Factor Structure Within and Across Three Family-Assessment ......Factor Structure Within and Across...

Journal of Family Psychology1993. Vol.6, No. 3, 278-289

Copyright 1993 by the American Psychological Association, Inc.O893-32OO/93/$3.OO

Factor Structure Within and Across Three Family-AssessmentProcedures

Dawn M. Gondoli and Theodore Jacob

Higher order factor structures within and across the Family Environment Scale (FES),Family Assessment Measure (FAM), and Family Adaptability and Cohesion EvaluationScales III were examined. A sample of 138 families was obtained; separate analyses wereconducted for mothers, fathers, and their adolescent children. Factor structures wereassessed with exploratory and confirmatory procedures. The FES exhibited 3 factorsconsistent with the domains of its underlying model, whereas the FAM exhibited a singlefactor pertaining to affect. When combined, the instruments exhibited 3 factors pertain-ing to affect-cohesion, family activities, and control. Correspondence across the instru-ments was confined to the affect-cohesion and control dimensions. Although resultswere generally consistent across family members, some differences were noted; mostimportant, mothers had more differentiated factor structures than did fathers orchildren.

During the past decade, there has been in-creasing interest in the development and evalu-ation of theoretical models that describe whole-family functioning (e.g., Moos & Moos, 1981;Olson, Portner, & Lavee, 1985; Steinhauer, San-ta-Barbara, & Skinner, 1984). Several of theseefforts articulated specific clinical-theoreticalapproaches to family assessment and treatmentor tried to integrate constructs from diverse the-oretical bases. Significant progress has also beenmade in the development of self-report instru-ments to measure key constructs within thesevarious frameworks. Notwithstanding thesegains, several studies suggested that such instru-ments may measure far fewer independent con-structs than purported by the underlying modelsand that further investigation of instrument di-mensionality and cross-instrument correspon-dence may be of great importance to a widerange of family-research endeavors (Fowler,1981; Jacob & Tennenbaum, 1988; Skinner,

Dawn M. Gondoli, University of Arizona; The-odore Jacob, Palo Alto Veterans Administration Med-ical Center, Palo Alto, California.

This research was supported by National Instituteon Alcohol Abuse and Alcoholism Grant 1-R01-AA08486 to Theodore Jacob. We thank Michael Win-die, Harvey Skinner, and two anonymous reviewersfor their comments on an earlier version of this article.

Correspondence concerning this article should beaddressed to Dawn M. Gondoli, who is now at theResearch Institute on Addictions, 1021 Main Street,Buffalo, New York 14203.

1987). The present study examined three self-report instruments intended to operationalizewhole-family models: the Family EnvironmentScale (FES; Moos & Moos, 1981), the FamilyAssessment Measure (FAM; Skinner, Stein-hauer, & Santa-Barbara, 1983), and the FamilyAdaptability and Cohesion Evaluation Scales III(FACES III; Olson et al., 1985).

The FES (Moos & Moos, 1981) operational-izes the typology of family social environments(Moos & Moos, 1976). Based on an interaction-ist perspective (e.g., Endler & Magnusson,1976), this model assumes that the family is asocial environment with relatively stable char-acteristics. Although the family environmentmay be described along various dimensions,Moos and Moos emphasized the descriptionand measurement of family "social climate."Specifically, the FES measures social climate inthree domains: Relationships, Personal Growth,and System Maintenance. Each domain con-tains at least 2 subscales for a total of 10 con-structs assessed.

A second multidimensional assessment pro-cedure, the FAM (Skinner et al., 1983), was de-veloped to operationalize the process model offamily functioning (Steinhauer et al., 1984).Drawing on small-group theory, this model pos-its that families exist because members sharecommon goals. Most important, the family"provides for the biological, psychological andsocial development, and maintenance of family

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FACTOR STRUCTURE 279

members, thus ensuring the survival of both thefamily and the species" (Steinhauer et al., 1984).As family members meet goals, they perform avariety of maintenance, developmental, and cri-sis tasks. Although tasks change over the lifecycle, they involve the same basic processes thatcomprise the model's seven dimensions.

A third approach to whole-family assessmentis illustrated by the FACES III (Olson et al.,1985). The FACES III operationalizes the twodimensions of the circumplex model of maritaland family systems developed by Olson and col-leagues (Olson, Russell, & Sprenkle, 1983; Ol-son, Sprenkle, & Russell, 1979). The circumplexmodel was rationally derived after a review ofthe family therapy, family sociology, and small-group literatures. Conceptual analysis of theseliteratures indicated that most concepts could besubsumed within two independent dimensions:Adaptability and Cohesion.

In summary, the FES, FAM, and FACES IIIrepresent quite different approaches to the studyof whole families, each reflecting a unique con-ceptualization of the family and each developedaccording to different assumptions and meth-ods. Despite such diversity, however, these in-struments contain a number of similarly de-scribed subscales. Each instrument, for example,contains a bonding subscale: Cohesion in theFES and FACES HI and Affective Involvementin the FAM. Control is also represented in eachinstrument: Control in the FES and FAM andAdaptability in the FACES III. Finally, two ofthe instruments contain subscales pertaining tocommunication: Expressiveness and Conflict inthe FES and Communication and Affective Ex-pression in the FAM.

Such areas of correspondence may well reflectprimary dimensions of family process. Modelsof interpersonal relations, for example, haveoften emphasized processes related to affect,control, and communication (e.g., Benjamin,1974; Leary, 1957; Parsons & Bales, 1955). Lit-erature specific to family relations has also sug-gested that a variety of behaviors can be orga-nized along a few primary dimensions (e.g.,Angell, 1936; Hill, 1949; Olson et al., 1979). Assuggested by Jacob and Tennenbaum (1988),most of the literature on family influences inpsychopathology has focused on four dimen-sions: affect, control, communication, and sys-tems properties.

In support of a primary-factor approach tofamily assessment, empirical studies suggestedthat family instruments based on multidimen-sional models contain far fewer dimensions thanproposed. Skinner (1987), for example, reportedsubstantial intercorrelation among the FAMsubscales, suggesting that the FAM may mea-sure a single factor, possibly related to affect.Factor-analytic studies of the FES suggest thatthis instrument may also measure relatively fewdimensions (Fowler, 1981; Oliver, May, & Han-dal, 1988). Although the considerable subscaleintercorrelations found in the FAM and the FESmay be due to limitations of self-report method-ology (e.g., it may not be possible for respon-dents to differentiate between closely relateditems), it is also possible that the underlyingmodels are overly complex.

Finally, support for the contention that a lim-ited number of dimensions may capture themost relevant aspects of family relations can bedrawn from studies that have examined cross-instrument correspondence. Miller, Epstein,Bishop, and Keitner (1985) examined relation-ships between the FACES II (Olson, McCubbin,Barnes, et al., 1983) and a precursor to the FAM,the Family Assessment Device (FAD; Epstein,Baldwin, & Bishop, 1983). Most important, re-sults indicated that Adaptability and Cohesionwere significantly correlated with nearly all FADsubscales. Substantial correlation between theFACES II and the FAD was also reported byFristad (1989), who examined the self-reportand clinical rating scales from these instru-ments. In a final study, Edman, Cole, andHoward (1990) reported that FACES III Cohe-sion was correlated with a FES cohesion index(composed of Cohesion and Independence) andthat FACES III Adaptability was correlated witha FES adaptability index (composed of Organi-zation and Control). Thus, subscales pertainingto family cohesiveness and flexibility from theFACES III and FES were substantially related.

Although the available research literaturesuggests that different family-assessment instru-ments may measure a number of the same con-structs, limitations in the literature are note-worthy: Much of the extant research was notdesigned to assess instrument correspondence;studies usually presented correlations betweensubscales as a small part of reliability and valid-

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280 DAWN M. GONDOLI AND THEODORE JACOB

ity assessments; and most studies focused onlyon bivariate correlations between instrumentsubscales.

In the current study, which is concerned withidentifying the major dimensions exhibited bythe FES, FAM, and FACES III, exploratory andconfirmatory procedures were used to examinethe higher order factor structures within andacross the instruments. Specifically, principal-components analysis was used to develop hy-potheses about instrument factor structure fol-lowed by confirmatory factor analysis to testthese hypotheses. Before conducting the explor-atory analyses, general hypotheses regarding thenumber and type of factors that would be ob-tained were made. Given the descriptive overlapacross the three instruments, it was predictedthat the subscales would be substantially corre-lated and that relatively few factors would beobtained. It was further predicted that the ob-tained factors would be similar to the major di-mensions found in the literature on family andother interpersonal relations. Thus, factors wereexpected to reflect broad dimensions pertainingto affect, communication, and control.

Method

Sample

The sample was obtained as part of a larger studyconcerned with the development and evaluation offamily-assessment methods (Jacob, 1989). The sampleconsisted of 138 family triads, composed of a mother,father, and one adolescent between the ages of 12 and18 years. To participate, all family members had tohave at least a sixth-grade reading level, English had tobe the first and primary language spoken at home, andparents had to have been married for at least 2 years.All families were recruited with newspaper advertise-ments and were paid $25.00 for their participation.

Procedure

Announcements that included a brief description ofthe study were placed in local newspapers. During aninitial contact, interested families were screened andprocedures were described. If a family met all studycriteria and agreed to participate, a packet containingthe FES, FAM, and FACES III was mailed to theirhome. During the first contact, families were also toldto not complete the instruments until after a staffmember had called to discuss instructions. These in-structions were repeated in a packet cover letter.

Several days after mailing the packet, a staff mem-ber called the family to discuss instructions with eachparticipant. Family members were told that theyshould complete their forms independently, that allinformation would be confidential, and that the familywould be paid after the packet was returned. Copies ofthe instructions were included in the packet. When allinstruments were completed, the packet was returnedusing a postage-paid envelope. Of 182 families whoagreed to participate, 24% dropped out after receivingthe instruments and 76% completed the study.

Instruments

Each family member completed the FES Real Form(Moos & Moos, 1981), the FAM General Scale (Skin-ner et al., 1983), and the FACES III (Olson et al.,1985). Brief demographic questions were also com-pleted by each parent.

The FES contains 90 items scored according to atrue-false format. As noted, the instrument assessessocial climate in three domains: Relationships, Per-sonal Growth, and System Maintenance. Each domaincontains at least 2 subscales for a total of 10 constructsassessed. Internal consistency reliability estimates (co-efficient alpha) for the subscales were reported as rang-ing from .64 to .78 (Moos & Moos, 1981). Test-retestreliabilities have been reported as ranging from .73 to.78 (Bagarozzi, 1984). Subscale intercorrelations havebeen reported as low to moderate, with an averagevalue of .20 (Moos & Moos, 1981). An extensive num-ber of studies supported the external validity of theFES (see Druckman, 1979; Karoly & Rosenthal, 1977;Moos & Moos, 1981, 1984; Scoresby & Christensen,1976).

The FAM General Scale contains 50 items scoredaccording to a 4-point Likert-type scale (stronglyagree, strongly disagree). The instrument containsseven subscales to assess model constructs (Task Ac-complishment, Role Performance, Communication,Affective Expression, Affective Involvement, Control,and Values and Norms) and two subscales to assessresponse style bias (Social Desirability and Denial-Defensiveness). Internal consistency reliability esti-mates (coefficient alpha) were reported as .93 for theGeneral Scale (Skinner et al., 1983). Studies focusedon external validity indicated that the FAM is capableof differentiating between distressed and nondis-tressed families (Skinner et al., 1983).

The FACES III is a 20-item instrument that assessesAdaptability (10 items) and Cohesion (10 items).Items are scored according to a 5-point Likert-typescale (almost never, almost always). Internal consis-tency reliability estimates have been reported as .62for Adaptability and .77 for Cohesion, and the corre-lation between Adaptability and Cohesion has beenreported as virtually zero (Olson et al., 1985). Valida-tion studies of the FACES III are currently underway;studies that focused on the original FACES and theFACES II indicated that these instruments adequatelydiscriminated between distressed and nondistressedfamilies (see Olson et al.. 1985).

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Results

Sample Characteristics

The parents were primarily White, fairly welleducated, middle class, and middle-aged. Ninetypercent of the mothers were White; 34% werehigh school graduates and 41 % had completed atleast 1 year of college; and 79% were employedoutside the home. Ninety-one percent of the fa-thers were White; 27% were high school gradu-ates and 34% had completed at least 1 year ofcollege; and 95% were employed outside thehome. The majority of the families were in themiddle (30%) and upper-middle classes (37%) asmeasured by the Hollingshead (1975) Four-Fac-tor Index of Social Status (a weighted index ofhusband and wife education and occupation).The average age of the mothers was 40.3 years,and the average age of the fathers was 42.5 years.Demographic information on the participatingchild was limited to sex and age: 57% of thechildren were female, and the average age forfemale and male children combined was 14.8years (R = 12-18, SD = 1.73).

Major Analyses

All analyses were conducted separately formothers, fathers, and children. Before conduct-ing the factor analyses, subscales with internalconsistency reliability estimates (coefficient al-pha) below .50 were eliminated. Principal-com-ponents analyses were then used to generate hy-potheses about instrument factor structurefollowed by confirmatory factor analyses to testthese hypotheses. The exploratory and confir-matory procedures were conducted for the FESand FAM separately to examine the factor struc-tures within these instruments. Because theFACES III contained only two subscales, thisinstrument was not analyzed separately. Theprocedures were then applied to the FAM, FES,and FACES HI combined to examine cross-in-strument factor structure and correspondence.

FES

Several subscales with unacceptable internalconsistency were eliminated. For mothers, Ex-pressiveness (.43), Independence (.36), andAchievement Orientation (.39) were eliminated;reliability estimates for the remaining subscales

ranged from .58 to .73. For fathers, Indepen-dence (.37) and Achievement Orientation (.45)were eliminated; reliability estimates for the re-maining subscales ranged from .58 to .76. Sim-ilarly, Independence (.44) and AchievementOrientation (.37) were eliminated for children;reliability estimates for the remaining subscalesranged from .57 to .82.

Results of the exploratory analyses werehighly consistent across family members. Foreach respondent, the FES exhibited three factorsthat accounted for a substantial proportion(>69%) of the variance. Composition of the ob-tained factors across family members, althoughnot identical, was highly similar. Generally, Fac-tor I was defined by Conflict, Cohesion, andOrganization; Factor II by Intellectual-CulturalOrientation, Active-Recreational Orientation,and Moral-Religious Emphasis; and Factor IIIby Organization, Control, and Moral-ReligiousEmphasis.'

The confirmatory analyses compared two FESmodels: a null model in which it was hypothe-sized that each subscale reflected an indepen-dent factor, and an alternative model based onthe exploratory results for each respondent. Inspecifying the alternative models, subscaleswere generally constrained to load on one factor.However, the factors were allowed to correlate.Covariance matrixes were used as data for allanalyses. Results of these procedures are re-ported next for mothers, fathers, and childrenseparately.

Mothers. Maximum likelihood (ML) esti-mates for the three-factor alternative model arereported in Table 1.

The null and the three-factor model wereevaluated with the chi-square test statistic andthree goodness-of-model-fit indices. On thebasis of chi-square, both models had an unac-ceptable fit to the data. For the null model, x2-(21, N = 138) = 203.38, p < .01, and for thethree-factor model, x

2(10, N = 138) = 27.37,p < .01. In practice, however, chi-square maybe overly restrictive, that is, significant even

1 The exploratory factor analyses were conductedusing SPSS-X Data Analysis System, Release 3.0 (Sta-tistical Package for the Social Sciences, Inc., 1988).The extraction method was principal-componentsanalysis, the criterion for extraction was eigenvaluesgreater than or equal to 1.0, and the rotation methodwas varimax. The confirmatory analyses were con-ducted using LISREL VII (Joreskog & Sorbom, 1988).

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Table 1Standardized Maximum Likelihood Estimates and Factor Interpretations for Mothers'Three-Factor Family Environment Scale Model

Subscale

CohesionConflictIntellectual-Cultural

OrientationActive-Recreational

OrientationMoral-Religious

EmphasisOrganizationControl

T

1IIIII

I

Maximum likelihood estimates.711

-.706

.729—

Factor intercorrelations

0.53-0.20

Factor

II

.764

.627

.354

—

0.02

III

.

.433

.806

—

when differences between observed and ex-pected covariance matrixes are trivial. In addi-tion, chi-square may be affected by sample size.Therefore, three fit indices that are less restric-tive and less affected by sample size were alsoexamined: the goodness-of-fit index (GFI), theadjusted GFI (AGFI), and the root-mean-square residual (RMR). The GFI is the ratio ofthe minimum fit function after a model is fittedto the minimum fit function before a model isfitted. The AGFI is the GFI adjusted for de-grees of freedom. Both indices yield values be-tween 0.0 and 1.0, with unity indicating perfectfit (Joreskog & Sorbom, 1988). Although thereis no statistical test for the adequacy of theseindices, cutoffs of .90 for the GFI and .80 forthe AGFI have been suggested in the literature(e.g., Anderson & Gerbing, 1984). The RMRindicates the average size of the fitted residualsand is interpreted in relation to the size of ob-served variances and covariances (Joreskog &Sorbom, 1988).

On the basis of the goodness-of-model-fit in-dices, the three-factor model had a good fit(GFI = .951; AGFI = .864; RMR = .067). Incontrast, the fit of the null model was poor(GFI = .673; AGFI = .564; RMR = .246).2 As afinal step in the comparison between models,the normed fit index (NFI) was calculated. TheNFI estimates improvement in fit and is calcu-lated by comparing relative sizes of chi-squarefor a null model versus an alternative model.

The index is "normed" to yield values between0.0 and 1.0. Although exact cutoffs have notbeen established, an alternative model is seenas offering substantial improvement if the NFIexceeds .90 (Bentler & Bonett, 1980). The NFIfor the current analysis was .865, indicatingthat the three-factor model offered improve-ment over the null model.

Fathers. A three-factor model similar tothat tested for mothers was examined. Thismodel could not be tested, however, becausethe obtained solutions contained negative vari-ance estimates or "Heywood cases." When ex-amined, these improper solutions appeared tobe the result of a lack of multiple, reliable indi-cators to measure adequately Factor III. Be-cause no additional indicators could be devel-oped for the third factor, it was decided toexclude it and attempt to confirm only Factor Iand Factor II. Thus, a new model that con-tained six subscales and two factors was de-vised. The two-factor model was then com-pared with a null model in which it washypothesized that each subscale reflected an in-dependent factor.

2 As discussed by Joreskog and Sorbom (1988), theRMR is best interpreted when all variables are stan-dardized; that is, when correlation coefficients areused as data. Therefore, all reported values for theRMR were generated from separate analyses usingcorrelation matrixes.

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ML estimates for the two-factor alternativemodel are reported in Table 2.

On the basis of chi-square, both the nullmodel and the two-factor model had an un-acceptable fit to the data. For the null model,x

2(15, N = 138) = 283.31, p < .01; for the two-factor model, x

2(8, N = 138) = 18.31, p < .01.On the basis of the goodness-of-model-fit indi-ces, however, the two-factor model had a goodfit (GFI = .956; AGFI = .884; RMR = .046). Incontrast, the fit of the null model was poor(GFI = .512; AGFI = .316; RMR = .369). Fur-thermore, the NFI was .935, indicating that thetwo-factor model offered substantial improve-ment over the null model.

Children. Again, a three-factor model simi-lar to that tested for mothers was examined. Aswith results for fathers, however, this model re-sulted in negative variance estimates. Again,the improper solutions appeared to be the re-sult of a lack of multiple reliable indicators forthe third factor. Because no additional indica-tors could be developed for Factor III, it wasdecided to exclude it and attempt to confirmonly Factor I and Factor II. Thus, as with theprocedure for fathers, a new model that con-tained seven subscales and two factors was de-vised. The two-factor model was then com-pared with a null model in which it washypothesized that each subscale reflected an in-dependent factor.

ML estimates for the two-factor model arereported in Table 3.

Table 2Standardized Maximum LikelihoodEstimates and Factor Intercorrelations forFathers' Two-Factor Family EnvironmentScale Model

Factor

Subscale I II

Maximum likelihood estimatesCohesion .901 —Expressiveness .605 —Conflict -.638 —Intellectual-Cultural — .777

OrientationActive-Recreational — .728

OrientationOrganization .608 —

III


0.73

On the basis of chi-square, both the nullmodel and the two-factor model had an unac-ceptable fit to the data. For the null model,X2(21, N = 138) = 327.01, p < .01; for the two-factor model, x

2(13, N = 138) = 28.62, p < .01.On the basis of the goodness-of-fit indices,however, the two-factor model had a good fit(GFI = .947; AGFI = .885; RMR = .052). Incontrast, the fit for the null model was quitepoor (GFI = .514; AGFI = .351; RMR = .344).Finally, the NFI was .912, indicating that thetwo-factor model offered substantial improve-ment over the null model.

FAM

Task Accomplishment was eliminated formothers because of unacceptable internal con-sistency (coefficient alpha = .47). The remainingsubscales had reliability estimates ranging from.63 to .76. No subscales were eliminated for fa-thers or children; reliability estimates for thesefamily members ranged from .63 to .80.

Results of the exploratory analyses werehighly consistent across family members; foreach respondent, the FAM contained one factorthat accounted for a substantial proportion(>66%) of the variance. The confirmatory anal-yses compared two FAM models: a null modelin which it was hypothesized that each subscale

Table 3Standardized Maximum LikelihoodEstimates and Factor Intercorrelations forChildrens' Two-Factor Family EnvironmentScale Model

Factor

Subscale I II

Maximum likelihood estimatesCohesion .972 —Expressiveness .555 —Conflict -.645 —Intellectual-Cultural — .694

OrientationActive-Recreational — .671

OrientationMoral-Religious — .504

EmphasisOrganization .615 —

III


0.76

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Table 4Standardized Maximum Likelihood Estimates for the One FactorFamily Assessment Measure

Subscale Mothers Fathers Children

Task AccomplishmentRole PerformanceCommunicationAffective ExpressionAffective InvolvementControlValues and Norms

.725

.723

.724

.743

.887

.800

.799

.800

.816

.843

.838

.853

.818

.737

.772

.841

.762

.813

.880

.876

reflected an independent factor, and an alterna-tive one-factor model based on the exploratoryresults for each respondent. Covariance ma-trixes were used as data for all analyses.

Mothers. ML estimates for the one-factormodel are reported in Table 4.

Again, the models were evaluated using thechi-square test statistic and the three goodness-of-model-fit indices. On the basis of chi-square,both models had an unacceptable fit to thedata; for the null model, x2(15, N = 138) =459.46, p < .01, and for the one-factor model,X2(9,N= 138) = 20.99, p < .01. On the basis ofthe goodness-of-fit indices, however, the one-factor model had a good fit (GFI = .952; AGFI= .887; RMR = .037). In contrast, the fit forthe null model was poor (GFI = .363; AGFI =.109; RMR = .500). Additionally, the NFI was.954, indicating that the one-factor model of-fered substantial improvement over the nullmodel.

Fathers. ML estimates for the one-factormodel are reported in Table 4. On the basis ofchi-square, both the null model and the one-factor model had an unacceptable fit to thedata; for the null model, x

2(21, N = 138) =742.36, p < .01, and for the one-factor model,X2(14, N = 138) = 27.97, p < .01. On the basisof the goodness-of-fit indices, however, theone-factor model had a good fit (GFI = .945;AGFI = .890; RMR = .027). In contrast, the fitof the null model was poor (GFI = .265; AGFI= .020; RMR = .588). In addition, the NFI was.962, indicating that the one-factor model of-fered substantial improvement over the nullmodel.

Children. ML estimates for the one-factormodel are reported in Table 4. As with the re-sults for parents, chi-square indicated that boththe null model and the one-factor model had

an unacceptable fit to the data. For the nullmodel, x

2(21, N = 138) = 719.82, p < .01, andfor the one-factor model, x 2 (K N = 138) =29.50, p < .01. On the basis of the goodness-of-fit indices, however, the one-factor model had agood fit (GFI = .949; AGFI = .898; RMR =.027). In contrast, the fit for the null model waspoor (GFI = .275; AGFI = .034; RMR = .574).Additionally, the NFI was .959, indicating thatthe one-factor model resulted in substantial im-provement over the null model.

Cross-Instrument Analyses

All subscales with acceptable reliabilities wereincluded in the following analyses. For mothers,10 subscales were included: 2 from the FACESIII, 7 from the FES, and 1 from the FAM (acomposite measure created by adding the rawscores of the 6 included subscales). For fathersand children, 11 subscales were included: 2 fromthe FACES HI, 8 from the FES, and a FAMcomposite (created by adding the raw scores ofall 7 subscales).3

Results of the exploratory procedures werehighly consistent across family members. Foreach respondent, the instruments exhibitedthree factors that accounted for a substantial

3 On the basis of conceptual and methodologicalconsiderations, we decided to use a FAM compositerather than enter all subscales separately in the confir-matory analyses. Results of our exploratory analyseswere unequivocal in suggesting that the FAM was uni-dimensional. Furthermore, when separate FAM sub-scales were used in the confirmatory procedures, highmulticollinearity resulted in improper solutions. Al-though creation of FES composites would have madethe analyses more consistent, we were interested inexploring the relationships between the different FESsubscales and the FAM and FACES III.

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proportion (>62%) of the variance. Composi-tion of the obtained factors across respondentswas highly similar; Factor I was defined bythe FAM composite, FACES III Cohesion, andFES Conflict, Cohesion, and Organization; Fac-tor II by FES Intellectual-Cultural Orientation,Active-Recreational Orientation, and Moral-Religious Emphasis; and Factor III by FES Or-ganization and Control and FACES HI Adapt-ability.

The exploratory models were subsequentlytested for each respondent. In specifying themodels, subscales were generally constrained toload on one factor. However, the factors wereallowed to correlate. To standardize the subscalevariances across instruments, correlation ma-trixes were used as data for all analyses.

Mothers. ML estimates for the three-factormodel are reported in Table 5. The model wasevaluated using the chi-square test statistic andthe three goodness-of-model-fit indices. On thebasis of chi-square, the model had an unaccept-able fit to the data; x

2(31, N = 138) = 58.17,p < .01. On the basis of the three goodness offit indices, however, the model had a good fit(GFI = .924; AGFI = .864; RMR = .062).

Fathers. As with results for the FES, thecross-instrument confirmatory analysis resulted

in negative variance estimates. Again, the prob-lem appeared to be the result of a lack of reli-able indicators to measure adequately FactorIII. Because no additional indicators could bedeveloped for the third factor, we decided toexclude it and focus only on Factor I and Fac-tor II. Thus, a new model that contained ninesubscales and two factors was devised.

ML estimates for the two-factor model arereported in Table 6. On the basis of chi-square,the two-factor model had an unacceptable fit tothe data; x

2(26, N = 138) = 54.82, p < .01. Onthe basis of the goodness-of-fit indices, how-ever, the model had a good fit (GFI = .924;AGFI = .868; RMR = .051).

Children. As with results for fathers, theinitial confirmatory analysis resulted in nega-tive variance estimates. Again, the problem ap-peared to be the result of a lack of multiple re-liable indicators for Factor III. Because noadditional indicators could be developed forthe factor, we again decided to exclude it and toattempt to confirm only Factor I and Factor II.Thus, a new model that contained nine sub-scales and two factors was devised.

ML estimates for the two-factor model arereported in Table 7.

Table 5Standardized Maximum Likelihood Estimates and Factor Intercorrelations for Mothers'Three-Factor Cross-Instrument Model

Scale I

Maximum likelihood estimatesFamily Environment Scale

CohesionConflictIntellectual-Cultural



EmphasisOrganizationControl

Family Assessment Measure: CompositeFamily Adaptability and Cohesion Evaluation Scales III:

CohesionAdaptability

Factor intercorrelationsiiIIIII

.772-.654

.646

-.761

.688—

0.550.07

Factor

II

.768

.621

.358

—

z0.02

III

-.444-.549

.518

—

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Table 6Standardized Maximum Likelihood Estimates and Factor Intercorrelations for Fathers'Two-Factor Cross-Instrument Model

Scale


CohesionExpressivenessConflictIntellectual-Cultural



EmphasisOrganization


Cohesion

Factor intercorrelationsT

1II

I

.847

.632-.645

.656-.810

.663

0.70

Factor

II

.820

.682

.373

—

—

On the basis of chi-square, the model had anunacceptable fit to the data; x2(26, N = 138) =58.68, p < .01. On the basis of goodness-of-fitindices, however, the model had a good fit(GFI = .916; AGFI = .854; RMR = .051).

Discussion

The current study indicated that the FES andFAM exhibited fewer specific dimensions thanproposed by their underlying models and thatcorrespondence across the FES, FAM, andFACES III was somewhat limited. The FES, forexample, exhibited two to three factors depend-ing on respondent. Factor I was primarily de-fined by Cohesion, Conflict, and Organizationand appeared to reflect affect and cohesion. Fac-tor II was defined by Intellectual-Cultural Ori-entation, Active-Recreational Orientation, andMoral-Religious Emphasis and appeared to re-flect family activities. Items from the subscalesthat load on this factor, for example, emphasizeshared activities (e.g., "We often go to movies,sports events, camping"; "Family members at-tend church, synagogue, or Sunday school fairlyoften"; "We rarely go to lectures, plays, or con-certs"). In addition, other items emphasize fam-ily communication (e.g., "We often talk aboutthe religious meaning of Christmas, Passover, or

other holidays"; "We often talk about politics orsocial problems"; "We hardly ever talk aboutimportant things").4 Factor III, although identi-fied for all respondents in the exploratory anal-yses, was confirmed only for mothers. This thirdfactor was defined by Organization and Controland thus appeared to reflect organizational andcontrol processes.

Current results for the FES are consistent withprevious efforts, suggesting that this instrumentmeasures a limited number of dimensions(Fowler, 1981; Oliver et al., 1988). In both the

4 Although Factor I and Factor II for the FES aresubstantially correlated, we believe they are distinctenough to justify their interpretation as separate di-mensions. Both dimensions appear to reflect familycloseness or togetherness; however, Factor I appears toreflect the psychological aspects of closeness, whereasFactor II appears to reflect the behavioral aspects (i.e.,family activities). Thus, an important distinctionwould be lost if the dimensions were combined. Analternative to interpreting highly correlated dimen-sions might be to constrain the solution to be orthog-onal. Given the simultaneous and interrelated natureof much of family life, however, it is probably unrea-sonable, from a theoretical perspective, to force inde-pendence among major dimensions that characterizefamily interaction. Thus, in the current study, the cor-relation between Factor I and Factor II is to be ex-pected to the extent that family members who sharepositive feelings tend to do things together.

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Table 7Standardized Maximum Likelihood Estimates and Factor Intercorrelations for Childrens'Two-Factor Cross-Instrument Model

Scale


CohesionExpressivenessConflictIntellectual-Cultural



EmphasisOrganization


Cohesion


III

I

.884

.626-.711

—

—

—

.624-.871

.817

0.72

Factor

II

———

.735

.640

.490

——

—

—

current and previous studies, the FES was char-acterized by two or three factors reflecting affect,psychological and behavioral closeness, andorganization-control. It should be noted, how-ever, that the factors obtained in the currentstudy do reflect the three domains of the FES.Affect and psychological closeness reflect theRelationships domain, family activities reflectsthe Personal Growth domain (perhaps better de-fined as "family growth"), and organization-control reflects the System Maintenance do-main. Thus, although the FES did not exhibit 10independent dimensions, it did appear to reflectthe broader domains of its underlying model.

In contrast to results for the FES, the FAMexhibited one factor, results that are consistentwith previous efforts focused on this instru-ment; most important, Skinner (1987) reportedsubstantial intercorrelation among the FAMsubscales, suggesting that the FAM may be mea-suring a single dimension related to affect. Thus,despite an intended emphasis on pragmatic as-pects of family functioning (e.g., Task Accom-plishment, Role Performance), the FAM ap-pears to measure evaluative judgments of familymembers.

Our cross-instrument analyses indicated thatthe FES, FAM, and FACES III combined exhib-ited two to three factors. Factor I was defined by

subscales from all three instruments and ap-peared to reflect affect and cohesion. Factor IIwas defined by FES Personal Growth subscalesand appeared to reflect family activities. A thirdfactor was identified in the exploratory analysesfor all respondents but was confirmed only formothers. This third factor was defined by FESOrganization and Control and FACES IIIAdaptability and appeared to reflect firm versuslax control. Thus, correspondence across thethree instruments was confined to areas of af-fect, cohesion, and control. This modest corre-spondence resulted from the limited dimension-ality of the FAM, the FACES III, and, to a lesserextent, the FES. Hypothesized relationships be-tween the FAM and the other instruments, forexample, could not occur because the FAM wasso strongly unidimensional.

Reasons for the limited dimensionality of ap-parently multidimensional instruments may bethe result of error in the underlying theory, prob-lems with self-report methodology, or both(Jacob & Tennenbaum, 1988). Regarding theo-retical issues, it is possible that the models forinstruments such as the FAM and FES areoverly complex. In reality, family relations maybe best described with a few primary dimensionsas suggested by various two-factor models ofgeneral interpersonal relations (e.g., Benjamin,

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1974; Leary, 1957; Parsons & Bales, 1955).Alternatively, it is possible that family relationsare multidimensional but that self-report in-struments cannot capture this complexity. Re-spondents, for example, may be unable to dif-ferentiate between closely related yet distinctitems. In addition, more general evaluations ofthe family or of specific members may influenceresponses. Given such methodological prob-lems, other approaches (e.g., observational tech-niques) may be needed to capture the differentdimensions of family relations. To examine thispossibility, however, multitrait-multimethodapproaches are necessary (Campbell & Fiske,1959).

Although the current study makes several im-portant contributions to the literature, limita-tions do exist. Most important, our analyses didnot use multitrait-multimethod data. Withoutsuch data, it is impossible to determine whetherthe limited dimensionality of the FAM and theFES is the result of theoretical or methodologi-cal problems. Future research would do well toassess theoretical constructs across severalmethods, including self-report, observational,and quasi-observational procedures. A relatedlimitation concerns the high intercorrelationsamong several of the factors in the confirmatoryanalyses. Although we expected some correla-tion among dimensions that reflect family inter-action (see footnote 4), these rather substantialcorrelations may be demonstrating a consistentmethod effect. Again, multitrait-multimethoddata are necessary to explore issues related tomethod variance.

A third limitation concerns the issue of corre-spondence in factor structures across familymembers. Our decision to eliminate subscaleson the basis of internal consistency criteria re-sulted in the elimination of different subscalesfor different members. In turn, these decisionsprecluded a standard multisample analysis todetermine similarity of factor structures acrossmembers (see Joreskog & Sdrbom, 1988). Al-though results were highly consistent across re-spondents in the exploratory analyses, the samefactor structures could not be confirmed for allfamily members. Instead, factor structures formothers were more differentiated than those ob-tained for fathers and children. Specifically,organization-control emerged as a robust factorfor mothers but not for fathers or children. Var-ious explanations for this disparity can be sug-

gested. Organization and control, for example,may be more salient to mothers to the extentthat women have disproportionate responsibil-ity for household management and care ofchildren. Alternatively, it is possible that theorganization-control factor would have beenconfirmed for fathers and children had the sub-scales that defined this factor been more reliableor had additional indicators of the factor beenavailable.

The current study raises additional questionsfor the conceptualization and measurement ofwhole-family functioning. Although multidi-mensional instruments are prevalent in theexisting literature, theoretical and empiricalsupport for such approaches remains to be dem-onstrated. As noted, family relations may bebest described with a few primary dimensions,suggesting that more attention should be paid tothe development of primary-factor models andinstruments and to the application of moregeneral models of interpersonal process tofamily description. On the other hand, multi-dimensional models may eventually prove tobe more accurate and valid perspectives for un-derstanding complex family processes thansimpler two- or three-factor models. To pursuethis line of inquiry, however, more attentionwill have to be directed toward the operation-alization of such models. Most important,self-report instruments must be subjected tomore rigorous and parametric evaluation thanhas occurred thus far, and other methods ofmultidimensional assessment need to be ex-plored within multitrait-multimethod researchstrategies.

In conclusion, future research on family as-sessment will need to balance the interrelateddemands of theory and method. Multidimen-sional models, although conceptually appealing,may be limited to certain types of methodology.Conversely, primary-factor models, althoughperhaps easier to operationalize, need to beclosely linked to family theory. Moreover, thesimilarities and differences between a primary-factor model specific to family relations (such asthe circumplex model) and primary-factor mod-els relevant to more general conceptualizationsof interpersonal relations need to be articulated.Given such efforts, the conceptualization andmeasurement of the family as a whole shouldcontinue to increase in both richness andveracity.

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Received February 3, 1992Revision received May 21,1992

Accepted May 21, 1992 •

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Factor Structure Within and Across Three Family-Assessment ......Factor Structure Within and Across...

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