Social Networks 12 (1990) 239-252 North-Holland

239

A GUlTMAN SCALE FOR THE STRENGTH OF AN INTERPERSONAL TIE *

Noah E. FRIEDKIN * *

University of California

Social psychological theory on interpersonal attachments suggests that the strength of a relation- ship develops in stages. This paper proposes a measure of the strength of an interpersonal tie that is consistent with this social psychological theory. Three findings are reported from a study of adult (Ego-Alter) dyads in six communities. (1) Ego’s claims of frequent discussion with Alter, seeking help from Alter, and friendship with Alter form a Guttman scale: the claim of friendship implies the claims of help seeking and frequent discussion; the claim of help seeking implies the claim of frequent discussion. (2) Ego’s level of attachment to Alter is related to Alter’s level of attachment to Ego. (3) The likelihood of perceived consensus and acknowledged interpersonal influence in a dyad increases with the strength of the Ego-Alter tie as measured by the total number of claims made by Ego and Alter about their relationship.

1. Introduction

Scale construction ought to be guided by extant theory or else explicitly involve the development of new theory (Coombs 1964: 5). This paper proposes a measure of the strength of an interpersonal tie that is consistent with social psychological theory on interpersonal attach- ments (Levinger and Snoek 1972; Altman and Taylor 1973; Secord and Backman 1974; Backman 1981). Three ideas in particular have guided the development of the proposed measure.

First; a relationship is most accurately described as consisting of two directed attachments (Ego -+ Alter and Alter + Ego) and any global assessment of the strength of the relationship must take into account these separate attachments. It is potentially misleading to seek an

* This research is based on data collected with Charles E. Bidwell as part of a project, supported by the Spencer Foundation, on decision making in school district policy groups. * * Direct correspondence to Professor Noah E. Friedkin, Graduate School of Education, Univer- sity of California, Santa Barbara, CA 93106, U.S.A.

037%8733/90/$3.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)

240 N.E. Friedkin / A Guttmnn scale of tie strength

answer to such questions as “Are Ego and Alter friends?” when two persons’ separate subjective orientations need not be identical.

Second; an Ego + Alter attachment develops in stages. Most pro- posals about the development of an attachment are consistent with Backman’s (1981) schema. A relationship is initiated when Ego be- comes aware of Alter; the awareness may be based on direct interaction or, in the absence of such interaction, on the receipt of information about Alter. From the information Ego receives about Alter, Ego estimates the value of pursuing the relationship. Positive valuation of the relationship usually is associated with efforts by Ego to strengthen the relationship through verbal or written contact. However, the rela- tionship may increase in strength without direct contact; for example, Ego’s fantasies about Alter may serve to strengthen the tie. To the extent that Ego finds the outcomes of the relationship rewarding, conditions have been established for more intimate processes of self- disclosure, trust, commitment, and strong positive sentiment. Again, these processes are typically (but not necessarily) based on direct interaction; for example, Ego may seek help from (or disclose intimate personal details to) a mass-media celebrity with whom Ego has become infatuated.

This developmental perspective on attachment processes suggests that it may be misleading to view tie strength as a simple linear combination of variables like interaction frequency, emotional inten- sity, and mutual confiding (Granovetter 1973; Marsden and Campbell 1984). Such a view misses the idea that qualitatively different interper- sonal processes occur at different stages of a relationship’s develop- ment; for example, if interaction is prior to feelings of intimacy, then these two dimensions of a relationship are not substitutable in the production of tie strength, The occurrence of intimacy implies both interaction and a higher level of tie strength than does any frequency of interaction without intimacy. In short, the appropriate scale for an Ego -+ Alter attachment may be Guttman in form.

Third; both the attainment of a particular level of tie strength and the maintenance of the tie at that strength depend upon the balance of rewarding and punishing outcomes (anticipated and actual) of the relationship. The main reward is reciprocity and the main punishment is its absence (Gouldner 1960; Kelly and Thibaut 1978; Kelly 1979). Ego and Alter are interdependent insofar as the development of Ego’s attachment to Alter is contingent upon the development of Alter’s

N.E. Friedkin / A Guttman scale of tie strength 241

attachment to Ego. Regular face-to-face contact is associated with strong ties because of the positive feedback (however minimal or imagined) such contact allows; a strong attachment is difficult to maintain in a strictly unilateral relationship because such a relationship does not permit those minimal cues (e.g. a gesture or word of encoura- gement) from which an Ego might draw sustenance and reward.

The crucial idea is reciprocity, but this reciprocity may be more or less delayed. Where there is no delay, then Ego and Alter’s attachments advance in tandem - so that they jointly move, if they move at all, to higher levels of tie strength. Where there is some delay, Ego and Alter’s attachments may each develop similarly (through the same set of stages) but at any given point in time their two states of attachment may not be identical. Although the extant theory on interpersonal attachments allows for a loose coupling of interpersonal sentiments and behaviors, the theory suggests that the strength of Ego’s attachment to Alter is unlikely to progress to (or be maintained at) a high level in the absence of some movement in the same direction by Alter. Hence, reciprocation and balance are crucial for both the occurrence and durability of strong relationships.

These three ideas - the directedness of attachments, their develop- ment in stages, and the importance of reciprocity - each have a place in a measure of tie strength that is constructed as follows:

Sli = sji = rij + y/i

where

rij = d,, + hij +hj

d,j = 1 if i claims frequent discussion with j (d,, = 0 otherwise); hij = 1 if i claims seeking help from j (hi, = 0 otherwise); and f;, = 1 if i claims j as a close personal friend ( f, j = 0 otherwise). Hence si j is the total number of claims made by Ego and Alter about their relation- ship. I will report on the properties and construct validity of this measure. We will see that the claims are patterned in a way that is consistent with social psychological theory on interpersonal attach- ments and that the scale scores ( sij) are associated with perceived consensus and acknowledged interpersonal influence.

242 N. E. Friedkin / A Guttman scale of tie strength

2. Data

The paper draws on data collected during case studies of decision-mak- ing processes in the policy groups of six school districts. The policy groups of these school districts consisted of persons who had some noteworthy influence on school board decisions during the several years preceding the study. The policy group in each school district was delineated by a snowball procedure which combined positional, reputa- tional, and behavioral selection criteria.

The delineation of the group started with a list of influentials that included each school board member, the district superintendent, and all other persons identified in local newspapers or school board minutes as currently or recently active in board meetings, district elections, or other efforts to affect board decisions. These individuals nominated persons on the district staff and in the community who were known or reputed to be currently or recently active in attempts to influence school board decisions. These nominees were asked for further nomina- tions according to the same two criteria. To guard against idiosyncratic nominations, only persons who were mentioned at least twice were added to the list of policy group members. The nominating procedure continued until dual nominations no longer occurred.

Each policy group member was then interviewed about the decision- making processes in their school district and was asked to fill out a questionnaire. The questionnaire contained, among other items, a list of the policy group members in the school district. Respondents were asked a set of questions concerning their interpersonal relationships with other policy group members to which they responded by checking off names, in separate columns, of those persons with whom they claimed the particular relationship existed. Seven of these network items enter into the present analysis:

Frequent discussion. “Check off any of the persons with whom you frequently discuss matters having to do with the . . . Schools.”

Help seeking. “When you need information or advice about prob- lems or issues having to do with the . . . Schools, to which persons on the list do you turn?”

Close friendship. “Check off any persons who are your close personal friends.”

N.E. Friedkin / A Guttman scale of tie strength 243

Perceived consensus. “When there are differences of opinions about school district matters, which of the persons on the entire list are usually on the same side of these issues as yourself? Which persons are usually on a different side of these issues from yourself.” From these two items, a measure of perceived consensus ( pij = p,,) was constructed as follows: pij = 1 if either Ego or Alter reported agreement and neither reported disagreement; pij = - 1 if either Ego or Alter reported disagreement and neither reported agreement; and pij = 0 otherwise.

Acknowledged injluence. “Check off the names of any person on the list who you would say probably had some influence on your own opinions on school related matters during the last year or so?” From the data derived from this item, a variable measuring the occurrence of acknowledged influence ( aij = aji) was constructed: aij = 0 if neither Ego or Alter acknowledged influence; aij = 1 if Ego or Alter but not both acknowledged influence; and aij = 2 if both Ego and Alter acknowledged influence.

The effective response rates are high, ranging from 88% to 98% among the groups. The analysis is restricted to respondent dyads because the measure of tie strength is based on the claims of both members of a dyad about their relationship. Among the n,, respon- dents of a group, there are n,(n, - 1)/2 dyads available for analysis. Table 1 shows the number of policy group members in each school district, the number of respondents to the network items in the questionnaire, and the corresponding number of respondent dyads.

Table 1

Sites of the dyadic relationships

Sites Group size

Number of

respondents Respondent dyads

A 42 38 703

B 42 37 666

C 60 59 1711

D 61 54 1431

E 59 57 1596

F 67 66 2145

Totals 331 311 8252

244 N.E. Friedkin / A Guttman scale of tie strength

3. Findings

3.1. Ego’s attachment to Alter

Ego may claim having frequent discussions with Alter, Ego may claim seeking help from Alter, and Ego may claim Alter as a close personal friend. These claims form a Guttman scale. Table 2(a) describes the distribution of claim patterns and Table 2(b) reports the coefficients of reproducibility, minimum marginal reproducibility, and scalability for the pattern:

r f h d 3 1 1 1 2 0 1 1 1 0 0 1

where f represents the claim of close friendship, h the claim of help seeking, d the claim of frequent discussion, and r = f + h + d. The high

Table 2 Claims of friendship (f), help seeking (h), and frequent discussion (d) form a Guttman scale

(a) Distribution of claim patterns

Patterns Sites

f hd A

111 20 110 1 101 15 100 10 011 64 010 21 001 104 000 1171

B C D E F

28 70 99 73 126 0 6 1 2 11 4 47 38 16 73 1 32 25 2 42

127 205 216 331 300 19 100 44 48 116

152 293 246 286 353 1001 2669 2193 2434 3269

(b) Goodness of fit

Coefficients

Coefficient of reproducibility

Minimum marginal reproducibility

Coefficient of scalability

Sites

A

0.98

0.92

0.73

B C D E F

0.99 0.96 0.97 0.99 0.96

0.88 0.89 0.85 0.87 0.87

0.91 0.68 0.83 0.89 0.71

N. E. Friedkin / A Guttman scale of tie strength 245

values of these coefficients indicate that r = 1 tends to correspond with a claim of frequent discussion and that r = 2 tends to correspond with claims of frequent discussion and help seeking; naturally, r = 3 implies all three claims. ’ This claim pattern fits the present data better than any of the eight other possible combinations of claim patterns that form a scale of zero to three. While it minimizes the number of prediction errors in each of the school district sites, it also succeeds in describing approximately 75% or more of the Ego + Alter attachments.

3.2. Ego and Alter’s joint attachment

Table 3(a) presents the ways in which Ego and Alter’s attachments may combine under the constraint that their attachments conform perfectly to the Guttman pattern. In addition, Table 3(a) contains simplified descriptions of the combined claims that Ego and Alter may make. For example, d, indicates unreciprocated claims of discussion, d, indicates reciprocated claims of discussion, and d,(hf). indicates reciprocated claims of discussion plus unreciprocated claims of help seeking and friendship. Note that the Guttman properties of the subscales constrain the interpretation of these descriptors; for example, it should be understood that d,(hf). implies that one member of a dyad is claiming friendship, help seeking, and discussion while the other is claiming only discussion.

Now suppose that if a relationship increases in strength it does so in elementary steps, that is, with one person changing their level of attachment at a time. There are just five alternative models of the development of such a relationship that preserve the Guttman char- acteristics of the two attachments; these five process models are de- scribed in Table 3(b).

’ Inspection of the frequency with which different patterns of claims occur indicates that the

Guttman errors are not evenly distributed. The relatively large contribution to these errors, in

each group, of the (010) pattern (i.e. help seeking without friendship or frequent discussion) stems

most likely from the instrumental character of the groups’ activities. In such groups, members will

occasionally draw on the specialized knowledge of others without, at the same time, engaging in

frequent general discussions of group affairs. At the same time, the strong association of help

seeking with frequent discussion suggests that even in these instrumentally oriented groups help

seeking is contingent upon the prior generation trust and credibility.

246 N.E. Friedkin / A Guttman scale of tie strength

Table 3

Formal analysis of interpersonal claims under the Guttman constraint

(a) Ways of attaining the total claim score s,, = r, , + r,,

Alter’s score

‘11

0

1

2

3

Ego’s score

0

s,, = 0

S,] = 1

d, s,, = 2 old), s,, = 3

(fhd) u

1 2 3

S,) =1 s,, = 2 s,, = 3

du W, WV u S,, = 2 S,, = 3 s,, = 4

d, ha, (fh)A S,, = 3 S,] = 4 SC,5

hA (hd), f,(hd), S,, = 4 s,, = 5 s,, = 5

@)A, f,Old), (fhd),

(b) Alternative process models

Models Total claim score s,,

1 2 3 4 5 6

Note that reciprocation is the most immediate in Model 1 and the most delayed in Model 5. Also note that there are at most two conditions of a relationship for any given total number of claims (s, j). Total claim scores of one correspond with d,, scores of two correspond with either d, or (hd),, scores of three correspond with either (fhd), or h,d,, scores of four correspond with (fh)d,., or (hd)., scores of five correspond with f,(hd),, and scores of six correspond with (fhd).. It is, of course, the Guttman constraints in combination with the “one-step- at-time” process assumption that have radically reduced the number of possible interpretations of the total claim score (si,).

The data in Table 4 show that, among dyads with identical total claim scores, the proportion of dyads that conform to the predictions of Models l-5 is high in each of the six school district sites. Leaving aside those dyads with total claim scores of zero and six (for which no errors of prediction are possible), the joint claim pattern of approxi- mately 69% or more of the dyads is correctly predicted at each of the sites.

N. E. Friedkin / A Guttman scale of tie strength 241

Table 4 Distribution of dyads among claim patterns

Total Dyads Sites claim claim

A B C D E F score pattern

0

1 du *

2 &, u *

3 VW u

Up, *

4 (fhM, WV, *

5 f,W), *

6 UW,

Goodness of Fit ** ***

529 429 1163 918 1084 1385 53 12 143 164 118 180 19 13 92 39 37 119

14 23 38 12 42 29

34 56 92 118 107 137 11 2 19 14 7 55

3 2 10 21 2 2-l

14 26 46 38 69 66

4 6 26 18 9 25 2 5 11 11 8 21

5 17 18 20 59 29

5 1 22 15 9 16

3 6 9 10 23 23

3 1 9 14 5 15 4 I 13 13 17 18

0.94 0.96 0.90 0.93 0.96 0.89 0.75 0.90 0.69 0.80 0.86 0.69

* Response patterns that do not conform to any of the models (l-5) described in Table 3(b). * * Proportion of dyads consistent with the models described in Table 3(b).

*** Proportion of dyads consistent with models in Table 3(b) among dyads with total claim scores in the range l-5.

Moderate positive associations of the separate claim scores rij and 5, (in light of the Guttman character of each) indicate a tendency toward reciprocation. The values of Goodman and Kruskal’s gamma and Pearson’s product moment correlation are, respectively, 0.765 and 0.474 in Site A, 0.703 and 0.483 in Site B, 0.727 and 0.488 in Site C, 0.595 and 0.380 in Site D, 0.817 and 0.605 in Site E, and 0.647 and 0.425 in Site F. Along the same lines, from the data in Table 4, it appears that total claim scores of two more often arise from (hd), than d,, that scale scores of three more often arise from hdp, than (fhd)., and that scale scores of four more often arise from (hd), than (fh)~I~; indeed, the odds favoring the one alternative over the other generally are better than 2 : 1. Consequently, these data appear to support Model 2 (in which reciprocation is moderately delayed) as the best single

248 N. E. Friedkin / A Gutiman scale of tie strength

description of the joint claim patterns of Ego and Alter. * We should allow for alternative ways of achieving given levels of attachment in a relationship. However, there appear to be grounds for rejecting Model 5 (where reciprocation is the most delayed) given the heavily favored odds of hgp, over (fhd)..

Table 5

Tie strength and acknowledged interpersonal influence

(a) Zero-order relationships

Site A Site B Site C Site D Site E Site F

* 0.885 0.781 0.819 ** 0.676 0.622 0.626

(b) Probability of no acknowledged influence

0.850 0.825 0.786 0.691 0.652 0.602

s.. Site A Site B Site C Site D Site E Site F

0 0.856 0.839 0.866 0.930 0.808 0.826 1 0.347 0.518 0.494 0.719 0.355 0.388 2 0.085 0.333 0.255 0.285 0.231 0.231 3 0.238 0.235 0.110 0.277 0.125 0.186 4 O.OfMl 0.000 0.020 0.087 0.039 0.091 5 O.ooO 0.000 0.111 0.083 0.036 0.053 6 0.000 0.000 0.077 0.000 O.OCO 0.000

(c) Probability of reciprocal acknowledgment of influence

s. Site A Site B Site C Site D Site E Site F .I

0 0.011 0.023 0.015 1 0.083 0.094 0.094 2 0.424 0.185 0.195 3 0.571 0.265 0.402 4 0.917 0.522 0.647 5 0.500 0.571 0.444 6 0.750 0.714 0.461

* Goodman and Bruskaf’s g-a.

* * Pearson’s product moment correlation.

0.065 0.021 0.024 0.034 0.161 0.124 0.111 0.301 0.258 0.325 0.450 0.458 0.565 0.632 0.439 0.500 0.821 0.632 0.846 0.706 0.778

’ The lack of reciprocity in claims of frequent discussion may simply illustrate the unreliability of individuals’ reports: after all, persons either engage in frequent discussions or they do not; and if

they do, then both parties to such discussions should acknowledge the occurrence. Such a view is

too simple, because it ignores the possibility of differences in the subjective significance of

relationships for the parties. Frequent discussions may be differentially salient to the parties involved in them; when such differential salience is marked a lack of reciprocity may be expected

and should not on theoretical grounds be classified as measurement error.

N. E. Friedkin / A Guttmnn scale of tie strength 249

3.3. Construct validity

We should find a positive association between tie strength and interper- sonal agreement. Newcomb (1953) has suggested that this correspon- dence should be particularly strong for perceived agreement (also see Scheff 1967). Along the same lines, we should find an association for acknowledged influence. Our evaluation of the construct validity of the scale focuses on these two subjective measures of social solidarity.

Acknowledged interpersonal influence Table 5 reports the values of Pearson’s product moment correlation and Goodman and Kruskal’s gamma for the association between tie strength ( sij) and acknowledged interpersonal influence ( aij). The magnitudes of the association are

Table 6 Tie strength and perceived consensus

(a) Zero-order relationships

* **

Site A

0.557 0.317

Site B

0.630 0.402

Site C

0.599 0.394

Site D

0.621 0.414

Site E

0.742 0.445

Site F

0.656 0.428

(b) Probability of perceived agreement

si, Site A Site B Site C Site D Site E Site F

0 0.287 0.205 0.194 0.218 0.229 0.189 1 0.542 0.588 0.506 0.473 0.671 0.512 2 0.746 0.605 0.664 0.722 0.769 0.715 3 0.809 0.794 0.878 0.795 0.850 0.780 4 1 0.913 0.922 0.913 0.934 0.894 5 1 1 0.889 0.917 1 0.947 6 1 1 0.846 1 1 0.944

(c) Probability of perceived disagreement

S‘j Site A Site B Site C Site D Site E Site F

0 0.113 0.161 0.142 0.178 0.208 0.154 1 0.153 0.082 0.170 0.177 0.129 0.127 2 0.102 0.123 0.107 0.049 0.058 0.077 3 0.048 0.029 0.049 0.060 0.062 0.042 4 0 0.043 0 0 0.026 0 5 0 0 0 0 0 0 6 0 0 0 0 0 0

* Goodman and Kruskal’s gamma. * * Pearson’s product moment correlation.

250 N. E. Friedkin / A Guttman scale of tie strength

moderately high and remarkably uniform across the six school district sites. It is useful to examine the proportions of dyads that report no influence ( aij = 0) at various levels of tie strength. These data also are shown in Table 5. The probability of no acknowledged influence declines rapidly from 0.80 or-more to zero; that is, it covers virtually the entire range of possible probability values as a function of tie strength.

Perceived consensus Table 6 reports the values of Pearson’s product moment correlation and Goodman and Kruskal’s gamma for the as- sociation between tie strength ( sij) and perceived consensus ( pii). A consistently moderate level of association appears in these data. Table 6 also shows the proportion of dyads that report disagreement ( pij =

- 1) and agreement ( pij = 1) at various levels of tie strength. It appears that the perception of disagreement is systematically related to tie strength and is virtually non-existent among dyads at tie strength scores of four and higher. With respect to the probability of agreement, the relationship is similarly pronounced.

4. Summary

The three main findings of this study are these. (1) Ego’s claims of frequent discussion with Alter, seeking help from Alter, and friendship with Alter form a Guttman scale: the claim of friendship implies the claims of help seeking and frequent discussion; the claim of help seeking implies the claim of frequent discussion. (2) Ego’s level of attachment to Alter is related to Alter’s level of attachment to Ego. (3) The likelihood of perceived consensus and acknowledged interpersonal influence in a dyad increases with the strength of the Ego-Alter tie as measured by the total number of claims made by Ego and Alter about their relationship.

5. Discussion

A definition of interpersonal relationships in terms of two directed attachments (Ego --j Alter and Alter + Ego) is consistent with a view- point on dyads as elementary social systems in which co-orientations

N.E. Friedkin / A Guttman scale of tie strength 251

emerge from an interplay of members’ actions and reactions. In these elementary social systems the rule of reciprocity helps explain why the movement of one actor’s attachment in a certain direction (strengthen- ing or weakening) is often followed by a movement of the other actor in the same direction. To be sure, the rule of reciprocity does not explain Ego’s initial movement and, thus, does not provide a complete account of why relationships become strong or dissolve. Nonetheless, reciprocity is exceedingly important because it allows us to see why the separate actions of individuals eventuate in similar co-orientations.

Inquiries that seek to build on the present work might probe the scope of the rule of reciprocity. For example, it is plausible that the rule of reciprocity is weaker in the superior-subordinate relationships of formal organizations than in peer relationships. Organizational superiors usually cannot reciprocate the affections and disclosures of their subordinates without some risk to their hierarchical status; the question is how subordinates respond to such imbalance. If the rule of reciprocity extends to these relationships, then superior-subordinate relationships should be unstable with respect to a long-run capacity for regular and effective unidirectional influence; such relationships are likely either to be reduced to minimal strength or to transform into strong solidary ties.

Future inquiries might also pursue the idea that social conditions affect the form of the developmental process in dyadic relationships. It is not difficult to imagine a population in which interpersonal relation- ships tend to proceed from help seeking to frequent discussion, and finally to friendship. For example, members of highly technical organi- zations may interact mainly in order to solve problems; in turn, these problem-solving relationships may develop into relationships of broader scope and intimacy. If we take the possibility of alternative forms of development seriously, then a line of inquiry is opened that would seek to understand why different developmental forms occur in different contexts and the implications of such variation.

Structuralists need to be concerned with tie strength to the extent that the effects of a social network importantly depend on the values of the lines that comprise the network. A cautious viewpoint treats a social network as a structure of opportunities for flows of information and influence. However, if we are to advance our understanding of social network effects, we must begin to replace conclusions about the opportunities of network flows with conclusions about the probabilities

252 N.E. Friedkin / A Guttman scale of tie strength

of such flows. Good measures of tie strength are likely to be an important foundation for such theoretical refinement.

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