Percentage (Ob-Ex:P)
(I) Intraregional, horizontal 21.1% 11.1% +10.6%
At top prestige level ~19.2~ ~10.5~ ~+8.1~At lower prestige levels 2.5 0.6 +1.9
(II) Intraregional, vertical 13.0 8.3 +4.1
Upvlard mobility ~ 8.6~ ~ 5.8~ ~+2.8~Downward mobility 4.4 2.5 +1.9
(III) Interregional, horizontal 38.0 43.3 -5.3
At top prestige level ~36.1~ ~4l.1~ ~-5.0~At lower prestige levels 1.3 1.6 -0.3
(IV) Interregional, vertical 21.3 31.2 -9.9
Upward mobility F1.1~ ~27.8~ ~-6.1~Downward mobility 5.6 9.4 -3.8
(V) Stayersa
At top prestige levelAt lower prestige levels
Number of movers
Number of stayers
Total
(22.8)( 1.6)
360
157
511
+21.3
~ose who stayed at the same institution where they received thebaccalaureate to get the doctorate. The stayer component is computedon the base of the total (movers plus stayers) and the other componentsare computed on the base of the movers only.
40
sub-components. The figure at the first column corresponding to each
component represents the proportion of scholars who received both their
baccalaureate and doctorate in a homogeneous manner with respeot to that
oomponent. The second column consists of the peroentage of soholars
whioh would be expected for each oomponent if there were no statistioal
assooiation between the institution where a soholar receives his baooa
laureate and the institution where he obtains his dootorate. As men
tioned earlier, the first four components are computed on the same base
and these four add up to 100 percent. The fifth component is based on
a different base, namely, the total including movers and stayers. The
third oolumn in the table presents a crude measure of the extent to
whioh the observed values for each component deviate from those which
would be expected on the basis of a random distribution model.
It is shown in Table 3 that 35 percent (22% + 13%) of movers who
reoeived their two degrees from different institutions moved within the
same region. This percentage is higher than would be expeoted (11% +
8% a 19%). It is also shown that 60 percent (22% + 38%) of movers moved
to the institutions of the same prestige level as their baooalaureate
institutions, and this figure is slightly higher than the expected
peroentage (11% + 43% = 54%). Within the same region, the horizontal
mobility with respeot to prestige level far exoeeds the expeoted mobil
ity, while the vertical mobility is slightly higher than the expeoted
mobility. The fifth component shows that more than 30 peroent of the
total soholars (movers plus sta.yers) stayed at the same institution
where they received the baocalaureate to get the dootorate, and this
figure is muoh higher than would be expeoted (3%). Thus, it appears
41
that the effects of two factors hYJ?othesized are substantiated in Table
3. The selective tendencies displayed here also suggest that the aca
demic stratification system in the baccalaureate to doctorate mobility
is better represented as a set of regional hierarchies rather than a
strict prestige hierarchy.
The results of chi-square tests to reinforce these conclusions can
be found in Appendix D. In the mobility matrix there are 7,310 cells,
and the difference between the observed and expected frequencies in each
cell can be considered as a Poisson distributed quantity. It is known
that grouping these 7,310 quantities in four categories and calculating
chi-square values will give a chi-square distribution with th~ee degrees
of freedom. The results of chi-square tests show large statistically
significant differences between the observed and expected frequencies.
The partition of the chi-square value into three factors (region, pres
tige level and interaction) reveals that the regional factor aocounts
for the most of the total chi-square value and the chil-square value for
the prestige factor tails to produce statistically significant differ-
ences.
Since Table 3 is an aggregated presentation of the data, the possi
bility exists that the general patterns revealed above may not Charac
terize each region and each prestige level considered separately. In
order to investigate this possibility, eaoh region is separately con
sidered in Table 4 and data for each prestige level are shown in Table 5.
The data in Table 4 reveal that the general tendencies observed
above exist in every region, although the sizes of the differences
between observed and expected percentages vary from one region to an
other. For example, the first row shows that the intraregiona1,
·e.,~ .:...
e
Table 4. Analysis of Regional Differences in Baccalaureate to Doctorate MobilityPatterns Among the 86 Major Institutions of Higher Education
"e
G R 0 UP I N GaREGIONALComponent ofMobility
Intraregional
New EnglandOb Exp Ob-Exp
1-Tidd1e AtlanticOb Exp Ob-Exp
MidwestOb Exp Ob-Ex]?
SouthOb Ex:P Ob-Exp
WestOb Exp Ob-Exp
2.0 2.0 0.0 11.8 6.8 +5.0 19.3 14.3 +5.0 10.4 5.1 +5.3 14.7 8.7 +6.0
(I) Horizontal
(II) Vertical
Int'erregional
24.5 12.5 +12.0 10.5 5.0 +5.5 32.1 19.4 +12.7 3.4 1.4 +2.0 30.9 11.8+19.1
(III) Horizontal..
(IV) Vertical
(v) Stayers
63.3 63.9 -0.6 40.8 43.8 -3.0 32.1 40.1 -8.0 22.4 21.4 +1.0 39.7 51.9 -12.2
10.2 21.6 -11.4 36.9 44.4 -7.5 16.5 26.2 -9.7 63.8 72.1 -8.3 14.7 27.6 -12.9
33.8 7.8 +26.0 31.5 1.8 +29.7 34.3 2.8 +31.5 8.7 0.2 +8.5 26.9 4.3 +22.6
Number of movers 49Number of stayers --l2.
Total 74
76
--2.2.111
109
--2.166
58
--l:.2.73
68
--1.2.93
aSince regional classification is based on the location of baccalaureate institutions, thedata in this table refer to sending patterns .from each region.
..f::>I\)
43
horizontal mobility tendency is weakest in the South and the Middle
Atlantic, but t4ey still have mOr~ mobility than the expected in this
respect. The intraregional, vertical mobility shown in the second row
also exceeds the expected mobi~itr with the exception of New England
where it isbal~ced. Pn the other hand, the percentage differences
for the interregiona.l mobility are all negative in sign, with the lone
exception of the South. But the plus sign appears only in horizontal
mobility. In other words, the South is sending its baccalaureate grad
uates to institutions of the same prestige level in other regions for
their doctorate slightly more ott~n than would be expeoted, while the
interregional, vertical mobilitr is still far less than the expected
mobility. It is also interesting to note that 86 percent of the movers
from the South went to other reS'ione and only 14 percent remained in
the South to get their doctorate. The tendency to remain at the same
institut.i,on is strongest ~ the ~dwest where the "Big Ten" are looated,
and it is weakest in the South which has few prestigious dootorate
producing institutions. In general, the results shown in Table 4 are
consistent with those ~ Table 3.
The data presente4 ~ Table 5 indicate that at each ~restige level
of baccalaureate institut;l.on&;l, the movement to doctoral institutions
tends to be oriented toward both the same region and the same prestige
level. ~ese tendencies are consistent with the ones observed above.
The patterns ot mobility at the lowest prestige level are similar to
those obse~ed for the South ;l.n Table 4. Examining the third row, it
appears that institutions in the lower prestige levels tend to send
their baccalaureate gra.duates to t~e f,1ame prestige level but in
.e e l,e
(v) Stayers 34.2 4.3 +29.9 29.3 0.8 +28.5 21.0 0.3 +20.7 11.4 0.8 +10.6
Number of movers 227 53 49 31Number of stayers ...l!§. ~ -.ll ---!
Total 345 75 62 35;./
aSince prestige classification is based on the prestige score of baccalaureate institution,the data in this table refer to sending patterns from each prestige level. ~
~
•
•.
45
different regions. This interregional, horizontal mobility at the low-
est level is, in fact, slightly more than would be expected on the
basis of a random model, but this is not the case at higher prestige
levels. Two other features of the data in Table 5 are noted. First,
rates of remaining in the same region~ prestige level are lowest at
lower prestige levels. Table 4 showed that these rates are lowest in
the South, for this region is charaoterized by having institutions
which are predominantly in the lower prestige levels. Second, rates of
remaining at the same institution as onets baccalaureate institution
beoome also lower as the prestige level decreases. Thus, in general
the selective tendencies shown in Table 5 for each prestige level are
consistent with those observed in Table 3.
In order to investigate possible trends in the baocalaureate-to-
doctorate mobility patterns, the young and old scholars are analyzed
separately. The re8ults of this investigation are presented in Table 6.
The young cohort in the table oonsists of those who received their
baocalaureate since 1950 and the old cohort includes those who received
their baccala~eate before 1950. The data reveal that both the young
and the old cohort do not deviate from the general mobility patterns
oriented toward the same region and the same prestige level. There is
some indioation that the regionalistic orientation is gradually decreas-
ing. The young cohort shows a slightly lower rate of intraregional,
horizontal mobility and the percentage remaining at the same institution
is much lower for the young oohort than for the old cohort. Eut the
differences between the oorresponding values for the young an.d old on
each component are quite s:mall, wit:p. the possible exception of the
.e e
Table 6. Analysis of Trends in Baooalaureate to Dootorate Mobility Patterns ofChemists Among the 86 Major Institutions of Higher Eduoation
"e
a bComponents of Old Cohort Young Cohort
Observed Expeoted Dif£erenoe Observed Expeoted DifferenoeMobility Percentage Peroentaf,.re (Ob-Exp) Percentage Peroentage (Ob-Exp)
Intraxegiona.l
(I) Horizontal 24.4 12.2 +12.2 19.6 10.3 +9.3At top level ~23.7~ ~11.51 ~+12.2~ ~15.7~ ~ 9.8~ ~ +5.9~At low'er levels 0.7 0.7 0.0 3.9 0.5 +3.4
(II) Vertioal 12.8 9.0 +3.8 13.2 7.8 +5.4Upward ~10.3~ ~ 7.l~ ~ +3.2~ ~ 7.4~ ~ 4.9~ ~ +2.5~Downward 2.5 1.9 +O.ti 5.8 2.9 +2.9
Interre~ional
(III) Horizontal 34.6 43.6 -9.0 40.7 43.1 -2.4At top level p2.7~ ~42.3~ .~ -9.6~ p9.7~ ~4l.2~ ~ -1.5~At lower levels 1.9 1.3 +0.6 1.0 1.9 -0.9
(IV) Vertioal 28.2 35.2 -7.0 26.5 38.8 -12.3Upward F2.4~ ~28.2~ ~ -5.8~ ~21.1~ ~27.5~ ~ -6.4~Downward 5.8 7.0 -1.2 5.4 11.3 -5.9
(V) Stayers 39.3 3.1 +36.2 21.5 3.0 +18.5At top level pO.4~ ~ 2.9~ ~+27.5~ ~15.4~ ~ 2.8~ ~+12.6~At lower levels 8.9 0.2 +8.7 6.1 0.2 +5.9
Number of movers 156 204Number of stayers ..1Q!
2~~Total 257
~ose who reoeived the bachelor's degree before 1950 ~0'\
Those who reoeived the baohelor's degree sinoe 1950
47
fifth component. Thus no great exceptions to the general patterns of
mobility so far presented occur when the sample is analyzed in terms of
these two broad cohorts.
Doctorate-to-Employment Mobility
The distribution of newly trained doctorates to positions in the
academic community is examined in this section. In order to obtain the
distribution patterns, the institution from which on individual received
his doctorate is related to the institution 'Vlhere he held a position.
Since the sample is longitudinal, there is more than one institution of
employment for those i'lho changed their job during the 1955-1967 period
covered in the study. In such oases, the institution of earliest employ
ment reoorded in the sample was used.
An analysis of mobility patterns from the institution of doctorate
training to the institution of employment is presented in ~able 7. Of
those who were not inbred into their dootoral institutions, 14 percent
obtained positions in the same region~ the same prestige level as
their dootoral institutions. This observed peroentage is somewhat
higher than the expeoted percentage. Twenty one percent of them moved
to institutions of different prestige levels in the same region, and it
is also higher than the expeoted percentage. Here again the tendenoy
toward intraregional mobility is apparent and it is oOIlsistent with the
tendenoy obs~rved in the mobility from the institution of baocalaureate
training to the institution of dootorate training. Examining the first
and the third oomponents together, it is found that the horizontal
mobility with respect to the prestige level accounts for 39 peroent
(14% + 25%) of the total movers. This observed peroentage is only
48
Table 7. Doctorate to Employment Nobility Patterns of ChemistsAmong the 86 Major Institutions of Higher Education
Components of Observed Expected Dif'ferenceNobility Percentage Percentage (Ob-Exp)
(I) Intraregional, horizontal 13.6 8.8 +4.8
At top prestige level ~12.8~ ~ 8.0~ ~+4.8~At lower prestige levels 0.8 0.8 0.0
(II) Intraregional, vertical 20.8 12.3 +8.5
Upward mobility ~ lo5~ ~ 1.9~ ~-0.4~Downward mobility 19.3 10.4 +8.9
(III) Interregional, horizontal 25.1 27.2 '-2.1
At top prestige level ~23.0~ ~24.8~ ~-1.8~At lower prestige levels 2.1 2.4 -0.3
(IV) Interregional, vertical 40.5 51.7 -11.2
Upward mobility ~ 3.2~ ~ 6.2~ ~-3.0~Downward mobility 37.3 45.5 -8.2
(v) Stayersa
At top prestige levelAt lower prestige levels
10.3 +9.0
Number of movers
Number of stayers
Total
617
_7)."
688
~ose who obtained the job at the same institution where theyreceived the doctorate. The stayer component is computed on the base ofthe total (movers plus stayers) and the other compcnents are computed onthe base of the movers only.
49
slightly higher than the expected percentage (9% + 27% = 36%). Thus it
would appear that the mobility is oriented toward horizontal patterns
but the deviation from the random model is quite small. Thus, regior.
alistic tendencies appear to be stronger than the selective prestige
level tendencies. The results of chi-square tests to support this con
clusion are presented in Appendix D.
Another feature of the data presented in Table 7 appears in the
second and the fourth components. Although the intraregional, vertical
mobility as a whole exceeds the expected mobility, the upward mobility
(decomposition of the intraregional, vertical mobility) shows the nega
tive deviation from the expected mobility. This tendency toward down
ward mobility may be considered as normal, since new doctorates tend to
move down from the prestige level of their doctoral institutions during
their early careers (Berelson, 1960, pp. 113-114; Caplow and MoGee,
1958, p. 181). In fact, 57 percent, examining the first column, of the
movement was downward mobility, while 39 percent remained at the same
prestige level and only four percent moved upward.
The fifth component in Table 7 shows percentages of stayers in the
doctorate to employment mobility, whioh indicate institutional inbreed
ing patterns. One out of ten soholars held position at the same insti
tution where he reoeived his dootorate. This rate of institutional
inbreeding is muoh higher than would be expected on the basis of the
random distribution model.
An analysis of regional differences in the doctorate to employment
mobility is presented in Table 8. First of a.ll, a. comparison of the
second and the third components ot ea.oh region indicates that seleotive
,e e
Table 8. Analysis o:f Regional Di:f:ferences in Doctorate to Emplo;yment Nobility patternso:f Chemists Among the 86 Major Institutions o:f Higher Education
..e
G R 0 U PIN GaREGIONALComponents o:fMobility
Intraregional
NeYT EnglandOb Exp Ob-Exp
Middle AtlanticOb E:xp Ob-Exp
Mid'"estOb Exp Ob-Exp
SouthOb Exp Ob-Exp
WestOb Exp Ob-Exp
(I) Horizontal
(II) Vertical
Interregional
(III) Horizontal
(IV) Vertical
(V) Stayers
13.3 5.6 +7.7 6.5 4.6 +1.9 18.1 14.2 +3.9 10.9 4.4 +6.5 10.9 5.0 +5.9
7.5 4.1 +3.4 16.3 9.9 +6.4 23.3 16.9 +6.4 56.5 20.4 +36.1 18.2 9.5 +8.7
35.8 33.4 +2.4 27.2 30.1 -2.9 18.5 21.9 -3.4 8.7 23.5 -14.8 33.6 31.8 +1.8
43.4 56.9 -13.5 50.0 55.4 -5.4 40.1 47.0 -6.9 23.9 51.7 -27.8 37.3 53.7 -16.4
5.5 1.0 +4.5 16.4 1.0 +15.4 8.1 1.4 +6.7 17.8 0.9 +16.9 11.3 1.5 +9.8
Number o:f movers 120
Number o:f stayers ---1.Total ·127
9218-
110
249....,gg
271
46
--19.56
110
-M124
aSince regional c1assi:fication is based on the location o:f doctoral institutions, thedata in this table re:fer to sending patterns :from each region.
\J1o
• 51
regional tendencies are stronger than selective prestige level tenden
ci.es for each region. In all five regions, the observed percentage of
movers "lho remained in that region but moved to a different prestige
level exceeds the expected percentage in this component" On the other
hand, the observed percentage of movers who moved to a different region
but remained in the same prestige level is lower than the expected per
centage in all regions with two exceptions of the New England and the
West" ,A.lthough the general patterns are similar in each region, there
emerge some regional peculiarities. For example, the South retained 67
percent of its doctorate graduates who are not inbred into their doctor
al institutions, while New England retained only 21 percent in this
respect. The South also had the highest rate of inbreeding (10%) and
the lowest rate of inbreeding is found in New England" Thus, the data
suggest that the regions with predominantly lower prestige institutions
tend to have higher inbreeding rates and stronger intraregional tenden
cies. This point will be further elaborated later.
Prestige level differences in mobility patterns of dootorates who
obtained positions in another institution of higher eduoation are exam
ined in Table 9. Due to the insufficient number of cases, the third
and fourth prestige levels are combined in this table. Stronger intra
regional than intraprestige level tendencies are consistently displayed
in each prestige level. Apart from these general tendencies, the data
show that institutions in the lower prestige levels tend to retain
their graduates more in their own institutions and send more to insti
tutions in the same region than institutions in the higher prestige
levels. The rate of inbreeding is eight percent at the highest prestige
,e e >,e
Table 9. Analysis of Prestige Level Differences in Doctorate to Employment MobilityPatterns of Chemists Among the 86 Major Institutions of Higher Education
Components of PRESTIGE GROUPINGSa
Mobility Level 1 (Hi@) Level 2 Level 3 & 4 (Low)Ob Exp Ob-Exp Ob Exp Ob-Exp Ob Exp Ob-Exp
Intraregional
(I) Horizontal 15.3 9.5 +5.8 1.5 4.6 -3.1 11.4 5.1 +6.3
(II) Vertical 18.5 11.2 +7.3 27.7 18.5 +9.2 40.0 20.0 +20.0
Interregional
(III) Horizontal 27.5 29.6 -2.1 16.9 15.4 +1.5 5.7 12.0 -6.3
(IV) Vertical 38.7 49.7 -11.0 53.9 61.5 -7.6 42.9 62.9 -20.0
(v) Stayers 7.7 1.4 +6.3 17.7 0.6 +17.1 28.8· 0.6 +28.2
Number of movers 517 65 35Number of stayers ---M. --M --M
Total 560 79 49
aSince prestige classification is based on the prestige score of doctoral institutions,the data in this table refer to sending patterns from each prestige level. \J1
(\)
•53
level, while the rate is more than three times higher (29%) at the low
est level. These tendenoies of higher inbreeding and intraregional
mobility at lower prestige levels oan be interpreted in the light of
the formation of aoademio labor market. Those who attend more presti
gious institutions and, presumably, reoeive a better eduoation, tend to
form a national market, while those attending less prestigious institu
tions more generally form a looal or regional market. The oonsequenoes
of the operation of these two kinds of labor markets seem to be refleot
ed in the data presented in Table 9. However, the most important obser
vations in Table 9 are tendenoies toward intraregional mobility whioh
are somewhat stronger 1;;han seleotive prestige level tendenoies.
Another deoomposition of the data in Table 7 may be oarried out by
a.na.lyzing the patterns of mobility for the young and old oohorts. This
analysis is given in Table 10. The two broad oategories are formed by
diohotomizing the sam~le aooording to the year of dootoral degree. The
young oohort oonsists of those who reoeived their dootorate sinoe 1955.
The analysis of the young oohort would reveal the mobility patterns of
neW dootorates to their first jobs, sinoe the sample of this study
oovers the Period beginning 1955. The results show that the general
tendenoies toward intraregional and intraprestige level mobility are
oonsistent in both oohorts. Although the differenoes between the oor
responding peroentages for the two oohorts on eaoh oomponent are quite
small, there is some indioation that the tendenoy toward intraregional
mobility is more prominent for the old oohort than for the young. The
rate of inbreeding is much higher for the old oohort (15%) than for the
young (5%). While there is more downward mobility than upward mobility
·e e
Table 10. Analysis of Trends in Doctorate to Employment Mobility Patterns ofChemists .Among the 86 Major Institutions of Higher Education
J,e
a bComponents of Old Cohort Young Cohort
Observed Expected Difference Observed Expected DifferenceMobility Percentage Percentage (Ob-Exp) Percentage Percentage (Ob-Exp)
Intraregional
(I) Horizontal 16.1 10.0 +6.1 11.1 7.5 +3.6At top level ~15.5~ ~ 9.0~ ~ +6.5~ ~10.1~ ~ 6.8~ ~ +3.3~At lower level 0.6 1.0 -0.4 1.0 0.7 +0.3
(II) Vertical 22.3 12.9 +9.4 19.2 11.7 +7.5Upward ~ 4.2~ ~'l 9~ ~ +2.3~ ~ 1.6~ ~ 1.9~ ~ -0.3)Downward. 18.1 11:0 +7.1 17.6 9.8 +7.8)
Interregional
(III) Horizontal 22.9 28.1 -5.2 27.4 26.4 +1.0At top level ~21.6~ ~26.1~ ~ -4.5~ (24.4~ ~23.4~ ~ +1.0~At lower levels 1.3 2.0 -0.7 ( 3.0 3.0 0.0
(IV) Vertical 38.7 49.0 -10.3 42.3 54.4 -12.1Upward ~ 3.5~ ~ 5.1~ ~ -~.6~ ( n 9~ ~ 7.2~ ~ -4.3~Downward 35.2 43.9 -0.7 C39:4 47.2 -7.8.• I.
(V) Stayers 15.3 1.9 +13.4 4.7 0.6 +4.1----~__ At top level ~10.1~ ~ 1.8~ ~ +8.3~ ~ 1.9~ ~ 0.3~ ~ +1.6)-----------.0 _,
+5.1 +2.5)!t ..LUwer levels 5.2 0.1 2.8 0.3
Number of movers 310 307Number of stayers ....2§. ---12
Total 366 322_. II
~ose who received the doctorate before 1955v"..j:::.
Those who received the doctorate since 1955
55
in both cohorts, the old cohort shows more upward mobility than the
young cohort. These slight differences between the young and old co-
horts may reflect the development of postdoctoral careers of scholars.
At earlier stages of their careers, scholars are more willing to accept
jobs at lower prestige institutions than their doctoral institutions
and more willing to move to other regions. As their professional ex-
periences increase, they tend to move upward to more presigious insti-
tutions and many of them return to their Alma Mater.
Postdoctoral Job Mobility
In order to obtain information about postdoctoral job mobility,
six origin-destination matrices were formulated for the follOWing six
biennial periods: 1955-1957, 1957-1959, 1959-1961, 1961-1963, 1963-1965
and 1965-1967. Although it is possible to analyze each of these
matrices separately, all six matrices were combined due to insufficient
number of cases in each matrix. The total number of moves identified
among the 86 institutions during the entire 12 year period adds up to
only 83. Thus, the fifth component is not considered in this section.
Analysis of job mobility patterns during the 1955-1967 period is
presented in Table 11. The positive differences in the first two com-
ponents indicate excess intraregiona1 mobility and the positive signs
in the first and third component reflect excess horizontal mobility
with respect to prestige level. About the same magnitude of differences
between the observed and expected percentage in the second and the third
components suggest that seleotive prestige level tendenoies are as
strong as selective regional tendencies in the job mobility. Further
evidence for this point is shown in the chi-square statistios presented
e"
56
in Appendix D. An examination of sub-components in the first and third
rows indicate that less prestigious institutions tend to exchange fac-
ulties with institutions in the same prestige in the same region, while
more prestigious institutions tend to exchange with institutions in the
same prestige level in other regions.
Table 11. Postdoctoral Job Mobility Patterns of Chemists Amongthe 86 Major Institutions of Higher Education
Components of Observed Expected DifferenceMobility Percentage Percentage (Ob-Exp)
(I) Intraregional, horizontal 8.4% 7.5% +0.9%
At top prestige level ~ 4.8~ ~ 5.5~ ~ -0.7~At lower prestige level 3.6 2.0 +1.6
(II) Intraregional, vertical 21.7 13.9 +7.8
Upward mobility ~ 4.8~ ~ 4.5~ ~ +O.3~Downward mobility 16.9 9.4 +7.5
(III) Interregional, horizontal 33.7 26.1 +7.6
At 'top prestige level ~28.9~ ~20.7~ ~ +8.2~At lower prestige levels 4.8 5.4 -0.6
(IV) Interregional, vertical 36.2 52.5 -16.3
Upward mobility ~ 9.6~ ~18.3~ ~ -8.7~DOvlll,,'ard mobility 26.6 34.2 -7.6
Number of moves 83
•57
Regional differenoes in the job mobility patterns are analyzed in
Table 12. Although the small number of oases in eaoh region do not
allow any detailed observations, seleotive prestige level tendenoies
seems to be stronger than regionalistio tendenoies in all regions
exoept for the :Middle Atlantio. Those who were employed in the :Middle
Atlantio seem to prefer to move to a different prestige level in that
region rather than moving to the same prestige level in other regions.
Prestige level differenoes are oonsidered in Table 13. Institu
tions in lower prestige levels are more strongly oriented toward intra
regional mobility than institutions at the highest level. Soholars in
higher prestige level institutions tend to move to institutions in the
same prestige level in other regions.
An attempt is made in Table 14 to investigate any possible trends
in job mobility by oarrying out separate analyses for the 1955-1961 and
1961-1967 periods. The oorresponding peroentages for the two periods
are quite similar. Thus, there seems to be no marked ohange in the job
mobility patterns.
In summary, the results reported in Tables 3 through 14 suggest
the following oonolusions about interinstitutional mobility patterns of
ohemists at various stages of their oareers. The oono1usions oan be
further baoked up by the ohi-square tests presented in Appendix D.
First, the mobility from the baooalaureate to the dootorate training is
charaoterized by stronger tendenoies toward regionalism than toward
prestige level homogeneity. The largest deviations from a model of
random mobility patterns are found for the stayers and the intraregiona1,
horizontal movements. These regiona1istio tendenoies seems to be more
·e e
Table 12. Analysis of Regional Differences in Postdoctoral Job Mobility Patternsof Chemists Among the 86 Major Institutions of Higher Education
·e
New Eng1oo~d Middle Atlantic ~lidwest South WestOb Exp Ob-Exp Ob Exp Ob-Exp Ob Exp Ob-E.."'q) Ob Exp Ob-Exp Ob Exp Ob-Exp
Components of:t-10bi1ity
Intraregiona1
REGIONAL G R 0 U PIN Ga
(I) Horizontal
(II) Vertical
Interregional
(III) Horizontal
(IV) Vertical
9.1 7.3 +1.8 5.6 3.9 +1.7 14.8 11.9 +2.9 0.0 4.3 -4.3 7.7 9.2 -1.5
18.2 0.9 +17.3 33.3 10.6 +22.7 14.8 22.2 -7.4 21.4 14.3 +7.1 23.1 11.5 +11.6
54.5 33.6 +20.9 16.7 38.3 -21.6 33.3 21.1 +12.2 28.6 20.0 +8.6 4G.l 30.8 +15.3
18.2 58.2 -40.0 44.4 47.2 -2.8 37.1 44.8 -7.7 50.0 61.4 -11.4 23.1 48.5 ~25.4
Number of moves 11 18 27 14 13
aSince regional classification is based on the location of institutions of origin, thedata in this table refer to sending patterns from each region.
\J1Q)
•59
Table 13. Analysis of Presti~e Level Differences in Postdoctoral Job Mobility Patterns of Chemists Amongthe 86 Major Institutions of Higher Education
Components ofMobility
Intraregional
(I) Horizontal
(II) Vertical
Interregional
(III) Horizontal
(IV) Vertical
Number of moves
PRESTIGE
Level 1 (High)Ob Exp Ob-Exp
7.8 9.0 -1.817.6 12.0 +5.6
47.1 33.9 +13.227.5 45.1 -17.6
51
Levels 2. 3 &4 (Low)Ob Exp Ob-Exp
9.4 5.0 +4.428.1 16.5 +11.6
12.5 13.8 -1.350.0 64.7 -14.7
32
aSince prestige classification is based on prestige scores ofinstitutions of origin, the data in this table refer to sending :patternsfrom each prestige level.
Table 14. Analysis of Trends in Postdoctoral Job Mobility Patterns ofChemists Among the 86 Major Institutions of Higher Eduoation
Components of 1955-1961 Period 1961-1967 PeriodMobility Ob Exp Ob-Exp Ob EX]? Ob-Exp
Intraregional
(I) Horizontal 9.5 6.6 +2.9 7.7 7.0 +0.7(II) Vertical 27.6 18.9 +8.7 19.2 13.0 +6.2
Interregional
(III) Horizontal 23.8 21.4 +2.4 39.5 32.8 +6.7(IV) Vertical 39.1 53.1 -14.0 33.6 47.2 -13.6
e Number of moves 29 54
60
prominent for the lower prestige level institutions. Second, in the
distribution of new doctorates to positions in academic institutions,
as in the baccalaureate-to-doctorate move, regionalistic tendencies
appear to be stronger than selective prestige level tendencies. Thus,
the academic stratification system in the doctorate to employment
mobility is one of a set of regional hierarchies rather than a rigid
prestige hierarchy. It is also noted that downward mobility is more
common at earlier stages of postdoctoral careers. The lower prestige
institutions seem to have relatively higher rate of inbreeding and a
stronger regionalistic orientation. Third, postdoctoral job mobility
patterns are characterized by about equally strong tendencies toward
homogeneity in region and in institutional prestige level. The region-
alistic tendencies appear to be relatively stronger for lower prestige
levels and tendencies toward prestige homogeneity are more operative
for higher prestige levels. Thus, chemists in high prestige level
institutions tend to move to the same prestige level in other regions,
while those in lower presti~ level institutions tend to move within
that region. Finally, it should be pointed out that these results are
based on a limited number of cases and the small number of cases might
impose limitations, more so in the job mobility analysis.
•
61
REGRESSION ANALYSIS
The purpose of regression analysis is twofold: (1) to extract the
main features of the relationships hidden or implied in the data and
(2) to examine possibilities of using such functional relationships for
forecasting institutional mobility from knowledge of other variables.
From the 86 institutions to be studied, there are 3,655 unordered
pairs and 7,310 ordered pairs that can be formed. As mentioned earlier,
the dependent variable is the signed departure of observed frequency
from the expected frequency for each of the ordered pairs in the 86 x 86
mobility matrix. Thus, the dependent variable matrix is asymmetric.
Among the independent variables, the distance between institutions is
symmetric. Other independent variables are formed from the "pair"
variables: prestige score and average faculty compensation of 86 insti-
tutions. The absolute difference and average of the pair are symmetric,
but the signed difference is asymmetric (they change sign when the order
of the pair is reversed). There are basically two kinds of variables:
symmetric and asymmetric •... In the study of analyzing pair data and point
data on sociometric relationships, Proctor (1969) suggested that these
tvlO kinds of variables ought not be mixed in the same regression ana1y-
sis. Thus, two kinds of regression analyses are performed; one for
the unordered pairs to analyze symmetric variables and one for ordered
pairs to analyze asymmetric variables. For the former, the dependent
variable is transformed to a symmetric variable by taking the average
of corresponding ordered pairs. In more familiar terminology in migra-
tion research, the dependent variable in the unordered pair regression
corresponds to gross migration, though the average rather than the sum
•
•
62
of two directional flows is used. The depenqent variable in the ordered
regression congerns the directional flows.
In both regression analys~s all the variables are transformed by
taking basically the logarithm of the original values. Since the loga-
rithmic transformation cannot be used directly for zero values and when
some of the values are negative, it is necessary to adjust all the
values before taking logarithms. When a variable contains some zero
values and negative values, not smaller than minus one, the adjustment
is made by adding one to each number prior to taking logarithms. This
transformation acts like the square root for small values and like the
logarithm for large values. When a variable contains some negative
values smaller than minus one, each number is divided by a positive
constant which is slightly larger than the absolute value of the small-
est negative value prior to adding one and taking logarithms.
The results of regression analyses are presented in Table 15 for
the baccalaureate to doctorate mobility, in Table 16 for the-doctorate
to employment mobility, and in Table 17 for the postdoctoral job mobil-
ity. These tables show the fitted regression coefficients obtained from
least-squares regression, their t-statistics, and the coefficient of
determination (R2). Although the coefficients of determination are not
impressive at all, the regression coefficients and the accompanying t-
values can be used to screen relationships.
Effects of Distance
The hypothesized inverse relationship is substantiated in every
case of unordered pair analyses presented in Table 15 through 17. The
accompanying t-value indicates that the regression coefficient is
,e e ..
\
,e ,
Table 15. Regression Analysis for Baccalaureate to Doctorate Mobility of ChemistsAmong the 86 Major Institutions of Higher Education
Young cohortRegression tcoefficient value
-0.0089*** -5.4810
-0.0179
-0.0059
-0.0343
-0.0005
-1.6163
-1.1776
-1.2883
-0.2895
2R = 0.0162
-0.0008 -0.1899
-0.0019
-0.0029
0.0191
-0.4731
-0.3571
1.7378
2R = 0.0016
* Significantly different from zero at .05 level of confidence** Significantly different from zero at .01 level of confidence
*** Significantly different from zero at .001 level of confidence
Ch\..N
.e e ~Je
Table 16. Regression Analysis for Doctorate to Employment MObility of ChemistsAmong the 86 Major Institutions of Higher Education
Young cohort
-0.0156** -2.6844
2R = 0.0023
Regression tcoefficient value
0.8496
-0.0732
-1.9413
-0.9404
-1.1337
0.0265
-0.0010
-0.0227
-0.0048
2R = 0.0110
-0.0007 -0.1422
-0.0023
-0.0058** -3.0618
-0.0302* ~2.3290
Total sample Old cohortRegression Independent Regression t Regression t
run variable coefficient value coefficient value
(I) Unordered Distance -0.0212*** -7.3691 -0.0166*** -8.9867pair
regression Average of -0.0558** -2.8487 -0.0099 -0.7864prestige scores
Absolute difference -0.0293* -2.3099 -0.0065 -1.1520in prestige scores
Average of 0.0174 0.3697 -0.0234 -0.7742compensation
Absolute difference -0.0065* -2.0901 -0.0040* -2.0147in compensation
2 2R = 0.0292 R = 0.0285
(II) Ordered North-South -0.0004 -0.1161 -0.0092 -1.5727pair distance
regression East-West -0.0029 -0.7871 -0.0090 -1.5589distance
Signed difference -0.0160* -2.3081 -0.0250 -1.9231in prestige scores
Signed differences -0.0062 -0.6174 0.0015 0.0934in compensation
2 2R = 0.0028 R = 0.0038
~
* Significantly different from zero at .05 level of confidence** Significantly different from zero at .01 level of confidence
*** Significantly different from zero at .001 level of confidence
0'\~
,e e 'e
Table 17. Regression Analysis for Postdoctoral Job ¥~bility of Chemists Amongthe 86 Yajor Institutions of Higher Education
-0.0010 -1.3201
-0.0012 -0.4928
0.0062 0.3862
2R = 0.0037
-0.0011 -0.6758
-0.9582
-0.7871
0.0031 0.7584
2R = 0.0003
-0.0013
-0.0021
-0.0029* -2.1547
-0.0060 -0.8523
1261-1967 periodRegression tcoefficient value
1955-1967 period 1955-1961 periodRegression Independent Regression t Regression t
run variable coefficient value coefficient value
(I) Unordered Distance -0.0028** -2.8991 -0.0031*** -3.8513pair
reb'Tession Average of -0.0059 -0.8834 -0.0052 -0.9320prestige scores
Absolute difference -0.0014 -0.4650 -0.0015 -0.3856in prestige scores
Average of 0.0057 0.3574 0.0054 0.2988compensation
Absolute difference -0.0012 -1.1696 -0.0011 -1.2728in compensa'tion
2 2R = 0.0038 R = 0.0051
(II) Ordered North-South -0.0011 -0.7699 -0.0021 -0.9823pair distance
regression East-West -0.0012 -0.8222 -0.0011 -1.0231distance
Signed difference -0.0026 -0.9299 -0.0031 -0.9825in prestige scores
Signed difference 0.0033 0.8051 0.0023 0.9253in compensation 2 2
R = 0.0004 R = 0.0008
* Significantly different from zero at .05 level of confidence** Significantly different from zero at .01 level of confidence
*** Significantly different from zero at .001 level of confidence,
0'\VI
•
•
66
significantly different from zero in every analysis. The distance vari
able appears to be the most important one among the independent vari
ables considered. The standard partial regression coefficients which
indicate the relative importance of the independent variables in rela
tion to the dependent variable can be found in Appendix D. These find
ings are consistent with the strong regionalistic tendencies described
in the previous section.
In the ordered pair regression analysis two distance variables were
included: north-south directional distance and east-west directional
distance. While the distance variable contributes significantly to the
explanation in the unordered pair regression analysis, these two direc
tional distances in the ordered pair analysis contribute very little to
the explanation. The consistent negative signs of coefficients in the
three types of institutional mobility suggest that there is more mobil
ity from the north to the south and from the east to the west rather
than the reverse directions. The only coefficient which is significant
ly different from zero appears in the east-west directional distance in
the old cohort of baccalaureate-to-doctorate mobility, but the coef
ficient of east-w3st directional distance for the young cohort is not
significant.
Effects of Prestige and Compensation
Two sets of prestige variables are used in the unordered pair re
gression analysis: the absolute difference and the average of prestige
scores. As far as interpretations of the results are concerned, the
absolute difference makes more sense than the average of prestige scores•
The negative coefficients of the absolute prestige difference indicate
•
67
that, when the differenoe in prestige scores increased~ institutional
mobility decreased. This relationship is oonsistent with the tenden-
oies toward horizontal mobility with respeot to prestige as observed
earlier. Although the hypothesized relationship between mobility and
llrestige is upheld in its anticipated direction, the strength of the
relationship and hence the contribution to the regression is somewhat
discouraging. The coeffioient is significantly different from zero
only in the dootorate-to-employment mobility analysis.
The average of prestige scores appears to be somewhat better in its
contribution to the unordered pair regression than the absolute prestige
differenoe (See Appendix D). The relationship between the average of .
prestige soores and the average mobility turned out to be negative.
This seems to suggest that there was more mobility in lower prestige
levels than in higher prestige levels. :But this statement oan not be
taken in a sheer quantitative sense, sinoe the mobility variable indi-
cates the extent to which the observed mobility deviates .from the ex-
pected mobility. The averaging of prestige soores of the top and bottom
institutions would produce a fairly high score~ but the mobility between
these two institutions would be the lowest in the light of the inverse
relationship observed between the absolute prestige differential and the
mobility. Therefore the results in this regard make less sense when any
interpretations are attempted.
The signed difference in prestige scores in the ordered pairanaly-
sis consistently yielded a negative relationship with mobility. This
relationship can best be interpreted as a propensity for mobility be-
tween institutions of similar prestige characteristics. Its regression
coefficient is significantly different from zero in the baccalaureate
•
68
to doctorate mobility and the doctorate to employment mobility.
Another set of independent variables concern faculty compensation.
Although this factor may be J.rrelevant for the baccalaureate to doctor-
ate mobility, compensation should be an important variable in the doc-
torate to employment mobility and especially for postdoctoral job mobil-
ity. The absolute difference in compensation in the unordered pair
analysis consistently produced negative signs and the regression
coefficient for the doctorate to employment mobility is significantly
different from zero. This negative relationship is expected consider-
ing the inverse relationship between prestige differential and mobility.
In fact, the prestige score is highly correlated with faculty compensa
tion (r-.77). On the other hand, average compensation of the pair
institutions contributes virtually nothing to the explanation and its
coefficient is not significantly different from zero in each unordered
pair analysis. The signs of coefficients are not consistent from one
analysis to another.
The compensation factor in the ordered pair analysis does not
significantly contribute to the regression. While the signed difference
in prestige scores consistently yielded negative relationships, the
signed difference in compensation produced positive relationships in
the baccalaureate to doctorate mobility and postdoctoral job mobility.
Surprisingly, the coefficient is positive and significantly different
from zero in the baccalaureate to doctorate mobility. But it is hard
to see any direct connection between the movement of students from the
baccalaureate to doctorate institution and faculty compensation. The
faculty compensation must be related to other factors which are
69
relevant to the student movement.
Examination of Residuals
In performing the regression analyses, particularly in using the
t-values, certain assumptions have been made about the errors. The
usual assumptions are that the errors are independent, have a constant
variance, and follow the normal distribution. The last assumption is
required for making F-tests and using t-tables. Thus it is always
helpful to examine whether the residuals tend to conform to these
assumptions. The problem of examining how closely the ideal conditions
are satisfied is a very broad one. The error distribution can be
checked by measuring its skewness and kurtosis. The dependence of the
residuals on the fitted values can be examined by computing the statis-
tics concerning heteroscedasticity and nonadditivity as suggested by
Anscombe (1961 and 1963). For the present study the error distribution
is first examined by a graphic method and then an aspect of suspected
dependence among the residuals is considered.
Since the 3,655 observations in the unordered pair regression and
7,310 observations in the ordered pair regression were so numerous, a
random sample of 73 observations (2% of the unordered pairs and 1% of
the ordered pairs) was drawn from eaCh analysis to plot the error dis-
tribution. The distributions of errors for unordered and ordered pair.~~~,
analyses are shown in Figure 2. The distributions are plotted in terms
of the standard error of estimate. These distributions should resemble
a normal distribution with zero mean if the regression model is correct
for each analysis. As the plots exhibit, the distributions are somewhat
irregular. The distributions of unordered analyses exhibit a positive
e,
Baccalaureate to DootorateMobility
e
UNORDERED PAIR REGRESSION
-S 4 3 2eDoctorate to Employment
Mobility
+Se
..e
2S 2 1 0 1 2 3 4 5 6+S7e e
Postdoctoral Job Mobility
-S ~ ~ ~ ~ I V I 2 3 ~S
e Baccalaureate to Doctorate eMobility
~S 7 6 5 4 3 2 1 0 1 2 3 ~S
e Doctoreate to Employment Mobility egs 1 0 1 2 3 4 5 b 7+S
8
epostdoctoral Job Mobility e
Figure 2. Distributions of Residuals Based on the Standard Error ofEstimate for Two Types of Regression Analyses
-Jo
•
•
71
ske,~ess. All distributions appear to be leptokurtic, hence positive
fourth cumulants are suspected.
Another good way to examine the residuals may be to prepare scatter
diagrams showing the dependence of residuals on the fitted values. In
Figure 3 every sampled observation for unordered and ordered analyses
of the baccalaureate to doctorate mobility is represented by a point
whose ordinate is the residual and whose abscissa is the fitted values.
Outliers can be seen rather readily as isolated points with extreme
ordinates. It has been suggested that it may be wise to reject or pre
ferably modify observations whose residuals are very large in magnitude.
A procedure of modification has been described as Winsorization (Tukey,
1962). Since most of outliers in Figure 3 represent most prestigious
institutions, a simple rejection or modification may not be wise.
Rather it may be preferable to perform a separate regression analysis
for different components of mobility such as the ones identified by
using regional and prestige groupings.
The diagram for the unordered pair analysis in Figure 3 exhibits a
somewhat greater dispersion of the residuals for smaller fitted values
than for larger values, apart from outliers. This indicates a depend
ence of variability on level or a non-homogeneous variance. Weighted
least squares or another type of transformation might be needed in
order to stabilize the variance.
In a general regression situation, when p parameters are estimated
from n observations, the n residuals are associated with only n-p de
grees of freedom. Thus the residuals cannot be independent and correla
tions exist among them. Eut it is suggested that the effect of
72
• +40 ,--• .. ""
+30
+20 ..
+10
• " .. 0
0 6 • •• • . ..... ......'... . •.. •• 0 ...'11 .-.... • •.. • .. ••• • • 'O •• ... ..;"10 ..
•
-20 -• Unordered Pair• Regression
-30 -
Fitted Values-40 5 6 7 8 9 10 11 12 13 14+404
• • -,
•+30 . -
+20
+10
0 ..... ~.
• - ~•• o"i~ o••
0 •• •.. • • •·~1O
•
-20Ordered PairRegression
-30
-40 I - I •
• F'igure 3. Scatter Diagrams of Residuals against Fitted Values forRegress:ion Analyses of Baccalaureate to Doctorate Mobility
•
•
73
correlation need not be considered when plots are made, except when the
ratio (n-p)!n is quite small (Draper and Smith, 1966, p. 94).
In the present study, however, there is a need to check an usual
aspect of dependence among the residuals. Since the observations were
taken from the 86 x 86 matrix, the residuals can be represented as eij
which is associated with institutions i and j (i'j). In the unordered
pair analysis, the subscripts i, j are taken with i) j. In this situa.-
tion the major departure from the ideal condition of independent errors
could be expeoted as a oorrelation between a certain e. . and theJ.J
associated errors of eij • or eitj where i~i' and j,cjt. The estimation
of a correlation matrix between eijts whose size reaches 3,655 x 3,655
for the unordered pair regression and 7,310 x 7,310 for the ordered pair
regression would be an impossible undertaking, and so some simplifica.-
tion is needed.
utiliZing an approach suggested by Proctor (1969), such a correla-
tion is estimated for unordered and ordered pair regressions of the
baccalaureate to doctorate mobility. Of the 6,677,685 pairs of errors
for the unordered pair regression, 307,020 or 4.6 percent would have a
subscript in common. It may be supposed that the eijt of overlapped
pairs were correlated, while the mutually exclusive pairs were not. A
random sample of 20 residuals was obta.1ned to estimate the correlation.
These 20 residuals formed 190 pairs of residuals among which 183
mutually exclusive and 7 (3.7%) overlapped pairs were found. The dif-
ference of the two residuals was reoorded for each pair and the
variance of these differences was calculated for the exolusive and
overlapped pairs separately: the results of the calculation were
• == 237.25 and S2 == 20.39, respectively.lap.
74
These computations are
•
shown in Table 18. From these data an estimate of correlation is de-
rived as follows:
If the subsoripts of eij and eitjt are mutually exolusive, it is
supposed that
but if they are not mutually exolusive, then
V(e .. - eitjt ) == Vee .. - e. t.) • 20"'2 (1 - tJ).~J ~J ~ J e \
Therefore, s12 /82 can be used as an estimate of (1 _P).ape exe. \
Thus, ~== 1 - ( s12 /s2 ) == 1 - (20.39/237.25) == .91\ ape exc.
Simila.:r;ly, the correlation is estimated for the ordered pair re
gression. There are 26,714,395 pairs of residuals of which 614,040 or
2.3 percent have a subscript in common (the order of subscripts con
sidered). From the sample of 20 residuals, 190 pairs were formed which
resulted in 6 overlapped and 184 exolusive pairs. Using the same compu-
tational prooedure used above, the oorrelation was estimated to be .998
(See Table 19). Although the estimation was based on a small sarr~le of
residuals, there appears to be a sizeable positive intraclass correla-
tion in this type of analysis of pair data.
Having examined the three assumptions of regression theory and
found all three to be somewhat unrealistic, one should be more cautious
in interpreting the t and F values. On the other hand, it should be
noted that the leptokurtosis has a conservative effect on F ratios, the
variance heterogeneity does not seem to be too extreme, and the non
zero correlations of errors affects only 4.6 peroent of the cases of
,e e •Table 18. Differences of Residuals and Estimation of Correlation for the Unordered Pair Regression
Resi- D iff ere n c e sin A b sol ute Val u e~
No. I. D. duals (1) (2) (3) (4) (5) (6) (1) (8) (9) (10) (11) (12) (13) (14) (15) (16) (11) (18) (19)
1.5
237.25
1e3
43416.77
Exclusive pairs
7
20.39
142.79
Overlapping pairs
f= 1 - (20.39/237.25) =.914
Sum of Sqs.
Avg. Sq. Dif.
No. of pairs
(1) (4,47) -2.6(2) (11,36) -0.5 2.1(3) (2,67) +1.7 4.3 2.2(4) (3,35) -6.9 4.3 6.4 8.6(5) (4,45) -0.4 12.21. 0.1 2.1 6.5(6) (20,58) -1.1 1.5 0.6 2.8 5.8 0.7(7) (23,81) +0.6 3.2 1.1 1.1 7.5 1.0 1.7(8) (25,64) -0.5 2.1 0.0 2.2 6.4 0.1 O.~ 1.1(9) (13,56) +3.4 6.0 3.9 1.7 10.3 3.8 4.5 2.8 3.9
(10) (26,40) -27.4 24.8 26.9 29.1 20.5 27.0 26.3 28.0 26.9 30.8(11) (46,74) +0.5 3.1 1.0 1.2 7.4 0.9 1.6 0.1 1.0 2.9 27.9(12) (20,83) +3.3 5.9 3.8 1.6 10.2 3.7 14.41 2.7 3.8 0.1 30.7 2.8(13) (6,73) -0.2 2.4 0.3 1.9 6.7 0.2 0.9 0.8 0.3 3.6 27.2 0.7 3.5(14) (11,83) -4,,4 10 8 ]3.91 6.1 2.5 4.0 3.3 5.0 3.9 7.8 23.0 4.9 17.71 4.2(15) (13,68) -0.6 2.0 0.1 2.3 6.3 0.2 0.5 1.2 0.1 14.0[26.8 1.1 3.9 0.4 3.8(16) (59,71) -0.3 2.3 0.2 2.0 6.6 0.1 0.8 0.9 0.2 3.7 27.1 0.8 3.6 0.1 4.1 0.3(17) (25,84) -0.5 2.1 0.0 2.2 6.4 0.1 0.6 1.1 10.01 3.9 26.9 1.0 3.8 0.3 3.9 0.1 0.2(18) (28,34) +36.4 39.0 35.9 34.7 43.3 36.8 37.5 35.8 36.9 33.0 63.8 35.9 33.1 36.6 40.8 37.0 36.7 36.9(19) (21,30) -0.4 2.2 0.1 2.1 6.5 0.0 0.7 1.0 0.1 3.8 27.0 0.9 3.7 0.2 4.0 0.2 0.1 0.1 36.8(20) (24,56) -1.9 0.7 1.4 3.6 5.0 1.5 0.8 2.5 1.4 15.3r25.5 2.4 5.2 1.7 2.5 1.3 1.6 1.4 38.3
Boxed figures represent differences for overlapping pairs.-.J\J1
e e ~
Table 19. Differences of Residuals and Estimation of Correlation for Ordered Pair Regression
586.07
184
107837.01
Exclusive pairs
6
1.26
7.54
Overlapping pairs
f = 1 - (1.26/586.07) = .998
Sum of Sqs.
Avg. Sq. Dif.
No. of pairs
Resi- D iff ere n c e sin A b sol ute Val u e sNo. I. D. duals ~1.Li.2) (3) ~4) (5) (6) (1) (8) (9) (10) (11) (12) (13) (14) (12) (16") (11) (18) (19)(1) (67,28) -6.3(2) (42,66) -0.4 5.9(3) (33,83) +2.0 8.3 2.4(4) (1,24) +0.3 6.6 0.7 1.7
, (5) (78,59) -2.9 3.4 2.5 4.9 3.2(6) (78,59) ...3.0 3.3 2.6 5.0 3.3 jO.l]
(7) (41,84) -0.6 5.7 0.2 2.6 0.9 2.3 2.4(8) (28,29) -9.1 2.8 8.7 11.1 9.4 6.2 6.1 8.5(9) (52,33) +0.4 6.7 0.8 1.6 0.1 3.3 3.4 1.0 9.5
(10) (30,18) -0.9 5.4 0.5 2.9 1.2 2.0 2.1 0.3 8.2 1.3(11) (22, 2) +1.0 7.3 1.4 1.0 0.7 3.9 4.0 1.6 10.1 0.6 1.9(i2) (41,36) -1,,8 4.5 1.4 3.8 2.1 1.1 1.2 11..21 7.3 2.2 0.9 2.8(13) (36,39) +0.3 6.6 0.1 1.7 0.0 3.2 3.3 0.9 9.4 0.1 1.2 0.7 2.1(14) (47,39) -1.4 4.9 1.0 3.4 1.7 1.5 1.6 0.8 7.7 1.8 0.5 2.4 0.4 J1.71(15) (55,42) +0.2 6.5 0.6 1.8 0.1 3.1 3.2 0.8 9.3 0.2 1.1 0.8 2.0 0.1 1.6(16) (52,21) +1.2 7.5 1.6 0.8 0.9 4.1 4.2 1.8 10.3 lO.8J 2.1 0.2 3.0 0.9 2.,6 1.0(17) (79,39) +0.2 60 5 0.6 1.8 0.1 3.1 3.2 0.8 9.3 0.2 1.1 0.8 2.0 10.11. 11.61 0.0 1..0(18) (40,77) +73.2 79.5 73.6 71.2 72.9 76.1 76.2 73.8 82.3 72.8 14.1 72.2 75.0 72.9 74.6 73.0 72.0 73.0(19) (62,26) +2.0 8.3 2.4 0.0 1.7 4.9 5.0 2.6 11.1 1.6 2.9 1.0 3.8 1.7 3.4 1.8 0.8 1.8 71.2(20) (5,15) -3.0 3.3 2.6 5.0 3.3 0.1 0.0 1.4 6.1 3.4 2.1 4.0 1.2 3.3 1.6 3.2 4.2 3.2 76.2 5,,0
~0'\
Boxed figures represent differences for overlapping pairs.
•77
unordered pairs and 2.3 percent of the cases of ordered pairs.
Implications for Mathematical MOdel Building
The regression analysis was undertaken specifically for analytical
purposes, but the possibility of using analytical information for build
ing a forecasting model may be worth examining. Although the analysis
gO far reported provide substantial information concerning tendencies
and patterns of mobility, the usefulness of regression equations for
quantitative solutions of forecasting seems to be limited, considering
the amount of variation accounted for by the equations. In order to be
useful the regression equations need to be improved by introducing
additional independent variables, disaggregating the mobility into
meaningful components, and applying some more suitable transformation
to the mobility rates.
Since the response variable in the regression equations represents
the extent to which the observed mobility deviates from the expected
mobility, additional consideration is necessary to develop a practical
model which would foreoast the volume of mobility. The full strategy
of building a forecasting mode:i may be first to perform this type of'
functional analysis at eaCh level of geographic and structural detail
and then to synthesize all components and linkages. This type of
strategy is often described as the systems approach. This approach can
be compared with the gravity models of migration. Although these two
types of models have similarities in many aspects, the main difference
lies in their conceptual formulation. While the gravity model is
essentially a formula with component parameters built in, the sytems
approach is a procedure for oonstructing a system analog. The relative
•T
78
superiority of the systems theory model to the gravity model was demon
strated in a study of recreational traffio flows in 11ichigan (Ellis and
Van Doran, 1966). It is not intended here to review the sY9tems model
formulation techniques which have been developed in physical sciences
especially in electrical engineering, but the findings in this study
seem to indicate that further investigation in this line of approach is
worth pursuing.
The high positive intraclass oorrelation among the residuals found
in this study is worthy of special attention in building any forecasting
models. This suggests that there exist system effects stemming from
the peouliar struoture of the system. Gravity models assume that the
interchange between each pair of institutions is independent of that
between each other pair. But it appeared that they are highly dependent.
•79
S~~y AND CONCLUSIONS
This study has been concerned with analyzing patterns of migratory
movements of scholars among colleges and universities in the academic
training phase as well as in the postdoctoral phase of professional
careers. The focus of the study was on the total higher educational
system in which institutions of higher education are interacting with
one another in the exchange of scholars. It also was hoped that this
analysis would suggest some strategies of developing a mathematical
model which can satisfactorily predict institutional mobility.
Review of migration research literature, mathematical models of
migration and sociological studies of institutions of higher education
provided a conceptual frame of reference for the present study. The
academic community was conceptualized as a two-dimensional system: the
geographic distribution of institutions and the prestige structure of
institutions. It was hypothesized that institutional mobility would
increase as the proximity increases along these two dimensions.
Realizing the advantageous saving of research funds and time in
secondary analysis, an attempt was made to utilize existing data such
as the data collected by the National Science Foundation for the Nation
al Register of Scientific and Technical Personnel. Since the data did
not allow the proposed analyses, it was decided to obtain a random
sample from the directories of professional societies. The American
Chemical Society's Directory of Graduate Research provided the neces
sary data for the present study.
The analysis of institutional mobility patterns of chemists was
based on a random sample of 1,128 scholars from directories of graduate
•..
80
faculties covering the 1955-1967 period. Although the size of sample
was small, these longitudinal data supported on analysis of three types
of mobility: (1) from the institution of baccalaureate training to the
institution of doctorate training, (2) from institution of doctorate
training to the institution of postdoctoral employment, and (3) the job
change from one institution to another. MObility patterns were analyzed
by examining the departures of the observed from the expected frequen
cies of movers. The results of the analysis can be summarized as
follows:
The mobility from the baccalaureate to the doctorate training was.
characterized by stronger tendencies toward regionalism than toward
prestige level homogeneity. It appeared that for their doctoral study,
students tended to stay at the same institution or move to institutions
of the same prestige level in the same region. Consequently, inter
regional and interprestige level mobilities were less than would be
expected on the random distribution model. The regionalistic tendencies
seem to be stronger for the institutions at the lower prestige level.
The mobility from the doctoral institution to the institution of
employment was also oriented toward stronger regionalistic tendencies
than selective prestige level tendencies. Thus, the academic stratifi
cation system in doctorate-to-employmentmobility can be said to be a
set of regional hierarchies rather than a rigid prestige hierarchy. It
was noted that downwaxd mobility was more common, espeoially at earlier
stages of postdoctoral careers. Institutions at the lower prestige
level had a relatively higher rate of inbreeding and a stronger region
alistic orientation.
•81
82
the persistence of regional inequalities in the quality of higher
education, ·the intelleotual style and perspective, a.."1d the setting of
cultural patterns. These kinds of inequalities serve both as possible
sources of unnecessary disputes in academic community and as possible
bases for the structural cleavages within American society. Regional
tendencies would impose restrictions on the development of institutions
at the lower spectrum of quality and newly emerging universities.
Regions '\'lhere higher education is comparatively less effective are
likely to remain so if migration is allowed to remain the primary equi
librium force and major adjustm~nt in regional differenoes in education
al quality are not undertaken.
As to the question whether the regionalistic tendency might be
decreasing, this study did not provide any substantial eveidence. The
indication was that the young cohorts were slightly less oriented to
ward regionalistic tendencies ~hat the old cohorts in the baccalaureate
to doctorate mobility and the doctorate to employment mobility. Fur
ther efforts to investigate trends in these pattems over time would be
J:.·elevant.
Two kinds of regression analyses were performed to investigate the
association among the pair variables such as flows of mobility from the
origin to the destination and the distance between them, and the point
variables such as various characteristics of the origin or the desti
nation point. The first regression analysis dealt with the unordered
pairs of institutions. In more familiar teminology in migration re
search, the indices of mobility (dependent variable) in the unordered
pair regression oorresponds to gross migration, though the average
83
rather than the sum of two directional flows is usede The second re
gression analysis was concerned with ordered pairs of institutionse In
this case, the dependent vaz-iable is directional flows of scholars from
one institution to anothere The results of both regression analyses
were not impressive in terms of the amount of variance accounted for,
but was useful in screening the implied relationships and provided
guidelines for further experimentatione
The distance variable consistantly yielded an inverse relationship
with the mcbilitYe The prestige and faculty compensation had some
effects on the mobility, that is, the greater the difference in pres
tige scores and compensation between two institutions, the smaller the
mobility between them. Considering the amount of variance accounted
for by the regression, there was a need for introducing additional rele
vant independent variables.
An examination of the residuals revealed a need for modifying
extreme outliers or for disaggregating the mobility into logical compo
nents for separate analyses. It was found that there was a high posi
tive intraclass correlation among the residuals\) wr.J.oh appeared to be
the refleotion of structural effects of the mobility system. Therefore
any models which assume independence among the pai:rwise interchanges of
mobility seems to be inappropriate. Any descriptive or forecasting
model would need to take into oonsideration the system effects by
building a separate functional relationship for each component of
mobility. An application of the system theory approach seems to offer
some help in this line of further investigation.
84
Finally, it should be pointed out that the small number of cases
has imposed certain limitations to the findings in this study. It is
hoped that the results of this study will lead to a larger study along
these lines.
85
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•Abbreviated Name
AlabamaArizonaArkansasBostonBrandeisBrooklyn Polytech.BrownBuffalo
California(Berkeley)
Ca.lifornia(Davis)
Cal. Tech.
Carnegie-MellonCase ReserveChicagoCincinnatiColoradoColumbiaConnecticutCornellDelawareDukeEmoryFloridaFlorida StateGeorgetownGeorgia Tech.HarvardHoustonIllinoisIllinois·Tech.IndianaIowaIowa StateJohns HopkinsKansasKansas StateKentuckyLouisiana State:M. I. T.
Maryland
91
APPENIlIX A
Institutions Included in the Study
Full Name and Location
University of Alabama (University, Ala.)University of Arizona (Tucson, Arizona)University of Arkansas (Fayetteville, Arkansas)Boston University (Boston, Mass.)Brandeis University (Waltham, ~Iass.)Polytechnio Institute of Brooklyn (Brooklyn, N. y.)Brown University (Providenoe, R. I.)state University of New York at Buffalo
(:Buffalo, N. y.)University of California (:Berkeley, Calif.)
University of California (Davis, Calif.)
California Institute of Technology(Pasadena, Calif.)
Carnegie-Mellon University (Pittsburgh, Pa.)Case Western Reserve University (Cleveland, Ohio)University of Chioago (Chicago, Ill.)University of Cincinnati (Cincinnati, Ohio)University of Colorado (Boulder, Colorado)Columbia. University (New York, N. y.)University of Connecticut (Storrs t Conn.)Cornell University (Ithaoa, Nc Y.)University of Delaware (NeWark
lDelaware)
Duke Uni:versity (Durham, J)T. C.Emory University (A-Uanta, Ga.University of Florid.a (Gainesville, Fla.)Florida State University (Tallahassee, Fla.)Georgetown University (Washington, D. C.) .Georgia. Institute of Technology (Atlanta, Ga.)Harvard Univeraity (Cambridge, Mass.)University of Houston (Houston, Texas)University of Illinois (Urbana, Ill.)Illinois Institute of Technology (Chicago, Ill.)Indiana University (Bloomington, Ind.)University of Iowa (Iowa City, Iowa)Iowa State University (Ames, Iowa)Johns Hopkins University (Baltimore, Md.)University of Kansas (Lawrence, Kansas)Kansas State University (Manhattan, Kansas)University of Kentucky (Lexington, Ky.)Louisiana Sta.te University (Baton Rouge, La.)Massachusetts Institute of Technology
(Cambridge, Mass.) .University of Maryland (College Park, Maryland)
•92
APPENDIX A (continued)
Abbreviated Name
MassachusettsMichiganMichigan StateMinnesotaMissouriN. Y. U.NebraskaNorth Carolina
N. C. State
NorthwestemNotre DameOhio StateOklahomaOklahoma StateOregonOregon StatePennsylvaniaPenn. StatePittsburghPrincetonPurdueRensselaerRiceRochesterRutgersSt. John'sSouthern Cal.
StanfordTempleTennesseeTexasTexas A & MTuftsTulaneU. C. L. A.utahVanderbiltVirginiaV. P. I.Washington
(St. Louis)
FIlII Name and Location
University of Massachusetts (Amherst, Mass.) .University of Michigan (Ann Arbor, Mich.)Michigan State University (East Lansing, Mich.)University of Minnesota (Minneapolis, Minn.)University of Missouri (Columbia, Mo.)New York University (New York, N. Y.)University of Nebraska (Lincoln, Nebraska)University of North Carolina at Chapel Hill
(Chapel Hill, N. C.)North Carolina State University at Raleigh
(Raleigh, N. C.)Northwestem University (Evanston, Ill.)University of Notre Dame (Notre Dame, Indiana)Ohio State University (Columbus, Ohio)University of Oklahoma (Norman, Oklahoma)Oklahoma State University (Stillwater, Oklahoma)University of Oregon (~ene, Oregon)Oregon State University (Corvallis, Oregon)University of Pennsylvania (Philadelphia, Pa.)Pennsylvania State University (University Park, Pa.)University of Pittsburgh (Pittsburgh, Pa.)Prinoeton University (Princeton, N. J.)Purdue University (Lafayette, Ind.)Rensselaer Polyteohnic Institute (Troy, N. Y.)Rioe University (Houston, Texas)
*University of Rochester (New York, N. Y.)Rutgers - The Sta.te University (Brunswick, N. J.)Saint John's University (Jamaioa, N. Y.)University of Southem California
(Los Angeles, Calif.)Stanford University (Stanford, Calif.)Temple University (Philadelphia, Pa.)University of Tennessee (KnOXVille( Tenn.)University of Texas (Austin, Texas)Texas A &MUniversity (College Station, Texas)Tufts University (Medford, Mass.)Tulane University (New Orleans, La.)University of Califomia (Los Angeles, Calif.)University of utah (Salt Lake City, utah)Vanderbilt University (Nashville, Tenn.)University of Virginia (Charlottesville, Va.)Virginia. Polytechnic Institute (Blacksburg, Va.)Washington University (St. Louis, Mo.)
*Name now changed to Rookefeller University.
• APPENDIX A (oontinued)
Abbreviated Hame Full Name and Looation
93
\vashington(Seattle)
Washington StateWayne StateWest VirginiaWisoonsinYale
University of Washington (Seattle, Washington)
Washington State University (Pullman, Washington)Wayne State University (Detroit, IvIioh.)West Virginia University (Morganton, W. V.)University of Wisoonsin (Madison, Wisoonsin)Yale University (New Haven, Conn.)
94• APPElIDIX 13
Regiona.l and Prestige Groupings of Institutions
Region PrestiGe Level Institution
New England 1 (High) Brandeis M. I. T.Brown YaleHarvard
4 (Low) Boston MassachusettsConnecticut Tufts
Middle Atlantic 1 (High) Brooklyn Polytech. Penn. stateColumbia PrincetonCornell
2 Carnegie-Mellon PittsburghPennsylvania Rochester
3 N. Y. U. RutgersRensselaer
4 (Low) Buffalo TempleSt. John's
Midwest 1 (High) Chicago MinnesotaIllinois NorthwesternIndiana Ohio StateIowa State PurdueMichigan Wisconsin
2 Ir,wa WashingtonKansas (St. Louis)Michigan State Wayne StateNotre Dame
3 Case Reserve Kansas StateCincinnati NebraskaIllinois Tech.
4 (Low) Missouri
South 1 (High) Johns Hopkins TexasRice
- 2 Duke North CarolinaFlorida
• APPENDIX B (continued)
95
Prestige Level Institution
South (conttd)
West
3
1 (High)
2
3
DelawareGeorgia Tech.Louisiana State
AlabamaArkansasEmoryFlorida Sta-teGeorgetownHoustonKentuckyN. C. State
California(Berkeley)
Cal. Tech.Stanford
California(Davis)
Colorado
ArizonaOregon State
MarylandVanderbiltVirginia
OklahomaOklahoma StateTennesseeTexas A & MTulaneV. P. I.West Virginia
U. C. L. A.Washington
(Seattle)
OregonSouthern Cal.Utah
Washington State
• 96
APPENJ)IX C
A Note on the Method Used in Calculating ExpectedFrequencies in Mobility ~~trix
In earlier studies of social mobility, the concept of "perfect
mobility" was introduced to describe the idealized situation where an
actor's social status at a given time is independent of his status at
an earlier time or his father's status (Glass, 1954, pp. 218-265).
This concept corresponds to the concept of independence in a contin-
gency table in elementary statistics textbooks.
The contingency analysis in testing for independence in a k x k
matrix involves computation of estimates of the 2k non-negative para-
meters, PI ••• Pk, Rl • • • ~, which determine the probability qij
associated with a given cell (i,j) according to the formula:
k ksuch that L P. = 1 and L R. '" 1-
i=l ~ j=l J
Then, the expected value of the frequency f ij in the cell (i,j) can be
written as:
where n is the total frequency for the table. Denoting the observed
totals in the i-th row and j ..th column by r i and cj ' the maximum likeli
hood estimators of P. and R. are:~ J
Pi = ri/n and Rj = cj/n
We can thus see that the maximum likelihood estimator of E(f.. ).. ~J
Fij = nP1.Rj = ricj/n
is:
•97
>Iodification of this statistical method is necessary in certain
circumstances when dealing with incomplete contingency tables. An in
complete table is one containing at least one cell for which no frequency
(zero or otherwise) is provided. Such a cell occurs (1) if for any
reason the appropriate value cannot be determined, (2) if one wishes
deliberately to eliminate one or more cells from consideration, though
their frequencies are known, and (3) if the cell has no meaning in a
particular problem.
An example is the transaction flow tabl" in which one is usually
concerned exclusively with flows between areas or institutions. In the
mobility analysis of industrial workers, it \vas suggested t.hat the stay
ers should be separated from the movers (Elumen, ~~., 1955). For
this p~rpose, the conoept of '.l quasi-perfect mobility'l was introduced
(Goodman, 1965) to desoribe the situation in which an actor's status is
independent of his father's status oonsidering only those individuals
who have moved out of their father's status strata. This model treats
mobility as a separate phenomenon from the statuB inheritance or tend
enoy of remaining in a social or geographi~ looation.
·vlhen the stayers at the main diagonal in a mobility matrix are to
be excluded from the analysis, the expected pattern of mobility for the
movers can be derived from the "quasi-perfect mobility" model and these
expectations can be estimated from the observed marginal distributions
of movers exoluding the stayers. This model oorresponds to the concept
of independence in a restricted or incomplete contingenoy table.
The analysis of restricted oontingency table where main diagonal
oells are to be excluded from oonsideration will be treated here. Since
•98
the expected frequencies for diagonal cells must effectively be restrict-
ed to zero, the parameters P. and R. defined above will no longer apply.J. J
Denoting by P.. the modified probability associated with the cell (i,j),J.J
in order to make the probability of falling in nondiagonal cells add up
to unity, we should define:
{
O,
Pij = P.R./[l - t P R l,J. J 1Il=1 m ill,;
We can rewrite the above formula as:
for i=j
for i=j
where Ui and Vj are positive constants which are such that
k k k k kL.: L. Pi' = [L L U.v·1 -L: U Vm III 1.i=l j=l J i=l j=l J. J mel m
The formula for the expected frequency in each nondiagonal cell bij is
where h is the total frequency in nondiagonal cells.
The maximum likelihood estimator of E(b .. ) isJ.J
Bij = hUIVj, for i~j
where U! and V~ are the maximum likelihood estimatore of Ui and VJ.,
J. J
respectively•
.An iterative method for determining the U! and V~ is given byJ. J
Goodman (1964). The iterative procedure given by Goodman not only leads
to the desired estimates but also reduces the number of arithmetic opera-
tions, compared with the corresponding procedure introduced earlier by
Savage and Deutsch (1960). Briefly, the procedure given by Goodman is
•99
as follows.
Let xi and Yj denote the totals in the i-th row and j-th column not
including the diagonal oell. The iterative procedure is initiated
taking
oW. = x.~ ~
The 2m-th step (m~l) is executed taking
Zi2m- l = yi /(w. 2m- 2 _ Wi2m- 2J
kwhere W. = 2: Wi. As the (2m+l)th step, take
i=l
W. 2m = x./(z.2m-l _ Z. 2m-lJ~ ~ ~
kwhere Z. = L. Z .•
j=l JThe iterative steps are continued for mal, 2, . . ,
until the desired accuracy is obtained. Then the expected value Bij for
a given nondiagonal cell can be obtained by
B. . = w. 2m Z. 2m-l for i'&j.~J ~ J
A generalized computer program to analyze contingency tables with
restrictions at the diagonal as well as nondiagonal is given by Coble
(1969). This program handles up to a 50 x 50 matrix with 50(50-2) or
less restricted cells. For the present study, this computer program was
expanded to handle up to 90 x 90 matrix and adapted for the IBM 360/75
at the Triangle University Computing Center.
•APPENDIX D
statistical Tables
Table D. 1 Chi-Square Statistics for Analysis of theBaccalaureate to Doctorate Mobility Patterns
Table D. 2 Chi-Square Statistics for Analysis of theDoctorate to Employment 110bility Patterns
Table D. 3 Chi-Square Statistics for Analysis of thePostdoctoral Job Mobility Patterns
Table D. 4 Zero-Order Correlation Matrix for UnorderedPair Regression
Table D. 5 Zero-Order Correlation Matrix for Ordered PairRegression
Table D. 6 Standard Partial Regression Coefficients
Table D. 7 Analysis of Variance Tables for Unordered Pairand Ordered Pair Regression
100
Table D. 1 Chi-Square Statistics for Analysis of theBaccalaureate to Doctorate MObility Patterns
101 --Factor and Component Observed Expected Chi-square
of Nobility Frequency Frequency Value
Re«ion and Prestige Level
(I) Intra-regional, 78 40horizontal
(II) Intra-regional, 47 30 ,; ... 57.72"*vertical
(III) Inter-regional, 137 156 d.f.... 3horizontal
(IV) Inter-regional, -2§. ..Jl.4.vertical
Total 360 360
Region e2(I) Intra-regional mobility 125 70 X = 53.64"*
(II) Inter-regional mobility ~ ..l2.Q. d•. f .... 1
Total 360 360
Prestis,e Level,
2(I) Horizontal mobility 215 196 it "" 4.04*
(II) Vertical mobility ..ill. ~ d.f. "" 1
Total 360 360
Interaction
By subtraction 2X. ... 0.03
d.f.... 1..
* Significant at .05 level** Significant at .01 level
"* SignU'icant at .001 level •
•102
Table D. 2 Chi-Square Statistics for Analysis of theDoctorate to Emp10ymant Mobility Patterns
Factor and Componentof Mobility
ObservedFrequency
ExpectedFrequency
Chi-squareValue
Region and Prestige Level
(I) Intra-regional,horizontal
(II) Intra-regional,vertical
(III) Inter-regional,horizontal
(IV) Inter-regional,vertical
Total
84 54
128 76 2 68.17***~ ...
155 168 d.f.... 3
..£2Q. ....ll2.
617 617
Region
(I) Intra-regional mobility
(II) Inter-regional mobility
Total
Prestige Level
212
....4.Q2
617
130
.Ml617
2X ... 65.53***
d.f.... 1
(I) Horizontal mobility
(II) Vertical mobility
Total
Interaotion
239 222 2X ... 2.03
.....ll§. ~ d.f.... 1
617 617
By subtraction
* Significant at .05 level** Signifioant at .01 level
*** Significant at .001 level
2X ... 0.61
d.f.... 1
•103
Table D. 3 Chi-Square Statistics for Analysis of thePost-doctoral Job Mobility Patterns
Factor and Componentof 1"'10hility
ObservedFrequency
ExpectedFrequency
Chi-squareValue
Region and Prestige Level
(I) Intra-regional,horizon~ual
(II) Intra-rf)gional,vertical
(III) Inter-~egional,horili.wntal
(IV) Inte~-regional,vertical
Total
Region
7 6.2
18 11.5 7.-2 = 9.85*
28 21. 7 d.f. = 3
-lQ. 43.6
83 83.0
(I) 1ntra-regional mobility
(II)! Inter-regional mobility
Total
,Eyestige Level
(I) Horizontal mobility
(II) Vertical mobility
Total
Interaction
25
27.9
55.1
8;.0
d.!. = 1
1 = 2.72
d.f. = 1
By subtraction
* Significant at .05 level** Significant at .01 level
*** Significant at .001 level
d.!•• 1
- -Table D. 4 Zero-Order Correlation Matrix for Unordered Pair Regression
. " e
- e
Table D. 5 Zero-Order Correlation Matrix for Ordered Pair Regression
, . e
• Table D. 6 Standard Partial Regression Coefficients
106
~ Independent Bacoalaureate Dootorate to Postdoctoralvariable to dootorate employment job
mobility mobility mobility
(I) Unordered pair regression
Distanoe -0.1208 -0.1209 -0.0482
Average of -0.0668 -0.0747 -0.0235prestige soores
Absolute differenoe -0.0040 -0.0426 -0.0087in prestige scores
Average of -0.0426 0.0100 0.0098oompensation
Absolute differenoe -0.0077 -0.0404 ..0.0229in oompensation
(II) Ordered pair re6#ession
North-South 0.0119 0.0015 0.0100distance
East-West 0.0228 0.0105 0.0110distanoe
Signed differenoe -0.0423 -0.0443 -0.0179in prestige soores
Signed differenoe 0.0862 -0.0117 0.0152in oompensation
• Table D. 7 ~a1ys1s of VariapQe Tables for UnorderedP41~ and Qrde~ed Pair Re~ession
107
Sum of Mean FType of Ana1ys~s SOlU'qe d.f. Sq,uares Sq\lare Va.lue
(I) Unordered Pair Re6Fess~on
(1) Baccalaureate to R~&Tession 5 22243.24 4448.65 20.43***doctora.te mobility
Re~id~al ~ 794412.00 217.71
Total ;654 816655.24
(2) Doctorate to Regr~~sion 5 37198.11 7439.62 21.92***emplo~ent ~ob~1~t1
ResidVta.l 2649 ·12~8635.34 339.45
~ot~l 3654 1275833.45
(3) Postdocto~al job R,gression 5 554.96 110.99 2.81*mobi;lity
Re~id,ua;L 3642 141222,81 39.53
Total ;654 144807.77
(II) Ordered Pair ReBfession
(1) ~acoa1aureate to RegJ;'ess,ion 4 3743.87 ~35.97 7.45***doctorate mo~il,ity
~~s~dual 1305 918268.95 125.70
~ota1 7309 922012.82
(2) Doctorate to ~eq,ress:Lon 4 7243.61 1810.90 5.22***emp1Qyme~t mobil,ity
Re~1d~1 7305 2534866.22 347.00;
Tol;al 7309 2542109.84
(3) Postdocto~a~ job . Reg;ress1on 4 147.04 36.76 0.64 •mobility
Res1d~ . 7~05 416724.02 57.05
.. Tot~l 7~09 416901.06
, ,e * Significant at .0' level** Signi~ioant a.t .01 :level
*** Signifio~lI a.t .0Ol;Level;