Geometry of Individual Variation

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Putilov AA. Geometry of Individual Variation in Personality and Sleep-WakeAdaptability. (Series: Psychology Research Progress). Nova Science PubInc, New York, 2010, 270 pp.

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C ONTENTS

Preface v

Int roduc tion Geometry and Applications of the Spherical Cube Modelxi

Par t 1 Spher ical Cube Represe nt a ti on of the S truc t ure of Sleep-Wake Adap tab ility

Chap ter 1 T axonomy of Chronotypes,T rototypes and Somnotypes:History and State of the Art 1

Chap ter 2 T hree-Dimensionality of the Structure of Sleep-WakeAdaptability 17

Chap ter 3 Validation of the Sleep-Wake Adaptability Scales Predicted bythe Spherical Cube Model 73

Par t 2 Spher ical Cube Represe nt a ti on of the S truc t ure of Perso nal ity Lex ico n

Chap ter 4 T axonomy of PersonalityT raits and Emotional States:History and State of the Art 99

Chap ter 5 T hree-Dimensionality of the Cross-Culturally UniversalStructure of Personality Lexicon 125

Chap ter 6 Evolutionary Psychology Perspectives on the SphericalCube Model of Personality Lexicon 221

Co nclus ion A General Approach to Uncovering Spherical CubeStructures 273


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Contentsiv

Appe ndix 1 Russian Version of the SWPAQ (Sleep-Wake PatternAssessment Questionnaire) 279

Appe ndix 2 Russian Version of the SCIoPS (Spherical CubeInventory of Personality Structure) 283

Refere nces 289

In dex 311


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P REFACE Scientific investigation is often aimed on generation and description of a low

dimensional simple form that is, however, an accurate representation of thestructure of numerous empirically obtained variables. In despite of this aim, somescientific descriptions of real world structures are difficult to visualize due to their dimensional complexity.T he book considers two such structures, the structure of personality lexicon and the structure of adaptive ability of the sleep-wake cycle.When factor analysis, most widely used method of data reduction, was applied tothe empirical data sets, it revealed six factorial dimensions of personality lexicon(i.e., Extraversion, Agreeableness, Conscientiousness, Emotional Stability,Intelligence and Self-Assurance), and six factorial dimensions of sleep-wakeadaptability (Morning and Evening Lateness, Anytime and Daytime Wakeability,and Anytime and Nighttime Sleepability). A principal question arises as to

whether these six factorial dimensions might be visualized in a three-dimensionalspace. T he author proposed the spherical cube model to explain why the answer tothis question must be yes.T he model provides a way of replacement of a six-factor representation by a more realistic representation with only three spatial(underlying) dimensions. In geometric terms, the model has a shape of sphericalcube. T he six pairs of this cubes edges on the surface of the sphere represent thesix largest factorial dimensions.T his cube serves as a system of coordinates for mapping any of a large number of narrow individual traits on the surface of thissphere. T he author proposed the original circumplex criteria for testing inquantitative terms whether the structure revealed by empirical study confirms wellto the structure predicted by the model.

T he model was first introduced for the structuring adaptive ability of thesleep-wake cycle. It helped to identify the exact number of broad adaptive traits of this cycle and to determine their relationship with the narrower and broader traits.Further research demonstrated that the same model can contribute to the


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Prefacevi

continuing debate about the structure of personality.T he spherical cube modelwas able to account for the correlations between 5-7 factorial dimensions that personality psychologists manage to recover by factor analysis of the long lists of personality descriptive terms or questionnaire items.T he numerous personality-relevant words were mapped on the surface of spherical cube with the cubesedges representing the six broad personality traits.

T he author provided an explanation of why the formally identical modeldemonstrated the applicability to two rather distinct real structures. Furthermore,the model opens a new perspective of uncovering three-dimensional structures of different kinds of reality described by using the multi-scale inventories.

T he book consists of six chapters.T wo chapters include reviews of modernliterature on individual differences. One concerns the studies of variation in

chronotype (morning-evening preference), trototype (wakeability), and somnotype(sleepability), and another concerns the debates around the scientific taxonomiesof personality traits and emotional states. Four other chapters of the book presentthe results of original researches of individual variation.T hey were aimed on thestructuring sleep-wake adaptability, the quantification of relationship between theindividual traits of sleep- and wake-related behavior and the responsiveness of thesleep-wake regulation to sleep loss, the structuring Russian personality lexicon,and the explaining origin and function of personality differences.

T he book appeals to lay audience and scientists who are interested in learningnew ideas and provocative observations about individual differences in human personality and sleep-wake traits.T he audience of this book also includes theresearches from those numerous branches of science that recognize the structuringindividual differences as an actual issue. Furthermore, original modeling andempirical results presented in the book can be used for teaching the universitycourses on statistical analysis, personality, emotion, neurophysiology, and psychophysiology.

In short, this book addresses an issue of uncovering the true shape (topology)of a multi-dimensional structure of the differences between individuals. It isaimed at demonstrating that the shape of the real structure might be more parsimonious than a shape yielded by factor analysis, a most widely used methodof data reduction. In addition, the book introduces an original approach toanalyzing empirical data sets that uncover realistic representations of the structureof individual variation. Finally, it shows a perspective of the implication of these

representations for the search for evolutionary origins and functions of individualdifferences.T he book is structured as follows.


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Preface vii

In a brief introduction section I describe the spherical cube model in generalterms and review the history of its application in the fields of differentialchronobiology and personality psychology.

T hereafter, I use the data on sleep-wake adaptability (Part 1) and personalitylexicon (Part 2) to test the predictions of the spherical cube model.T he analysisconfirms that: (1) the six largest factorial dimensions can actually have a three-dimensional structure; (2) this structure can be directly revealed by performingthree-dimensional scaling; and (3) evidence for similarity between empiricallyand theoretically predicted structures can be provided by applying circumplexcriteria. Parts 1 and 2 are independent of one another.T his means that if a reader is mostly interested in understanding the structural features of personality, he/shecan read the second rather than the first part.

T

he books conclusion includes a brief discussion of the perspective of applying a general approach to the analysis of empirical data sets in theframework of the spherical cube model.


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INTRODUCT ION : G EOMETRY AND APPL ICAT IONS OF THE SPHER ICAL C UBE

M ODEL T his book is centered on uncovering a real structure underlying a

large set of individual trait variables.T he spherical cube model canexplain a link between the actual (three-dimensional) and factorial(six-factor) structures of individual variation in sleep-wakeadaptability (Part 1) and personality lexicon (Part 2).

Ge neral Me thodolog y of S truc tur in g In d ividual Var ia tion in Tra it Var iables

A scientific taxonomy offers a standard vocabulary that facilitatesaccumulation and communication of empirical findings. Such a taxonomymust provide an understanding of a large number of specific instances in asimplified way that makes unnecessary separate examination of each specificinstance. Any taxonomy proposes a structure that has a shape (topology).T hemost scientifically valuable shapes are those that are parsimonious in terms of geometry and dimensionality. Consequently, a scientific investigation focuseson discovering a low dimensional simple form representation (approximation)of the empirically revealed structure (see Maraun, 1997 for detail).

T he most preferable shapes are just two- or three-dimensional ones because they can be visualized. Furthermore, these shapes must remain simpleforms, for example two-dimensional shapes such as squares or circles or three-dimensional shapes such as cubes or spheres.

More generally, the aim of scientific investigation is to generate anddescribe a low dimensional simple form that is an adequately accurate


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representation of the structure of numerous empirically obtained variables. Inother words, the scientific representation must, despite its parsimony, retainthe most important features of the empirical structure.

T he shape of the empirical structure can be revealed by the analysis of themeasures of relatedness (or proximity or association) between the variablesconstituting the structure under investigation (Maraun, 1997).T he measure of relatedness that has dominated scientific research for a century is the inter-correlation among variable (e.g. between individual trait variables).T hestructure of variables is usually revealed by the analysis of the pattern of correlations among them. In a good deal of empirical studies such analysis islimited to factor analysis of a matrix of pairwise coefficients of correlation.For at least the last six decades the factor-analytic approach has become the

most influential method for generating low dimensional representations of individual trait variables. By applying factor analysis researchers hope toreduce the dimensionality of representation of the empirical structure withoutgreat loss of information.T his is a variable-reduction procedure in whichmany variables are organized by a few factors that summarize theinterrelations among them.T his analysis provides coordinates called factor loadings that locate the variables as points in the n-dimensional commonfactor space. Usually, n is much smaller than the number of individual traitvariables (e.g. lists of questionnaire items or of personality-relevant words).

However, the practice of factoring individual trait variables indicates thatthe original set often cannot be replaced by only two or three factors. In thissense the structure under investigation is more than three-dimensional and thuscannot be visualized.

T he model presented in this book can be visualized in three-dimensionalspace as a spherical cube.T his is a cube that divides the surface of a sphereinto six equal parts (six spherical squares).T he major prediction of the model a prediction that is fully testable is that any individual trait variable can bemapped on the surface of this spherical cube. Another important prediction isthat the six largest factors yielded by the factor analysis can be alsoaccommodated by this model.T o emphasize this feature of the model suchfactors will be specified below as factorial dimensions.T hey are visualized asthe six pairs of edges opposing one another on the surface of the sphericalcube. T hese predictions will be tested here by analyzing two empirical

structures, the structure of sleep-wake adaptability and the structure of personality lexicon.


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Introduction xiii

Ma in Ideas of the Book

When one performs factor analysis of a long set of trait variables, thereality might be confused with the appearance of 5-7 orthogonal factors. Onecan interpret this factor-analytic result as revealing a 5-7-dimensional reality.However, the real dimensionality might be much simpler.T he spherical cubemodel postulates the possibility of replacing trait taxonomies with 6 1 factors by the three-dimensional taxonomy in the shape of a spherical cube. Namely,the space structure of trait variables might be represented in a shape composedof six spherical squares with corners of 120 each. Such representation assumesthe rather unusual angular location of six broad factorial dimensions revealed by factor analysis of the individual trait variables.T hey are visualized as the

six pairs of edges of the spherical cube. Such locations of factorial dimensionsmight be proven by performing a multidimensional scaling analysis or byapplying a set of circumplex criteria proposed here. Furthermore, the results of either factor or multidimensional scaling analyses might be used to map a hugenumber of separate individual trait variables on the surface of the sphericalcube.

T he empirical evidence supporting the spherical cube model is provided by detailed analysis of the original data.T hey were collected in studies aimedat uncovering trait structure in two domains of individual differences. Onestructure was developed to understand the diversity of the adaptive abilities of the sleep-wake cycle (Part 1). Another structure offers an explanation of thediversity of personality traits (Part 2).T he findings indicate that the sphericalcube model can help detect, describe and understand the natural structure of individual traits. In particular, the empirical results suggest that, although thetraditional factor analysis tends to overestimate the underlying dimensionalityof the structure of individual trait variation, its results can be easily explainedin the frame of the spherical cube model and confirmed by the results of multidimensional scaling.

In general, this book illustrates the heuristic potential of the spherical cubemodel for research aimed at discovering the precise nature of linkages betweenindividual traits. T he present modeling and empirical findings allow us toconclude that a spherical cube representation of individual traits variation is amore elegant, parsimonious, universal and insightful model compared to

traditional multi-factor representations, and that these multi-factor representations can be incorporated in the framework of the spherical cubemodel.


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Geome t r ical Fea tures of the Spher ical Cube Model

T o obtain a spherical cube, a cube is inscribed in a sphere so that thecentral points of the sphere and cube coincide and all corners of the cube lie onthe spherical surface. In other words, if the edges of the cube are projectedonto the sphere by tracing radii that pass through the cubes edges, then greatcircle arcs are formed on the sphere that divide it into six equal parts, each part being a spherical square (Figures 1.1, 1.2, 1.17, 1.21, 1.22, 2.1, 2.2, 2.17, and2.21-2.24).

T he geometry of a cube (Figures 1.1, 1.2, 1.6-1.11, 1.13, 1.15, 1.17, 2.1,2.2, 2.6-2.11, 2.13, 2.15, 2.17, 2.21 and 2.24) assumes that it has:

1)

three axes or vectors running through the center to connect above with below, left with right, and front with back (i.e., axis A , axis B , andaxis C );

2) three pairs of faces or squares, top opposes bottom, left opposes right,and front opposes back (i.e., A opposesa , B opposes b , and C opposesc);

3) four pairs of vertices or corners opposing one another (i.e., AbC opposesaBc , Abc opposesaBC , ABc opposes abC , and ABC opposesabc ); and

4) six pairs of edges or ribs (lines connecting the corners) opposing oneanother (i.e., AB opposes ab, aB opposes Ab, AC opposes ac, aCopposes Ac, BC opposes bc, and bC opposes Bc).

Spher ical Cube Represe nt a ti on of the S truc tures of In d ividualTra it Var iables

T he spherical cube model is based on the assumption that the realstructure of individual traits can be represented as a sphere or three-axiscircumplex (see, for instance, Figure 2.21, top). Any element of this structure i.e. any specific individual trait can be located on the surface of the sphereor three-dimensional circular shape.T he cube is inscribed in the sphere toaccommodate six factorial dimensions that are not proposed to be fully

orthogonal, and to allow the possibility of relating any specific individual traitto one or two or three or four of these six factorial dimensions.In geometric terms, the spherical cube is defined by only three orthogonal

axes (see, for instance, Figure 2.17).T hey are named spatial or underlying


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Introduction xv

dimensions A , B , and C , or A/ a , B/b , and C/ c. T here is one very importantdeduction which follows from the geometry of the spherical cube model.Factor analysis performed to reveal from 5 to 7 rotated factors fails to providethe direct measurements of coordinates of the hundreds of specific traits onthree spatial (underlying) dimensions, A , B , and C . T he models view of factorial dimensions rests on an assumption that the six largest rotated factorsare visually represented by six pairs of the edges (ribs) of the spherical cube,AB/ab, aB/Ab, AC/ac, aC/Ac, BC/bc, and bC/Bc. In other words, since thespherical cube has only three axes, there are no psychometric axes in thismodel which can be directly provided by 5-7-factor solutions. Instead, each of the six largest factorial dimensions (for instance, AB/ab) is jointly determined by combining the poles (high or low) of two spatial (underlying) dimensions

(for instance A/

a and B/b

). Due to the broad variation of the 3rd spatialdimension (for instance, C/ c), each of six factorial dimensions can beinterpreted as actually Big (broad) individual trait. It can be characterized bya broad bandwidth of content mapping along two antipodal edges (ribs) of thespherical cube (for instance, AB and ab).

Since the six factorial dimensions are conceptualized as the edges (ribs) of the cube, one can transform the information on factor loadings of any specifictrait variable in information on position of this variable relative to the edges of the cube. T hus, these edges can be used as a system of coordinates for mapping any specific trait exemplified by one or several closely related traitvariables (see, for instance, Figure 2.21, top). Namely, 6 specific dimensionsmight be related to only one factorial dimension (e.g., AB/ab), 24 specificdimensions might be related to two factorial dimensions (e.g., ABAC/abac), 4specific dimensions might be related to three factorial dimensions (e.g.,

ABC/abc ), and 3 specific dimensions might be related to four factorialdimensions (e.g., A/ a).

Moreover, at is shown in Parts 1 and 2, there exists a direct way to obtainthe coordinates of specific trait variables on the surface of the spherical cube.T he coordinates can be calculated by performing three-dimensional scaling.T he results of multidimensional scaling demonstrate the possibility of representing the whole domain of individual trait variables in terms of three polarized spatial dimensions, A/a , B/b , and C/ c. Comparison of the results of factor and multidimensional scaling analyses indicates that the differences

between them can be conceptualized in terms of the spherical cube model. In particular, the locations of the six largest dimensions yielded by factor analysisroughly coincide with the locations of the edges (ribs) of the cube, while three


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dimensions revealed by three-dimensional scaling correspond to three axes of the sphere and cube (see, for instance, Figure 2.6).

Developme nt and Appl ica ti ons of the Spher ical Cube Model

I introduced the spherical cube model initially as a structuralrepresentation of adaptive ability of the sleep-wake cycle.T he earlier studieson this representation are briefly reviewed in the first chapter of the book among other investigations of individual variation in sleep-wake behavior.T hemodel was applied for prediction of a new scale and new subscales of thesleep-wake pattern questionnaires.T he predicted constructs were developed

and validated in both questionnaire and experimental studies. In thequestionnaire study, the tetra-circumplex criterion was introduced to provide aquantitative approach to testing whether the structure of a questionnairecorresponds to the structure predicted by the model. In the experimental study,subjects were deprived of sleep for one night in order to compare thesubjectively assessed measures (i.e., the traits of sleep-wake behavior, levelsof sleepiness and performance, sleep history, etc.) with the principalcomponents of waking EEG (i.e., those components that provide the objectivemarkers of the parameters of sleep-wake regulation such as sleep debt andsleep pressure).T he results of these studies showed that the model offers acommon theoretical and methodological framework for the development of theunified taxonomy of the individual chronobiological variation associated witha persons chronotype (morning-evening preference), trototype (wakeability)and somnotype (sleepability).

T he same model was also applied to structuring personality traits. Many personality researches share the belief that if factor analysis of the long list of personality attributes reliably yields a set of 6 1 orthogonal factors then thereal dimensionality of the structure of personality lexicon cannot be smaller than 5. At the same time they often report the significant inter-correlationsamong these factors, as well as among the 5 or more scales developed on the basis of these factors.T hese inter-correlations indicate that the dimensionalityof the model of personality structure can be reduced.T he original results presented in the book suggest the possibility of structuring the long lists of

personality-relevant terms with only three orthogonal dimensions.T

he particular way of such reduction of dimensionality was exemplified by thestructure of Russian personality terms. Again, the correspondence between


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Introduction xvii

empirically derived structure and the structure predicted by the model wasconfirmed by applying the tetra-circumplex criterion.

T he spherical cube model was also supported by the comparison betweendimensions revealed by factor and multidimensional scaling analyses. It wasshown that, geometrically, the edges and axes of the spherical cube can berelated, respectively, to the six factorial dimensions yielded by the former analysis and to the three spatial dimensions yielded by the latter analysis.Moreover, three-dimensional scaling provided the possibility to introduce newcircumplex criteria (tri-circumplex criterion and hexa-circumplex criterion) for quantitative comparison of empirically and theoretically derived structures.

In addition, the attempts to develop and implicate the spherical cubemodel in the field of personality psychology led to the following findings.T he

structural representations of personality traits and emotional states wereunified within the same three-dimensional structure proposed by the model. Itwas shown that the model offers the external criteria for detecting convergence between the competing 5-7 factor models of personality structure. Moreover, itwas shown that three axes of the spherical cube structure might represent therotational variants of the well-known three-dimensional classifications, such asthe three Osgood dimensions of meaning (Evaluation, Activity, and Potency)and the three broadest personality factors (i.e., broad Extraversion,Agreeableness, and Conscientiousness, or Dynamism, Affiliation, andStructure). Finally, the spherical cube model was applied to explain the naturalorigin and function of personality structure and to explain the evolutionarymechanisms responsible for the maintenance of individual variation in personality traits.


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Ack nowledgeme nt s

Preparation of this book was facilitated by grant 01-06-85009 / from the

Russian Foundation for the Humanities. Empirical research was partlysupported by grant 06-06-00375 from the Russian Foundation for theHumanities, and by grants 07-06-00263a and 10-06-00114 from the RussianFoundation for Basic Research. I am indebted to Olga Donskaya for her participation in data collection and to Dr. Evgeniy Verevkin for his help indata analysis. I am also very grateful to Dmitriy Putilov who helped me withso many things, including collecting data, data analysis, and drawing somefigures for this book. Finally, I have benefited greatly from the support,encouragement and editorial help of Dr. Frank Salter.


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PART 1. SPHER ICAL C UBE R EPRESENTAT IONOF THE STRUCTURE OF SLEEP -WAKE

ADAPTAB IL ITY T his Part 1 is centered on uncovering the topology of a multi-dimensional

structure of between-individual differences in behavior associated with thealternations of sleep and wakefulness.T he spherical cube model wasemployed to discover the precise nature of the linkages between the individualadaptive traits of the sleep-wake cycle.T he first chapter serves as anintroduction to the second chapter containing the results of questionnaireresearch concerning the structuring of adaptability of sleep-wake habits.T heempirical research presented in the third chapter provides evidence for thevalidity of the scales of multi-dimensional questionnaire predicted by the

spherical cube model.


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Ch apter 1

TAXONOMY OF C HRONOTYPES ,

T ROTOTYPES AND SOMNOTYPES : H ISTORY AND STATE OF THE ART

ABSTRACT

Individual variation in human sleep-wake behavior is mostlystudied by researchers in the field of sleep physiology andchronobiology the scientific study of biological rhythms.T hischapter contains a brief review of the literature in these fields onquestionnaire studies of individual variation in sleep-wake behavior.T

his review also includes the first publications of the author on thedevelopment and application of the spherical cube model.

Q UEST IONNA IRE ASSESSMENT OF M ORN ING -E VEN INGP REFERENCE

Everyone recognizes the differences between individuals in their everydayhabits related to the sleep-wake cycle. Compared to the rather intense interestshown by lay people in their individual sleep-wake pattern, the individualvariation in this pattern is rarely considered to be an important topic of scientific research. Rather, the investigators in such fields as chronobiologyand sleep physiology tend to treat the study of individual traits as an area of applied rather than fundamental research. For example, the assessment of individual differences can be aimed at prediction of tolerance to shift and night


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work. In one of our previous publications (Putilov and Putilov, 2005), wenoted that the scientific literature lacks publications aimed at explaining thestructure of variation in human sleep-wake behavior in terms of achronobiological model. Moreover, nobody yet had tried to use the theoreticalknowledge and empirical facts about individual variation to develop ageneralized model of physiological mechanisms regulating sleep and wakestates.

Any research aimed at ranking and typing people makes no sense withoutspecifying the dimensions of traits on which the individuals differ.T he firstscientifically recognized dimension of individual differences in human dailyrhythms has become the preference for timing of sleep, wake and work.T hetwo extreme chronotypes on this dimension are often nicknamed larks and

owls.One of the tools for assessment of morning-evening preference, the 19-item Questionnaire for Self-Assessment of Morningness-Eveningness, was produced by Horne and stberg in 1976. It has been translated into a dozenlanguages and applied in thousands studies (i.e., Kerkhof et al., 1981; Ishiharaet al., 1984; Adan and Almirall, 1991;T aillard et al., 2004).

T he research indicates that this and other similar scales for distinguishing between morning types and evening types (i.e.,T orsvall and kerstedt, 1980;Smith et al., 1989; Brown, 1993; Bohle et al., 2001) can be associated withindividual circadian phase position and with individual tolerance to shift andnight work (Breithaupt et al., 1978; kerstedt andT orsvall, 1981; Kerkhof,1985; Hrm et al., 1988; Bohle andT illey, 1989; Costa et al., 1989; Moogand Hildebrandt, 1989; Bailey and Heitkemper, 2001; Duffy et al., 2001).

However, the morning-evening questionnaires were criticized for poor or lack of statistical analyses that could provide the basis for their psychometricevaluation (i.e., Smith et al., 1989; Brown, 1993). It is noteworthy that for many years the researchers of chronotypological differences did not askedsuch questions as: (1) is the preference for sleep-wake (rest-work) timing asingle trait; (2) what are other individual traits of sleep-wake patterns; and (3)can researchers measure them with multi-dimensional questionnaires?

Factor analysis is the instrument most frequently used for the delineationof the dimensions on which the individuals differ.T his mathematic techniquecan distill large numbers of separate questionnaire items associated with

specific traits into a smaller number of higher order traits (called factors) thataccount for most of the differences between individuals. For a long period of time factor analysis was not applied to evaluate the instruments developed for assessing morning-evening preference, probably because of the belief that


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T axonomy of Chronotypes,T rototypes and Somnotypes 3

morningness-eveningness is a unitary construct which simply reflects the position of the individual phase of the circadian rhythm.

However, when factor analysis and other conventional psychometricmethods were employed to evaluate earlier published questionnaires, theresults pointed to the need to improve them (Larsen, 1985; Smith et al., 1989;Brown, 1993). For instance, instruments such as the 19-item Questionnaire for Self-Assessment of Morningness-Eveningness (Horne and stberg, 1976) still widely used have been found to be somewhat imperfect as they containquestions with low item-total correlations and several separate dimensions(Moog et al, 1982; Larsen, 1985; Brown, 1993).T he multi-dimensionality of the morningness-eveningness construct was confirmed by many other studies.Even factor analysis of a shortened (7-item) version of the morning-evening

questionnaire, DiurnalT

ype Scale (T

orsvall and kerstedt, 1980), sorted outtwo groups of items. One group was associated with morning questions, andanother group mostly included evening questions. Furthermore, multi-dimensionality was reported for the modified variants of earlier proposedquestionnaires. For instance at least three broad factors were revealed by factor analyzing the 13-item modified version of morningness-eveningness scalecalled the Composite Scale of Morningness (Smith et al., 1989; Caci et al.,2005; Randler, 2009). Furthermore, two broad factors were revealed in thereduced (7-item) version of this scale (Randler, 2009).

M ULT I-D IMENS IONAL APPROACH TO ASSESSMENT OFADAPT IVE ABIL ITY OF THE SLEEP -W AKE C YCLE

T he attempts to introduce a multi-dimensional approach to questionnairestudies of individual variation in adaptive features of circadian rhythms were pioneered by Folkard, Monk and Lobban (1979).T heir research indicated thatmorning-evening preference is not the only individual trait determining thesuccess or failure of biological adaptation to night and shift work.T hree highorder factors were yielded by factor analysis of responses to the 20 items of the Questionnaire for Prediction of Adjustment to Shift Work (Folkard et al.,1979). In addition to the traditional morning-evening factor, Folkard et al(1979) defined two new factors, rigidity-flexibility (of sleeping habits) and

languidness-vigorousness (or inability-ability to overcome drowsiness). Later,the initial questionnaire was developed in CircadianT ype Inventory (Di Miliaet al., 2005).


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I applied a psychometrically based approach to two Russian languagechronobiological questionnaires (Putilov, 1987, 1997a).

One, the 13-item Scale for Assessment of Circadian Lateness, wasdesigned as a uni-dimensional morning-evening scale. It was developedthrough a series of four surveys involving 66, 155, 343 and 442 respondents.T he number of questions and the number of answers were both consequentlyreduced (20p 16p 15p 13 and 10p 7p 6p 5, respectively) after evaluationsof the distribution of responses to each question and inter-relations amongresponses to different questions (see Putilov and Putilov, 2005, for moredetail).

By contrast the second instrument, the Sleep-Wake Pattern AssessmentQuestionnaire (SWPAQ), was originally constructed as a multi-dimensional

inventory (Putilov, 1990, 1993a). It is designed to self-assess the adaptiveability of sleep-wake patterns (sleep-wake adaptability). An initial list of 200 statements with 5 response choices was reduced to 40 statements with 2choices (yes or no) through a series of four surveys involving 117, 221, 306and 356 participants (see Putilov, 1993a, 2000; Putilov and Onishenko, 2005;Putilov and Putilov, 2005, for details of the construction process).T hese 40statements were selected to represent a 5-factor solution yielded by applyingvarimax rotation aimed at obtaining uncorrelated factors of the 5 largest principal components (see also Chapters 4 and 5 of this book for a moredetailed description of the factor-analytic technique).

Evidence that a variety of adaptive abilities are engaged in the sleep-wakecycle was provided by applying cluster- and factor-analytic methods for elaborating the relationship between the items of several chronotypologicalquestionnaires (Putilov, 1990, 1993a; Putilov D. et al., 2007). For example, the40-item version of the SWPAQ (Putilov, 1990) includes 10 groups of 4 closelyrelated items (subscales or tetrads) reflecting the abilities to wake late in theevening, to wake at night, to sleep in the morning, to get up at fixed times, towake early in the morning, to wake at anytime, to fall asleep at anytime, to fallasleep in the evening, to sleep deeply after midnight and to sleep until morning(Putilov, 1990, 1993ab, 1997a, 2003b, 2005).T he factor analysis of theSWPAQ sorted 40 items into the first five factors. Consequently the tetradswere combined to form five scales for assessing more general abilities namedEvening Lateness, Morning Lateness, Anytime Wakeability, Anytime

Sleepability and Nighttime Sleepability (scales E, M, W, F and S,respectively). T he psychometrical evaluation of the 40-item SWPAQ revealedthat some of its 5 scales have substandard levels of reliability (most probablydue to too small numbers of items).T herefore, 12 new items were added to


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improve the reliability of three of the five SWPAQ scales (Putilov, 1993b,2000; Putilov and Onishenko, 2005).T he resulting (52-item) version of theSWPAQ consisted of the same 5 scales. Each of these scales, E, M, W, F andS, included two or three subscales (tetrads) each of which consists of two positively and two negatively keyed statements. Each subscale is meant to beassociated with a specific adaptive ability of the sleep-wake cycle.

Namely, three abilities to wake in the evening rather than in themorning, to wake late in the evening, and to wake at night were recognizedas falling within the broad sleep-wake category of Evening Lateness (scale E).

Four other broader traits were interpreted as follows. Morning Lateness(scale M) includes the inability to get up at fixed times, to wake early in themorning, and to delay sleep on weekends. Anytime Wakeability (scale W)

includes the abilities to shift sleep-wake timing, and to wake at anytime.Anytime Sleepability (scale F) includes the abilities to fall asleep at anytimeand to nap regularly. And Nighttime Sleepability (scale S) includes theabilities to sleep deeply either in the evening or in the middle of the night or inthe morning.

American and Russian students completed the English and Russianversions of a battery of four chronobiological questionnaires (the 19-itemQuestionnaire for Self-Assessment of Morningness-Eveningness, the 13-itemScale for Assessment of Circadian Lateness, the 20-item Questionnaire for Prediction of Adjustment to Shift Work, and the 40-item SWPAQ).T he scoreson 10 scales were subjected to factor analysis.

T he results suggested the possibility of grouping these scales in at leastthree groups (Putilov and Putilov, 2005). More specifically, the three-factor varimax solution yielded three very broad factors: the Lateness factor (E andM scales of the SWPAQ and the single scales of the 19-item Questionnaire for Self-Assessment of Morningness-Eveningness and the 13-item Scale for Assessment of Circadian Lateness), the Wakeability factor (W scale of theSWPAQ and the scale for ability to overcome drowsiness of the Questionnairefor Prediction of Adjustment to Shift Work), and the Sleepability factor (F andS scales of the SWPAQ and the scale for flexibility of sleeping habits of theQuestionnaire for Prediction of Adjustment to Shift Work). Such grouping wasconfirmed in further questionnaire studies (i.e., Putilov and Onishenko, 2005;Putilov A. et al., 2007).


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Arcady A. Putilov6

M ODEL ING SELF -A SSESSED D IFFERENCES IN SLEEP -W AKE P ATTERNS

In order to explain the factorial structure of sleep-wake adaptability athree-dimensional model was propounded (Putilov and Putilov, 2005, 2006;Putilov, 2006, 2007). It postulates that the structure of individual variation insleep-wake adaptive behavior originates from the interaction between onlythree underlying parameters. In terms of this model any subjectively assessedtrait at any level of generality might be located in a three-dimensional spacedetermined by these three parameters. Geometrically, a trait occupies a certainarea on the surface of a sphere (a three-dimensional circumplex) formed bythree orthogonal spatial dimensions representing these three underlying

parameters (Putilov, 2006, 2007).T he difference in generality of sleep-wake traits might simply reflect the

difference in the size of the areas occupied by these traits on the surface of three-dimensional circumplex. If all three dimensions are fixed, this is anarrow (specific) trait. It may correspond to a subscale of a scale (i.e. to asingle tetrad of the SWPAQ). If two of three dimensions are fixed, while the3rd dimension varies, this is a more general (broad) trait. It may be represented by a questionnaire scale (i.e. a scale of the SWPAQ). If only one of threedimensions is fixed, this is one of the three most general traits. It may beassociated with one of three superfactors revealed by a three-factor solution.For instance, the Lateness superfactor includes the items of the scales E,Evening Lateness, and M, Morning Lateness of the SWPAQ.

Figures 1.1, 1.2, 1.6, 1.7, 1.17, 1.21, 1.22 andT able 1.6 illustrate the mainidea behind the model: the possibility of reduction of all subjectively assessedtraits to three hypothetical underlying parameters which are the orthogonalaxes of sphere.T he model might be visualized in the form of a spherical cube,as shown in Figures 1.1, 1.2, 1.19, 1.21, and 1.22, or in the form of a cubeinscribed in a sphere (cube-in-globe), as shown in Figures 1.6, 1.7, 1.13 and1.15. T he inscription of the cube in the sphere is necessary to show thelocations of the largest factors revealed by factor analysis and for locating thenarrow traits of sleep-wake adaptability (Putilov, 2007).T he six largest factors(factorial dimensions) are represented by the six pairs of edges of the cube.T hey are drawn by fixing two spatial (underlying) parameters and allowing the

3rd underlying parameter to vary (T able 1.6).In other words, the model predicts that any of a number of subjectively

assessed traits of different levels of generality might be conceptualized as a


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certain combination of only three underlying dimensions.T he traits can form ahierarchy of sleep-wake adaptability traits by imposing certain limitations onthe range of variation along these dimensions. For instance, threesuperfactors (broadest traits) can be distinguished by limiting variationalong one dimension and allowing variation along the two other dimensions.Six factors (broad traits) can be distinguished by limiting variation along twoof the three dimensions and allowing variation along the third dimension.Finally, a much larger number of subfactors (narrow traits) can be delineated by limiting variation along all three dimensions (Figures 1.1, 1.2, 1.6, 1.7,1.13, 1.15, 1.17-1.22 andT able 1.6).

Possibly each of the three orthogonal dimensions proposed by the modelmight be associated with a separate parameter of chronophysiological

regulation of the sleep-wake cycle. For example, the first two parameters can be related to two processes proposed as two major components (circadian andhomeostatic) in the two-process models of regulation of the sleep-wake cycle(Borbly, 1982; Daan et al., 1984; Putilov, 1995a). As for the third parameter,it can represent the circadian clock arousal process suggested by Edgar et al. in1993 or it can be viewed as a more general arousal dimension that wasrecognized by a number of models explaining the phychophysiological basisof personality and emotion (see, i.e., Panksepp, 1982; Eysenck and Eysenck,1985; Ellis, 1987, and Chapter 4).

Because factor analysis says nothing about the fundamental processesunderlying the proposed three-dimensional structure, the validation of thechronophysiological background requires experimental research. Suchresearch can be aimed at testing correlations between subjectively assessedtraits and objectively measured chronophysiological signatures of the sleep-wake regulatory mechanisms.

T EST ING P RED ICT IONS C ONCERN ING THE NUMBER ANDSIZ E OF F ACTOR IAL D IMENS IONS

In our first publications (Putilov and Putilov, 2005, 2006; Putilov, 2006,2007), we recognized that some predictive features of the three-dimensionalmodel might be tested without elaborating its chronophysiological

background. T hese fully testable and falsifiable predictions includesuggestions about the exact numbers of adaptabilities of different levels of generality that can be examined by factoring chronobiological questionnaires


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Arcady A. Putilov8

(Putilov and Putilov, 2005). In 2005, Putilov and Putilov compared thenumbers of abilities predicted by the model and assessed by thequestionnaires. It was noted that, although the results of factor analysis of thechronotypological questionnaires provided an empirical basis for the model,there exists a certain disagreement between the factorial structure proposed bythe model and the factorial structure of the 52-item SWPAQ.T he geometry of the model predicts six factorial dimensions of similar size while theempirically developed 52-item SWPAQ includes five rather than six scales,and these scales were dissimilar on the number of 4-item subscales (two for the scales W and F and three for the scales E, M, and S).

Consequently, a questionnaire study was undertaken to test these particular predictions of the model concerning the number and features of

factorial dimensions of the SWPAQ (Putilov and Putilov, 2006; Putilov, 2006,2007). T he relationships between the five scales helped to specify the featuresof the sleep-wake cycles adaptive abilities that were predicted but not yetassessed by means of the SWPAQ. One new scale and two new subscales wereconstructed through a series of three questionnaire surveys (Putilov andPutilov, 2006). T he SWPAQ was enlarged to 72-items by adding a secondwakeability scale (Daytime Wakeability, V) and third subscales for the W andF scales (Putilov, 2007).T he items of the SWPAQ are listed in Appendix 1and their English translations are given in Figure 1.20.

In addition to earlier studies aimed at validating the first five scales of theSWPAQ (Cherepanova and Putilov, 1993; Melnikov et al., 1999; Putilov,2000; Putilov et al., 2002; Danilenko et al., 2004), a special experimentalstudy was undertaken. Its goal was to demonstrate that the new wakeabilityscale (V) shows the expected pattern of association with the objectiveelectrophysiological indices of wakefulness level under the condition of sleeprestriction (Putilov D. et al., 2007; Verevkin et al., 2008; Putilov A. et al.,2009ab, 2010).

In general, the questionnaire and experimental studies (Putilov andPutilov, 2005, 2006; Putilov, 2007; Putilov D. et al., 2007; Putilov A. et al.,2009ab; Verevkin et al., 2008) demonstrated that the modeling approach to thestudy of individual variation in sleep-wake habits might be employed todevelop chronobiological instruments for conducting fundamental and appliedresearch. T he findings of these studies provided support for the assumption

that subjectively assessed features of the sleep-wake cycle reflect underlyinginter-individual differences in parameters of chronophysiological regulationmechanisms and can be used for evaluating biological risks of night and shiftwork (Putilov et al., 2009ab, 2010).


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In its recent (72-item) form, the SWPAQ alone or as part of a battery of chronobiological questionnaires can be applied to quantify individualdifferences in such most broad sleep-wake adaptability traits as Lateness (i.e.morning-evening preference), Wakeability (i.e. tolerance to sleep pressure),and Sleepability (i.e. propensity to fall asleep and to sleep deeply). Followingthe terminological distinction suggested by Lavie and Zwuluni (1992) andfurther developed by Van Dongen et al. (2005), any individual can beclassified as representing, at least, three different types of variation in sleep-wake behavior. Chronotype can be determined by Lateness score (i.e. the sumof E and M scores of the SWPAQ) which reflects later or earlier timing of wakefulness and sleep.T rototype can be self-assessed with wakeability score(the sum of W and V scores) which provides information about greater or

smaller vulnerability to sleep loss. Somnotype can be self-assessed withsleepability score (sum of F and S scores) reflecting higher or lower sleep propensity (Putilov et al., 2009ab, 2010).

C IRCUMPLEX C R ITER ION BASED ON THE SPHER ICALC UBE M ODEL

Paradoxically, the results of factor analysis of chronobiologicalquestionnaires served as an empirical basis for developing the model, but themodel disagrees with the factor-analytic assumption that six varimax-rotatedfactors might represent six fully orthogonal dimensions. Instead, three-dimensionality rather than six-dimensionality of the structure of sleep-wakeadaptability is one of the most important predictions of the model.

T o evaluate the theoretical model empirically its constructs must betranslated into geometrically based measurement procedures.T he question of whether the structure of sleep-wake adaptability fits the three-dimensionalmodel was addressed with the tetra-circumplex criterion (Putilov, 2007).T hiscriterion allows us to empirically test whether actual structure (i.e. a structureof chronobiological questionnaires) exhibits such predicted geometricalfeatures as circumplexity and three-dimensionality.

Geometrically, the proposed theoretical structure, a sphere, is a three-dimensional circumplex. An infinite number of two-dimensional circumplex-

like shapes might be obtained by slicing this sphere into two approximatelyequal halves. However, when the cube is inscribed in this sphere, it can beused as a system of coordinates for cutting the sphere such that it produces a


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Arcady A. Putilov10

small number two-dimensional circumplex-like shapes that optimallyrepresent its circumplexical features (Putilov, 2007).T he sets of two-dimensional representations of the three-dimensional circumplex permitavoidance of difficulties in displaying and evaluating an empirical structure inthree-dimensional space.

Indeed, as can be seen in Figure 1.7, there exist only four two-dimensionalcircumplex-like shapes each of which connects in a circle the centers of sixcubes edges.T he vast majority of the narrow traits distributed on the surfaceof the sphere can be arranged in these four circumplexes (Figures 1.8-1.12) inorder to provide the possibility of empirically examining the relations betweenthe traits included in each of four circumplexes. It is assumed (Putilov, 2007)that these relations reveal the principle of circumplex structure.T his

circumplex principle was proposed by Guttman (1954) and introduced for thefirst time in the area of interpersonal research by Leary (1957). It contends thattrait variables are arranged around a circle in two-dimensional space. As aconsequence, it is expected that the correlations between trait variablesgradually change in accordance with gradual changes in the traits meaning.For instance, the adjacent trait variables must demonstrate the highest positivecorrelation and the highest extent of similarity of their meaning, while thetraits opposing one another in the circle must demonstrate the lowest(negative) correlation and antipodal meanings (for more details aboutcircumplexes see Chapters 2, 4 and 5).

T hus, the tetra-circumplex criterion (Putilov, 2007) assumes that a set of four almost two-dimensional representations can be used to examine the extentof similarity between the actual and theorized structures of sleep-wakeadaptability. T he criterion was developed and applied (Putilov, 2007) for determination of the extent of deviation of the SWPAQ structure from thestructure of sleep-wake adaptability predicted by the model (Putilov andPutilov, 2005, 2006; Putilov, 2006).

T he results of the analysis of inter-correlations among 18 subscales(tetrads) of the 72-item SWPAQ indicated that these subscales might beconfigured into four two-dimensional circumplex-like shapes. It wasconcluded (Putilov, 2007) that, at least at the level of scales, the questionnaireexhibits a clear three-dimensional circumplex structure in accordance withtheoretical expectations, and that this finding provides empirical evidence of

similarity between the actual and theorized structures of sleep-wakeadaptability (Putilov, 2007). However, although the empirical testing mostlyyielded promising findings, it also showed some measurable difference between the SWPAQ structure and the theoretically predicted structure of


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sleep-wake adaptability. It was suggested that applying the tetra-circumplexcriterion may accelerate the process of developing more accurate instrumentsfor assessing the broad and narrow traits of sleep-wake adaptability (Putilov,2007).

In sum, the proposed taxonomic model of individual differences inadaptive abilities of the sleep-wake cycle (Putilov and Putilov, 2005, 2006;Putilov, 2006, 2007) postulates that the structure of sleep-wake adaptabilitycan be visually represented by a sphere (three-dimensional circumplex)formed by three orthogonal axes.T he model predicts that: (1) any ability can be located on the surface of this three-dimensional sphere; and that (2) the six pairs of edges of the cube inscribed in this sphere represent six broad abilitiescorresponding to the six largest factors (factorial dimensions) yielded by factor

analysis of a set of chronobiological questionnaires.T

he tetra-circumplexcriterion was introduced to examine the correspondence between the structure predicted by the model and an empirically derived structure of a multi-dimensional chronobiological questionnaire.

L IM ITAT IONS OF F ACTOR ANALYS IS AS A T OOL FOR UNCOVER ING O RTHOGONAL D IMENS IONS

Different statistical approaches can be employed to group the studied phenomena, such as the numerous individual traits of the sleep-wake cycle.Factor analysis is most widely used statistical method for this purpose.T hismethod divides up the total amount of variation into a small number of dimensions called factors. Such division might help to evaluate the relativeimportance of each particular individual trait represented by a separate factor.For instance, the analysis determines which factors account for more variancethan others. Such differences are often interpreted as indicating that the factorsdiffer in the extent of their generality (i.e. in the number of differentquestionnaire items or questionnaire subscales in which the factor accounts for some variance).

T he application of factor analysis in questionnaire studies began withattempts to determine the structure of personality traits descriptors. In therecent literature, the empirically derived 5-7 factor models, such as the Big

Five model, have become the most popular representations of personalitystructure (see Chapter 4 for detail).


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Arcady A. Putilov12

However, the theoretical basis for such factorial structures has not been provided. One of the main methodological problems is rooted in the long termtradition of using factor analysis as a tool for inductive discovery of thedimensions of personality structure. An empirically supported criticism pointsto inherent limitations of this method. For instance, when a linear factor analysis is used with dichotomous (nonlinear) data, there is a tendency tooverestimate dimensionality (e.g. van Schuur and Kiers, 1994).T heoverestimation of dimensionality of personality structure is evident from theobservation that, although the factors are forced into orthogonality by meansof a varimax rotation, significant inter-correlations are always found amongquestionnaire scales constructed for measurement of the individual differenceson these factors (see Block, 1995). Notably, Maraun (1997) empirically

demonstrated that the Five Factor model might simply be a methodologicalartifact of imposed constraints of factor analysis. By changing the method of analysis to better suit personality data (i.e., when multidimensional scaling isapplied), the five factors can be reduced to just two dimensions (Maraun,1997). It seems that multidimensional scaling may produce analyses that areclearer and more parsimonious than those of factor analytic solutions(MacCallum, 1974; Davison, 1985; Fitzgerald and Hubert, 1987). Particularly,it is superior compared to factor-analytic method in the analysis of correlationmatrices that have circumplex structure (Kluger andT ikochinsky, 2001).

In fact, the above mentioned weaknesses of factor analysis as a tool for uncovering orthogonal dimensions of circumplex structure were addressed bythe invention of the spherical cube model.T he model limits the concept of sleep-wake adaptability to three dimensions in despite of factor-analyticresults yielding six factorial dimensions. It holds that as few as threeorthogonal dimensions are required to explain the six factorial dimensions of sleep-wake adaptability.T herefore, the question arises whether the applicationof other methods of data reduction, such as multidimensional scaling, can leadto the isolation of only three fully orthogonal dimensions.

SUMMARY OF P REV IOUS R ESULTS OF THE STRUCTURALM ODEL OF SLEEP -W AKE ADAPTAB IL ITY

Summing up, the proposed formal geometric model (Putilov and Putilov,2005, 2006; Putilov, 2006, 2007) describes a three dimensional structure in theshape of a cube inscribed in a sphere, with three underlying parameters as


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vertical, width, and depth dimensions (supposedly they are associated with thethree independent parameters of chronophysiological regulation of the sleep-wake cycle).T he surface of the sphere formed by these dimensions representsall observed variability of subjectively assessed adaptive traits of the sleep-wake cycle. T he cube is inscribed in the globe to visualize the way by whichthese subjectively assessed traits of sleep-wake adaptability are related to theunderlying parameters. Namely, it is postulated that the six pairs of edges of the cube correspond to the six largest factors revealed by factor analysis of multi-dimensional chronobilogical questionnaires, such as the 72-itemSWPAQ.

T he predictions of the model concern both the structure of questionnairesfor assessment of subjectively recognized traits of sleep-wake behavior and the

nature of objective chronophysiological variables behind these traits.T

hetetra-circumplex criterion was introduced (Putilov, 2007) to provide empiricalevidence based on the results of comparing the questionnaire structure with thetheoretically predicted structure. Empirical support for the model was provided by both questionnaire (Putilov, Putilov, 2006; Putilov, 2007) and experimentalstudies (Putilov D. et al., 2007, Putilov A. et al., 2009ab, 2010; Verevkin et al.,2008). T he preliminary results (Putilov, 2007) indicate that the formalgeometrical model reflects the natural structure of sleep-wake adaptability andthat the questionnaire structure meets such predictions of the model as three-dimensionality and circumplexity of sleep-wake adaptability.T he results of the application of the tetra-circumplex criterion can be useful for further improving the instruments used for assessment of individual habitual traits of the sleep-wake cycle.

It remains, however, to be clarified: (1) why the six factorial dimensionssuggested by this model are not fully orthogonal; and (2) why, unlike these sixfactorial dimensions, the three underlying dimensions of the structure of sleep-wake adaptability (its three axes) are not revealed by factor analysis of questionnaire data.

SOME GENERAL CONCLUS IONS

y Individual variation in adaptive features of the human sleep-wake

cycle has been studied in the field of chronobiology and sleep physiology for several decades.


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y T he psychometrical evaluation of chronobiological questionnairesrevealed the multi-dimensional nature of individual adaptive ability of the sleep-wake cycle.

y Such a finding suggests the necessity of clarifying both the exactstructure of this ability and the chronophysiological background of subjectively assessed variability in the adaptive features of the sleep-wake cycle.

y T he results of factor analysis of a battery of chronobiologicalquestionnaires served as an empirical basis for developing the three-dimensional (spherical cube) model that explain the multi-dimensional nature of variation in human sleep-wake behavior.

y T he model postulates the possibility of reducing all varieties of

individual habitual traits of the sleep-wake cycle to three underlyingsources of variance.y T he model also provides a valuable taxonomy of adaptive abilities of

the sleep-wake cycle.y It clarifies the relationship between actual (spatial) and artificial

(factorial) dimensions of the structure of inter-individual variation insleep-wake adaptability.

y T he six factorial dimensions appear to originate from pairwisecombinations of polarized spatial dimensions.

y T he model offers the testable assumptions concerning the structure of trait variables designed to represent individual variation in the sleep-

wake pattern.y For instance, it predicts the three-dimensional circumplexity of thisstructure and the possibility of distinguishing six factorial dimensionsof sleep-wake adaptability.

y When the model was developed, its predictions were used to provideempirical evidence that the model yields the natural structure of sleep-wake adaptability and to further enlarge multi-dimensionalinstruments for assessing sleep-wake patterns (i.e. such as theSWPAQ).

y By using the SWPAQ, individuals can be differentiated on the threemost broad individual traits of sleep-wake adaptability, Lateness (i.e.morning-evening preference or chronotype), Wakeability (i.e.tolerance to sleep pressure or trototype), and Sleepability (i.e. sleep propensity or somnotype).


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y T he geometry of the spherical cube model suggests the possibility of applying the tetra-circumplex criterion to examine the correspondence between theoretically and empirically derived structures, such as thefactorial structure of the SWPAQ, and the possibility of applying atheoretically based approach to further improve the structures of chonobiological questionnaires.

y T he preliminary results from application of the tetra-circumplexcriterion for testing the SWPAQ structure indicate that, incorroboration of the spherical cube model, the SWPAQ comprisesfour two-dimensional circumplex-like shapes.

y It was concluded that future revisions of the SWPAQ may primarilyfocus on improving its structural characteristics by examining and

correcting the precise location of some of items, subscales (tetrads)and scales with respect to their structural fit to the four two-dimensional circumplexes.

y T he model postulates the three-dimensionality of the structure of sleep-wake adaptability and, hence, disagrees with an assumption thatthe six largest varimax-rotated factors can represent six fullyorthogonal dimensions of sleep-wake adaptability.

y T he question arises whether the application of other than factor analysis methods of data reduction, such as multidimensional scaling,can lead to the isolation of only three fully orthogonal dimensions of the SWPAQ structure.


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Ch apter 2

T HREE -D IMENS IONAL ITY OF THE

STRUCTURE OF SLEEP -WAKEADAPTAB IL ITY

ABSTRACT

T his chapter includes some new results obtained by applying thespherical cube model to further explore the structure of adaptiveability of the sleep-wake cycle.T he model postulates that the six broad traits of sleep-wake adaptability revealed as the six largestfactors can be visualized as the six pairs of edges of a cube inscribed

in a sphere formed by three orthogonal dimensions (a three-axiscircumplex), and that any adaptive trait of the sleep-wake cycle can bemapped at the surface of this sphere.T his research seeks: (1) toidentify the three dimensions underlying the structure of sleep-wakeadaptability; and (2) to suggest ways of further improving tools for assessing this ability. T he responses to 72 items of the SWPAQ provided by 1068 adults and adolescents were subjected to both factor and multidimensional scaling analyses. In general, the results provided empirical support for the applicability of the model tostructuring sleep-wake adaptations. Specifically, multidimensionalscaling helped: (1) to identify three orthogonal axes of the sphericalcube representation of the structure of sleep-wake adaptability; and(2) to locate narrow adaptive traits of this ability on the surface of the

spherical cube.T he three-dimensional coordinates of items, subscalesand scales of the SWPAQ were mapped on the surface of thespherical cube, and directions for further developing the questionnairewere determined.


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Arcady A. Putilov18

M ETHOD

Theore ti cal Framework

T he three-dimensional (spherical cube) model was introduced in a searchfor the natural structure of sleep-wake adaptability (Putilov and Putilov, 2005).It depicts all subjectively assessed behavior traits in spherical form andvisualizes the six broad traits of sleep-wake adaptability as the six pairs of edges of the cube inscribed in this sphere (cube-in-globe).

T he originality of the model is rooted in distinguishing two kinds of

dimensionality, spatial and factorial (Putilov and Putilov, 2006; Putilov, 2006,2007). T he model implies that variation exists along only three underlying parameters (spatial dimensions) which determine the three-dimensional spacefor all variability of adaptive traits of the sleep-wake cycle. By combiningthese three orthogonal dimensions, a larger number of the subjectivelyrecognized dimensions of sleep-wake adaptability might be generated. In particular, to generate any of the six broad traits revealed by factor analysis of chronobiological questionnaires as one of the six largest factors (factorialdimensions), two underlying parameters must be set to minimal or maximalvalue, while the third parameter might be left to vary between minimal andmaximal values (T able 1.6). Geometrically, this varying parameter draws a pair of edges of a cube on a surface of a sphere to represent one of the six broad abilities of the sleep-wake cycle (Figures 1.1 and 1.17). Further, byfixing this parameter, any broad trait might be divided into narrower traits(Figures 1.1, 1.6, 1.21 and 1.22). One of them might be named a core (or pure)trait, since its two poles are located around the centers of the edges. Other might be called borderline (or mixed or blended) traits because their poleslocations are shifted relative to a center of edge. For instance, the traits shiftedalong the edges toward the vertices of the cube might be considered to beadmixtures of three adjacent broad abilities (Figures 1.1 and 1.6).

Prel im in ar y Resul ts of Compar in g Theore ti cal a nd Emp ir ical

Struc tures of the SWPAQ

In the earlier studies (Putilov and Putilov, 2005), the results of factor analysis of the battery of chronotypological questionnaires were used as the


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T hree-Dimensionality of the Structure of Sleep-Wake Adaptability 19

empirical facts supporting the model of individual variability of the adaptive behaviors related to the alternations of the sleep and wake states. It was foundthat assessing the maximal number of broad and narrow traits predicted by themodel can be done with one of the questionnaires included in this battery, theSWPAQ (Putilov, 1990, 2000; Putilov and Onischenko, 2005).T he model wasthen successfully applied for prediction of the properties of the omitted broadand narrow traits. In order to assess these traits one new scale and two newsubscales (tetrads) were constructed (Putilov and Putilov, 2006).T wenty newquestionnaire items relevant to these predicted abilities were proposed andcorrected through a series of three questionnaire surveys.

T he new version of the SWPAQ comprises 72 true-false items.T hey aregrouped into 6 scales for measuring 6 broad traits of the sleep-wake cycle.

Each of these scales is composed of 3 subscales (tetrads) representing narrowtraits (Putilov, 2007).Factor analysis of the 72-item SWPAQ revealed the six-factor structure of

sleep-wake adaptability.T he six-dimensional space is impossible to visualizeand represent pictorially. However, the model predicts that, despite theapplication of varimax rotation, the six largest factorial dimensions are notfully orthogonal dimensions. Rather, these six factorial dimensions mightrepresent a three-dimensional reality (Putilov and Putilov, 2006; Putilov, 2006,2007). T he model hypothesizes a three-dimensional structure with only three(vertical, width, and depth) axes. Geometrically, this structure can bevisualized as a spherical cube (Figures 1.2, 1.17, 1.21 and 1.22) or as acombination of two simple forms, a cube included in a sphere (metaphoricallynamed cube-in-globe in earlier publications; Figure 1.6).T he six pairs of edges on the surface of this spherical cube (Figure 1.2, 1.17, 1.21 and 1.22) arethe locations of the six broad adaptive traits of the sleep-wake cycle. Factor analysis of the responses to the items of the chronobiological questionnairescan permit the isolation of these six traits as the six largest rotated factors.T hereafter, these edges of the cube can serve as a system of coordinates for mapping the more numerous narrow adaptive traits (i.e., core subtraits of broad traits and the mixtures of 2-3 broad traits).

It was suggested that the geometric assumptions underlying the model permit the possibility of applying a test, the tetra-circumplex criterion, for justifying the correspondence between the empirical and theoretical structures

of sleep-wake adaptability.T

he criterion (Putilov, 2007) was used to comparethe model predictions with the results of organization of the SWPAQ tetrads infour circumplex-like shapes.T hese four empirically constructed circumplex-like structures showed the desirable circumplex properties (Putilov, 2007).


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Arcady A. Putilov20

In particular, it was demonstrated (Putilov, 2007) that, in accordance withthe circumplex expectations, the subscales (tetrads) forming four circlesshowed rather gradual changes of their meaning. Moreover, the results mostlyconfirmed the numerical supposition of gradual reduction of correlationcoefficients with increase of the inter-subscale distance.

Figure 1.1. Spherical cube visualization of the structure of sleep-wake adaptability.T he three-dimensional spherical cube model was applied for explanation of thevariability of sleep-wake traits. If one assumes that the individual variation in onlythree underlying parameters is responsible for the appearance of any subjectivelyassessed trait of sleep-wake adaptability, as few as three spatial (underlying)dimensions might be sufficient for graphing structural representation of thisadaptability. T hese three spatial dimensions (three axes) of the adaptability structurewere determined by means of three-dimensional scaling (seeT able 1.2).T hey werealphabetically labeled A , B , and C . T he vertical dimension can be interpreted as

Arousing or Wakeability (i.e., easy/hard, A/ a ), the width dimension can be interpretedas Bedtiming or Sleepability (i.e., easy/hard, B/b ), and the depth dimension can beinterpreted asC lock delaying or Lateness (i.e., easy/hard,C/ c). T he spherical cubemodel postulates that the three- and six-factor solutions yielded by factor analysis(T able 1.1) can be visualized on the surface of the three-dimensional spherical cube.T he six pairs of cubes edges correspond to the approximate locations of six factorialdimensions (T able 1.1). Such geometrical interpretation assumes that these dimensionsmight be regarded as the pairwise combinations of the extremes of the three spatial(underlying) dimensions (T able 1.6). T hese six factorial dimensions constitute the six broad traits of the sleep-wake adaptability assessed with six scales of the Sleep-WakePattern Assessment Questionnaire (SWPAQ), E, M, W, V, F, and S, or EveningLateness, BC/bc, Morning Lateness, aC/Ac, Anytime Wakeability, AB/ab, DaytimeWakeability, AC/ac, Anytime Sleepability, aB/Ab, and Nighttime Sleepability, Bc/bC(T able 1.4). Left: the three superscales and six scales of the SWPAQ labeled near along the vertices and edges of the cube, correspondingly. Right: 13 of 18 subscales(tetrads) that are linked to six pairs of edges of the cube, three pairs of faces of thecube, and four pairs of vertices of the cube.


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T he tetra-circumplex criterion permits estimation of the extent of inconsistency between theoretical and empirical structures of sleep-wakeadaptability. Although the results on four circumplexes indicated that, ingeneral, the 72-item SWPAQ structure meets the assumption of circumplexityand three-dimensionality, they also revealed that the location of some of theSWPAQ subscales is not optimal.T herefore, the conclusion was drawn(Putilov, 2007) that some details of the SWPAQ structure might desire further correction, if one wants to increase the level of fit of this structure to the idealthree-dimensional circular structure.

Figure 1.2. Spherical cube structure of sleep-wake adaptability: opaque and transparentversions. T he two-dimensional representation of the SWPAQ (bottom) can be regardedas a transparent version of the three-dimensional spherical cube structure (top). Leftand right top shapes are, correspondingly, front and rear views of the three-dimensional spherical cube representation of the six-scale SWPAQ structure, left bottom shape presents a transparent version of the top representation, and right bottomshape presents a transparent version of the three-dimensional representation of thirteensubscales of the SWPAQ shown in Figure 1.1 (bottom).T wo spatial dimensions( Arousing or Wakeability, A , and Bedtiming or Sleepability, B ) are identical in two-

and three-dimensional versions, while the third spatial dimensionC

(C lock delaying or Lateness) is absent in the two-dimensional version.T his interpretation of two-dimensional representation of the adaptability structure was confirmed by empiricalresults illustrated inT able 1.2 and Figures 1.3-1.5.


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Arcady A. Putilov22

Despite the promising results of previous research on structuring sleep-wake adaptability in the framework of the model, a detailed analysis of theSWPAQ structure is still required with a new data set. It is expected that suchanalysis will, again, generally confirm the correspondence between thetheoretical and empirical structures. However, it is also expected to berevealed that the SWPAQ is not an optimal representation of the structure predicted by the spherical cube model, because some area of this structuremight be overrepresented, while other might be underrepresented by theSWPAQs subscales.

Emp ir ical Da ta

T he SWPAQ was designed to assess the individual traits of the sleep-wake cycle (Putilov, 2000, 2007). Each of 72 true-false items is a shortstatement describing sleep-wake habitual behavior. Appendix 1 provides theRussian version of the two-sided single-page questionnaire.T he Englishtranslations of the 72 statements are shown in Figure 1.20.T he SWPAQcomprises six scales (E, M, W, V, F and S) that were empirically derived bymeans of factor analysis.T he six scales of the SWPAQ represent six broadtraits of sleep-wake adaptability. Each is assessed by the equal number of positively and negatively keyed items.T he scales are labeled EveningLateness (E), Morning Lateness (M), Anytime Wakeability (W), DaytimeWakeability, (V), Anytime Sleepability (F), and Nighttime Sleepability (S).Any one scale includes three subscales or tetrads (four closely related items)that are meant to represent 18 narrow traits.

Earlier studies (Putilov and Putilov, 2005, 2006; Putilov, 2006, 2007)demonstrated that six varimax rotated factors derived by factor analysis of chronobiological questionnaires roughly correspond to the six scales (E, M,W, V, F and S), and that three varimax rotated factors (superfactors) roughlycorrespond to three couples of scales (superscales EM, WV, and FS).T hesethree most general traits were named Lateness (Morning-Evening Preference),Wakeability (Languidness-Vigorousness), and Sleepability (Flexibility-Rigidity of Sleep Habits). Following the terminological distinction suggested by Lavie and Zwuluni (1992) and further developed by Van Dongen et al.

(2004), the EM score can be interpreted to indicate subjects chronotype (later or earlier timing of wakefulness and sleep), WV score can represents thesubjects trototype (smaller or greater vulnerability to sleep loss), and FS scorecan represent the subjects somnotype (higher or lower sleep propensity).


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Figure 1.3.T wo-dimensional scaling plots of the 72 items of the SWPAQ.T wo-dimensional scaling of Z-scored responses to 72 statements of the SWPAQ (see alsoT able 1.2). T op: combined sample (all data sources, n=1068); bottom: only newsample (n=718). Spatial dimension A corresponds to West-East direction in top plot,and to the South-North direction in bottom plot. Spatial dimension B corresponds toNorth-South direction in top plot, and to the East-West direction in bottom plot.Abbreviated labels of items: first letter signifies scale (i.e., e belongs to the scale E,Evening Lateness), second letter signifies positive (p) or negative scoring (n) of anitem.


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Arcady A. Putilov24

Figure 1.4.T wo-dimensional scaling plots of the 18 subscales of the SWPAQ.T wo-dimensional scaling of Z-scored sums of responses to two items of the same pole of asubscale (tetrad).T op: combined sample (all data sources, n=1068); bottom: only newsample (n=718). Spatial dimension A corresponds to the West-East direction, andspatial dimension B corresponds to the South-North direction. Abbreviated labels of

the halves of subscales (sums of responses to two items): first letter signifies scale (i.e.,e belongs to scale E, Evening Lateness), number signifies subscale of a given scale(i.e., e3 is evening-morning preference subscale of the scale E), and second letter signifies positive (p) or negative scoring (n) of two items of the half of subscale.


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Figure 1.5.T wo-dimensional scaling plots of the 6 scales of the SWPAQ.T wo-dimensional scaling of Z-scored sums of responses to six items (a half of a scalecharacterizing one of its two poles).T op: combined sample (all data sources, n=1068); bottom: only new sample (n=718). Spatial dimension A corresponds to the West-East direction, and spatial dimension B corresponds to the South-North direction.Abbreviated labels for the halves of scales (sums of responses to six items): first letter signifies positive (p) or negative scoring (n) of items, second letter signifies scale (i.e.,E is the Evening Lateness scale).


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Arcady A. Putilov26

T wo questionnaire surveys were employed in the present study. In bothsurveys, the subjects completed the 72-item SWPAQ by indicating their agreement or disagreement with each statement (either Yes or No).T herespondents of the first survey completed the final version of SWPAQ(Putilov, 2007). An earlier survey was conducted (Putilov, 2007) with theversion which only slightly differs from the final version (20 of 72 items weresubjected to minor corrections, and the order of items was changed).T he newsample consisted of 358 female and 360 male respondents with mean age of 24.6 (SD=10.8) and 22.7 (SD=7.0), respectively. An older sample included212 female respondents with mean age of 24.9 (SD=14.5), and 138 malerespondents with mean age of 23.7 (SD=13.0). In the majority of T ables (1.1-1.5, 1.7-1.10 and 1.14), the results are presented for the combined sample and

separately for the new sample.

Perform in g Fac tor A nal ysis

Factor analysis was employed to the data set as a tool for identifying thefactorial dimensions of sleep-wake adaptability. Because the model makesdirect predictions about the numbers of spatial and factorial dimensions (threeand six, respectively), a set of responses to 72 items was subjected to principalcomponent analysis with three and six factors respectively rotated to thevarimax criterion.

Rotated factor solutions were examined and interpreted by inspecting thehigh-loading questionnaire items. In particular, such inspection was aimed atexamining: (1) the correspondence of the six rotated factors to the six scales of the SWPAQ; and (2) the correspondence between the three rotated factors tothe three superscales of the SWPAQ.

T able 1.1 summarizes the results of factor analysis of the new data set andthe combined data set consisting of both new and older samples (n=718 andn=1068, respectively).

Perform in g Mul ti d ime nsional Scal in g

The aim of applying the multidimensional scaling analysis was to test thedimensionality and circumplexity of the SWPAQ structure. Such scaling

provides coordinates of each item or each pole of a subscale or each pole of scale in n-dimensional space.T wo- and three-dimensional spaces were of


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major interest because they provide the structures that can be visualized.T hesolutions with two, three and four dimensions were obtained and compared onstress and fit measures.T he results are reported inT able 1.2.

Each of three coordinates of each item provided by three-dimensionalscaling was compared with the standard deviation (SD) calculated for all itemsto determine whether it could be considered as characterizing the pole of adimension predicted by the spherical cube model (i.e., these might be the itemswith, at least, one coordinate either higher than +1SD or lower than -1SD).

Figure 1.6. Cube-in-globe representation of scales and subscales of the SWPAQ.Cube is inscribed in sphere (globe) to depict the six broad traits of sleep-wakeadaptability. T he six pairs of cubes edges correspond to the six broad traitsconceptualized as pairwise combinations of the extremes of the three spatial(underlying) dimensions A , B , and C (T able 1.6).T hey are labeled along the edgessimilarly to the corresponding SWPAQ scales (E, M, W, V, F, and S, or EveningLateness, Morning Lateness, Anytime Wakeability, Daytime Wakeability, AnytimeSleepability, and Nighttime Sleepability). Each scale includes three subscales (tetradse1-3, m1-3, w1-3, v1-3, f1-3, and s1-3). Some of them correspond to core (pure)narrow traits located near the centers of the edges (e2, m2, w2, v2, f2, and s2). Some of other subscales correspond to mixed (blended or intermittent) narrow traits locatednear the vertexes (corners), the meeting points of three edges (i.e., e1, m1, v1, and f1).T he remaining subscales (shown in Figure 1.1, bottom) may correspond to narrowtraits located near the centers of faces (i.e., e3, v3, and s3).T op globe also illustratesthe locations of hypothetical narrow traits that are predicted but not assessed with the18 SWPAQs subscales (i.e., e?, m?, w?, v?, f?, and s?). Bottom globe shows onlythose 10 SWPAQs subscales that were included in four two-dimensional circumplexesshown in Figures 1.8-1.11.


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Arcady A. Putilov28

Figure 1.7.T

etra-circumplexical slicing of cube-in-globe representation of theSWPAQ. Cube in globe shape (Figure 1.6, top) was reproduced four times toillustrate the way by which four almost two-dimensional slices (circumplexes) wereobtained by connecting the centers of three factorial dimensions in the two-dimensional circles (see also Figure 1.12). Each of these four quasi-circumferencesruns through the areas of three SWPAQ scales. Because each scale of the SWPAQsubsumes three subscales (tetrads), the sequence of, at least, 6 of these 9 subscales can be ordered without long gaps. In general, such ordering suggests possibility of inclusion of, at least, 10 SWPAQs tetrads (shown in Figure 1.6, bottom) into four circumplexes (shown in Figures 1.8-1.11). It is predicted that the subscales included ineach circumplex must gradually change their meaning (Figures 1.8-1.11), and that theassociation between them must decline gradually with the increase of inter-subscaleinterval, up to turning into the negative association when the inter-subscale distanceexceeds of circumference. It is expected that random errors in selection of items for

the questionnaire are likely to average out when mean correlations are calculated for equidistant subscales (tetrads), and that, hence, a simple chain of correlations canrepresent the pattern of decline of association among the subscales included in each of four circumplexes (T able 1.7).


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Compar ison of Int er-Correla ti ons Amo ng a nd Be twee n Spa ti aland Fac tor ial D ime n sion s

T o show that, despite applying the procedure of varimax rotation, thefactorial dimensions are still inter-correlated, the matrix of inter-correlationsamong factor loadings was calculated (T ables 1.3 and 1.4).T he matrix of inter-correlations among three factors was compared with the matrix of inter-correlations among the three coordinates obtained by multidimensional scalingwhich should have been fully orthogonal (T able 1.3). T he matrix of inter-correlations among factorial loadings on six factors is presented along with thematrix of inter-correlations among the scores on six scales inT ables 1.4.Additionally, T able 1.5 illustrates the pattern of inter-correlations among pure

subscales of the six scales.

Mapp in g Narrow , Broad , and Broades t Tra it s in Three-Dime nsional Space

T he model does not provide any keys for determining which pair of cubesedges represents a particular SWPAQ scale.

T herefore it is necessary to construct such a cube-like shape that fits wellwith the empirical relationships between questionnaire scales.

First, the inter-correlations among the factors, scales, and subscales(tetrads) might indicate which of them are the most probable neighbors.

Second, item loadings and the loadings averaged over scales or subscalesmight be used as indicators of their proximity to one or more edgesrepresenting the six broad factorial dimensions of sleep-wake adaptability.

T hird, the three coordinates of any item, subscale or scale might bedirectly calculated by performing three-dimensional scaling.

Consequently in order to determine the positions of each of six factorialdimensions relative to the positions of the edg

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