Bryant and Smith 2001 - Refining the Architecture of Aggression

8/12/2019 Bryant and Smith 2001 - Refining the Architecture of Aggression

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Journal of Research in Personality 35, 138167 (2001)doi:10.1006/jrpe.2000.2302, available online at http://www.idealibrary.com on

Rening the Architecture of Aggression: A Measurement Modelfor the BussPerry Aggression Questionnaire

Fred B. Bryant and Bruce D. Smith

Loyola University Chicago

Among the most popular measures of aggression is the 29-item, self-report Ag-gression Questionnaire (AQ; Buss & Perry, 1992; Buss & Warren, 2000). Structuralanalyses of the AQ have revealed four underlying factors: Physical Aggression,

Verbal Aggression, Anger, and Hostility. However, these four factors explain toolittle common variance (i.e., about 80%) to be an adequate measurement model. Inthe present study, we used conrmatory factor analysis with a total sample of 1154respondents to compare four alternative measurement models for the AQ that arecurrently in use. Replicating earlier work, none of these models t the data well,and the original four-factor model achieved only mediocre goodness-of-t in threeindependent samples (GFI .76 .81). To develop a more appropriate measure-ment model, we omitted items with low loadings or multiple loadings based onprincipal components analysis and excluded items with reverse-scored wording.

This yielded a 12-item, four-factor measurement model with acceptable goodness-of-t (GFI .94). Secondary analysis of two independent data sets conrmed therened models generalizability for British (Archer, Holloway, & McLoughlin,1995; GFI .93) and Canadian (Harris, 1995; GFI .94) samples. The renedmodel yielded equivalent factor structures for males and females in all three sam-ples. We also replicated the rened four-factor model in two additional Americansamples, who completed a new short form of the AQ containing only the subset of 12 items in random order. Additional analyses provided evidence supporting themodels construct validity and demonstrated stronger discriminant validity for the

rened Hostility factor compared to its predecessor. The new short form of the AQthus not only contains fewer than half as many items as the original, but also ispsychometrically superior. 2001 Academic Press

The authors thank John Archer and Julie Harris for graciously providing us with data fromtheir published articles. We also gratefully acknowledge the helpful advice of Mary Harris,the invaluable research assistance of Rebecca Guilbault, and the insightful editorial feedback of Craig Colder and an anonymous reviewer. Earlier versions of this article were presented

at the American Psychological Association convention, Chicago, IL, August 1997, and at theJoint Meeting of the Classication Society of North America and the Psychometric Society,Urbana, IL, June 1998.

Address correspondence and reprint requests to Fred B. Bryant, Department of Psychol-ogy, Loyola University Chicago, 6525 North Sheridan Road, Chicago, IL 60626. E-mail:[email protected].

1380092-6566/01 $35.00Copyright 2001 by Academic PressAll rights of reproduction in any form reserved.


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ARCHITECTURE OF AGGRESSION 139

Much work has emphasized the role of physical aggression, verbal aggres-sion, anger, and hostility as subtraits in a global conceptualization of aggres-sion (Buss, 1961; Buss & Durkee, 1957; Buss & Perry, 1992; Harris, 1995;Zillmann, 1979). Early measurement of aggression used an experimental

methodology, required a laboratory, and suffered difculties in interpretingaggressive intent (Zillmann, 1979). To reduce the time, effort, and resourcesinvolved in measuring aggression, Buss and Durkee (1957) developed a 75-item self-report instrument, the BussDurkee Hostility Inventory, which ag-gression researchers have often used.

To improve the psychometric properties of this instrument, Buss andPerry (1992) more recently developed a 29-item self-report questionnaire,the Aggression Questionnaire (AQ; Buss & Perry, 1992; Buss & Warren,2000). They designed the AQ to measure four dispositional subtraits of ag-gression, which they dened as follows: Physical and verbal aggression,which involve hurting or harming others, represent the instrumental or mo-tor component of behavior. Anger, which involves physiological arousaland preparation for aggression, represents the emotional or affective com-ponent of behavior. Hostility, which consists of feelings of ill will and in- justice, represents the cognitive component of behavior (Buss & Perry,

1992, p. 457).In constructing this questionnaire, Buss and Perry (1992) borrowed some

items intact from the earlier Hostility Inventory, revised other BussDurkeeitems to improve clarity, and added many new items to generate an initialpool of 52 questions. They then administered this set of 52 questions tothree successive samples of 406, 448, and 399 college students and analyzedthe structure of responses using exploratory principal components analysiswith oblique rotations. Although they had originally generated items for sixa priori components of aggression (Physical Aggression, Verbal Aggression,Anger, Indirect Aggression, Resentment, and Suspicion), only four corre-lated factors emergedPhysical Aggression, Verbal Aggression, Anger, andHostilityon which a core set of 29 items loaded, and this four-factor struc-ture appeared to replicate across all three samples. Buss and Perry (1992)next used conrmatory factor analysis to evaluate the goodness-of-t of threealternative measurement models for the set of 29 items: (a) a global one-

factor model that assumes all items reect a single general aggression factor;(b) a four-factor model that represents the structure found in the principalcomponents analysis; and (c) a hierarchical factor model that assumes thefour correlated, rst-order factors reect a single, second-order super fac-tor of aggression. Figure 1 presents a graphical representation of each of these three measurement models.

As a sole measure of each models goodness-of-t, Buss and Perry (1992)computed the ratio of chi-square to degrees of freedom (cf. Hoelter, 1983).Based on the notion that ratios under 2 reect acceptable t, Buss and Perry


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FIG. 1 Three measurement models currently in use for the 29-item Aggression Question-naire (AQ; Buss & Perry, 1992). Squares represent measured variables (or AQ items), andcircles represent latent constructs (or AQ factors). Arrow-headed straight lines connecting

latent constructs to measured variables represent item factor-loadings ( s). Two-headed,curved lines connecting latent factors represent factor interrelationships ( s). The small, arrow-headed straight line to each measured variable represents unique variance associated withmeasurement error, or the joint effect of unmeasured inuences and random error ( ). Theunidimensional model (top) assumes that a single, rst-order factor (Global Aggression) ex-plains the covariation among the 29 AQ items. The multidimensional model (center) assumesthat four, interrelated rst-order factors (Physical Aggression, Verbal Aggression, Anger, andHostility) explain the covariation among the 29 AQ items. The hierarchical model (bottom)assumes that a single, global second-order factor (Global Aggression) underlies the covariationamong the four rst-order factors. The small, arrow-headed straight line to each rst-orderlatent factor in the hierarchical model represents specic variance that is unrelated to thesecond-order latent factor ( ).


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(1992) concluded that both the four-factor model ( 2 / df 1.94) and thehigher-order factor model ( 2 / df 1.95) t the pooled data reasonably well,whereas the one-factor model ( 2 / df 2.27) did not. Recalculating the modelchi-squares from the known degrees of freedom reveals that both the four-

factor model, 2(371) 719.7, and the higher-order model,

2(373) 727.4,

t the data signicantly better (both 2s 128.3, ps .00001) than didthe one-factor model, 2(377) 855.8. Because Buss and Perry (1992) re-ported no other goodness-of-t measures, however, we know nothing aboutthe proportion of variancecovariance information that these models ex-plained in their data or how much better these models t relative to a worse-case null model that assumes there are no common factors. Such measuresof absolute and relative t would be useful in deciding whether either of themultidimensional frameworks represents an acceptable measurement modelfor the AQ.

Although Buss and Perry (1992) proposed their four-factor solution as ameasurement model for the AQ, more recent analyses (Archer, Kilpatrick, &Bramwell, 1995; Harris, 1995; Williams, Boyd, Cascardi, & Poythress,1996) suggest that this structure explains too little common variance amongthe 29 items (i.e., about 80%) to serve as a measurement model. Accordingly,

the primary goal of the present study was to develop an acceptable measure-ment model for the AQ and to assess its construct validity.

As a means of improving the measurement precision of the AQ, previousresearchers have proposed discarding AQ items that are relatively unreliableindicators of Hostility. Indeed, omitting Buss and Perrys (1992, Table 1,p. 454) sixth and eighth indicators of Hostility has been found to increasethe reliability of the Hostility factor in both Canadian (Harris, 1995) andDutch (Meesters, Muris, Bosma, Schouten, & Beuving, 1996) samples. Yet,this approach is not without its critics (Bernstein & Gesn, 1997). The keytheoretical issue here is whether it is better to have a global, somewhat het-erogeneous construct of known theoretical utility or to have a more specicand psychometrically puried construct (cf. Bryant, Yarnold, & Grimm,1996).

Researchers using the AQ have typically adopted one of two dominantstrategies for scoring the instrument. The rst strategy assumes that all AQ

items reect a single underlying construct reecting a persons global predis-position toward aggression. With this unidimensional approach, researcherssimply sum responses to the 29 items to construct an AQ total score (e.g.,Buss & Perry, 1992). The second strategy assumes that aggression consistsof four correlated dimensions reecting a persons predisposition toward ag-gression in the physical, verbal, emotional (Anger), and cognitive (Hostility)domains. With this multidimensional approach, researchers construct fourseparate subscale scores by summing or averaging responses to the set of AQ items tapping each domain of aggression (e.g., Felsten & Hill, 1998).


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142 BRYANT AND SMITH

Yet, neither of these two approaches adequately captures the variation inpeoples responses to the AQ. More specically, measurement error andother constructs in addition to aggression have an unacceptably large inu-ence on responses to the set of 29 AQ items. Although the theoretical model

underlying the AQ is conceptually well grounded in the aggression literature,researchers need a better operational framework for quantifying responsesto the instrument. With this aim in mind, we sought to improve the correspon-dence between the conceptual and operational denitions underlying the AQand to develop a more reasonable measurement model for the AQ.

We worked with ve independent data sets: three primary data sets thatwe collected for this study and two archival data sets that others had collectedearlier. First, we collected a new data set to evaluate and compare the explan-atory power of four different measurement models for the AQ that are cur-rently in use in the literature. We also used these new data to develop abetter-tting rened version of Buss and Perrys (1992) four-factor modeland to compare the convergent and discriminant validity of this rened modelwith that of the original. We then obtained two preexisting AQ data setsa British sample (Archer, Holloway, & McLoughlin, 1995) and a Canadiansample (Harris, 1995)with which we assessed the cross-sample generaliz-

ability of both the original and rened models. Finally, we collected newdata from two additional American samples to evaluate the rened modelsreplicability using a new short form of the AQ, containing only the subsetof 12 items in random order.

METHODParticipants and Procedure

Sample 1. The rst sample consisted of new data from 307 American undergraduates (173females, 131 males, and 3 who did not report gender) at a private metropolitan university whovoluntarily participated. Average age was 18.94 ( SD 1.21). Respondents completed a batteryof tests, including the 29-item Aggression Questionnaire (AQ; Buss & Perry, 1992; Buss &Warren, 2000).

Sample 2. The second sample, which we used for cross-validation, was originally collectedby Archer, Holloway, and McLoughlin (1995). The sample consisted of 200 British undergrad-uates (100 females and 100 males). Average age was 25.13 ( SD 6.17). Participants com-pleted the 29-item AQ using the same 5-point scale. The data consisted of the raw AQ data

analyzed by Archer et al. (1995).Sample 3. The third sample, also used for cross-validation, was originally collected by Harris(1995). The sample consisted of 306 Canadian undergraduates (151 female and 155 male).Average age was comparable to U.S. college samples (cf. Harris, 1995). Participants completedthe 29-item AQ using the same 5-point scale. The data consisted of the covariance matrixanalyzed by Harris (1995).

Sample 4. The fourth sample was used to assess the replicability of the rened four-factormodel using a new short form of the AQ. The sample consisted of 171 American undergrad-uates (123 females and 48 males) at a private metropolitan university who voluntarily partici-

pated. Average age was 18.35 ( SD

0.84). Respondents completed a shortened version of the AQ containing only the 12 items comprising the rened four-factor measurement model.


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Sample 5. The fth sample was also used to assess the replicability of the rened four-factor model using the new short form of the AQ. The sample consisted of 170 Americanundergraduates (124 females and 46 males) at a private metropolitan university who volun-tarily participated. Average age was 18.64 ( SD 1.57). Respondents completed the shortened12-item version of the AQ.

Aggression Questionnaire

Original AQ. Respondents in Samples 13 completed a battery of tests, including the 29-item Aggression Questionnaire (Buss & Perry, 1992; Buss & Warren, 2000). Participants ratedhow well each AQ item described themselves using the original 5-point scale, ranging fromextremely uncharacteristic of me (1) to extremely characteristic of me (5), as dened by theoriginal instrument. Following Buss and Perrys (1992, p. 453) instructions, each sample re-ceived a different random ordering of the 29 AQ items.

Short form of the AQ. Respondents in Samples 4 and 5 completed a new, shortened versionof the AQ containing only the 12 items comprising the rened four-factor measurement model.Using Buss and Perrys (1992, p. 454) Table 1, the randomized order of the items was 11,23, 8, 25, 21, 14, 15, 2, 13, 24, 6, and 20. Participants rated each AQ item using a 6-pointscale, ranging from extremely uncharacteristic of me (1) to extremely characteristic of me(6). Changing from the original 5-point scale to a 6-point scale eliminated the scales midpoint,thereby forcing respondents to decide whether each statement was characteristic of them. Aresponse scale with an even number of points also better enables researchers to use a median-split on single items to categorize respondents as aggressive versus nonaggressive in specic

situations (cf. Sudman & Bradburn, 1982). As a precedent, Velicer, Govia, Cherico, and Corri-veau (1985) have modied the response scale of the BussDurkee Hostility Scale to makethis instrument more reliable.

Criterion Measures

In addition to completing the AQ, a random subset of 180 participants in Sample 1 (70males and 110 females) also lled out a set of criterion measures for use in evaluating theAQs construct validity. These criterion measures served as standards for assessing the conver-

gent and discriminant validity of the dimensions comprising both Buss and Perrys originalfour-factor model and the new, rened measurement model for the AQ.Physical Aggression. As a criterion measure of physical aggression, we used the Assault

subscale from the BussDurkee Hostility Inventory (Buss & Durkee, 1957). Buss (1961) re-ported a 5-week testretest reliability of .78 for this subscale. As validity evidence, men whohave committed domestic violence score higher on the Assault subscale compared to controls(Maiuro, Cahn, Vitaliano, Wagner, & Zegree, 1988). Although the original BussDurkee As-sault subscale consisted of 10 items, we decided to use only those Assault items that had notbeen adapted by Buss and Perry in constructing the AQ. Specically, 5 Assault subscale items

were worded almost identically in Buss and Perrys AQ (BussDurkee items 9, 17, 25, 65,and 70). We chose to exclude these items from the Assault subscale because their comparablewording might otherwise spuriously inate the degree of association between this criterionmeasure and the AQ (cf. Nichols, Licht, & Pearl, 1982).

Verbal Aggression. As a criterion measure of verbal aggression, we used the Verbal Hostilitysubscale of the BussDurkee Hostility Inventory (Buss & Durkee, 1957). Buss (1961) reporteda 5-week testretest reliability of .72 for this subscale. Supporting construct validity, VerbalHostility score is a stronger predictor of hostile content in stories told in response to projectivestimuli (Buss, Fischer, & Simmons, 1962) and of verbal aggression in role-playing responses to

frustrating everyday events (Leibowitz, 1968) compared to the other BussDurkee subscales.Although the original Verbal Hostility subscale had 13 items, we omitted 5 of these (Buss


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Durkee items 7, 19, 23, 43, and 63) because of their nearly identical wording with AQ itemsto avoid articially inating the correlation between the AQ and this criterion measure (cf.Nichols et al., 1982).

Anger Arousal. As a criterion measure of anger, we chose the Anger Arousal subscale of the Multidimensional Anger Inventory (MAI; Siegel, 1986). We selected the Anger Arousal

subscale of the MAI as an anger criterion measure because it more closely matches Buss andPerrys (1992) conceptual denition of anger as involving physiological arousal (p. 457)compared to other anger scales and because it has been found to be more reliable than theanger-range, anger-in, and anger-out MAI subscales (Siegel, 1986). Siegel (1986) reportedreliability coefcients for this subscale of .83 for a college sample and .82 for a sample of factory workers. As validity evidence, Siegel (1986) found Anger Arousal scores correlatedsignicantly with the magnitude and duration subscales of the Harburg Anger-In/Anger-OutInventory (Harburg, Erfurt, Hauenstein, Chape, Schull, & Schork, 1973) and with the magni-tude subscale of the Novaco Anger Inventory (Novaco, 1975). Although the original MAI

Anger Arousal subscale contained eight items, we used only four of these (MAI items 9, 10,14, and 26) and omitted items with wording that overlapped the BussPerry items to avoidarticially inating the correlation between the AQ and this criterion measure (cf. Nichols etal., 1982).

Hostility. As a criterion measure of global hostility, we chose the CookMedley HostilityScale (Ho; Cook & Medley, 1954). Based on a subset of 50 truefalse items from the Minne-sota Multiphasic Personality Inventory, the Ho is intended to assess primarily cynicism andparanoid alienation. Scores on this instrument have a 3-year testretest correlation of .84(Shekelle, Gale, Ostfeld, & Paul, 1983). As evidence of prospective validity, the scale appears

to be an independent predictor of later coronary disease (Barefoot, Dahlstrom, & Williams,1983).

Measurement Models Evaluated in This Study

A systematic literature search uncovered four different measurement models for the AQcurrently in use: (a) a unidimensional total score model that assumes a single, global Ag-gression factor explains responses to all 29 AQ items; (b) Buss and Perrys (1992) originalfour-factor model (Physical Aggression, Verbal Aggression, Anger, and Hostility) for the 29-

item AQ; (c) Buss and Perrys (1992) hierarchical version of this four-factor model that as-sumes a single second-order Aggression factor underlies the covariation among the four rst-order factors; and (d) a modied four-factor model for 27 AQ items, consisting of Buss andPerrys original Physical Aggression, Verbal Aggression, and Anger factors, along with Har-riss (1995) reduced Hostility factor (omitting its sixth and eighth indicators).

We also evaluated the goodness-of-t of two new factor structures that we developed aspotential measurement models for the AQ. The rst of these new models consisted of ourrened version of Buss and Perrys original four factors for a subset of 12 AQ items. Thesecond new model was a hierarchical version of this rened four-factor model that assumes

a single-order Aggression factor underlies the covariation among the four rst-order factors.

Overview of Analyses

Our analyses addressed four main questions. (1) Do the existing one-, four-, or hierarchical-factor structures provide an acceptable measurement model for the AQ? To answer this ques-tion, we used conrmatory factor analysis (CFA) to impose each of these factor models onthree different data sets and to evaluate each models goodness-of-t across samples. (2) If available models prove inadequate, then what might be a more appropriate measurement model

for the AQ? Here we used principal components analysis to eliminate unreliable AQ itemsin order to develop an acceptable measurement model. (3) Are the same measurement models


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warranted for males and females? To address this question, we used multigroup CFA to testhypotheses about the invariance of the rened AQ measurement model with respect to gender.(4) Is there any evidence for the convergent or discriminant validity of the multiple AQ factors?Here we used CFA to test hypotheses about the relationships among the AQ factors and thecriterion measures of aggression.

Analysis Strategy

Stage One. The analysis unfolded in four stages, each using CFA via LISREL 8 (Joreskog &Sorbom, 1996). In Stage One, we began by using the data from Samples 13 to examine thet of the four, existing measurement models for the AQ. To evaluate each models goodness-of-t to the data, we used three measures of absolute t and two measures of relative t (cf.Hu & Bentler, 1998). These multiple measures of model t provide complementary informa-tion about how well a particular model explains the data and should not be construed as

redundant (cf. Bollen, 1989; McDonald & Marsh, 1990).As measures of each models absolute t, we used the ratio of chi-square to degrees of freedom ( 2 / df; Hoelter, 1983), the goodness-of-t index (GFI; Joreskog & Sorbom, 1996),and the root-mean-square error of approximation (RMSEA; Steiger, 1989). Although the rsttwo of these measures of model t have limited utility (Hu & Bentler, 1998), we have reportedthem in order to maximize the comparability of our results with those of prior researcherswho reported these t measures for the same models. In judging absolute t, smaller ratiosof chi-square to degrees of freedom reect better absolute t, with ratios near two consideredacceptable (Hoelter, 1983). Analogous to R2 in multiple regression, GFI reects the proportion

of available variationcovariation information in the data that the given model explains, withlarger GFI values representing better model t. Bentler and Bonett (1980) have suggested thatformal measurement models have a GFI .90. RMSEA reects the size of the residuals thatresult when using the model to predict the data, with smaller values indicating better t. Ac-cording to Browne and Cudeck (1993), RMSEA of .05 or lower represents close t,RMSEA between .05 and .08 represents reasonably close t, and RMSEA above .10 repre-sents an unacceptable model. We also directly compared the absolute t of nested modelsby contrasting their goodness-of-t chi-square values and computing the p value associatedwith the difference in these nested chi-squares (with accompanying difference in degrees of

freedom).As measures of each models relative t, we used the comparative t index (CFI; Bentler,1990) and the nonnormed t index (NNFI; Bentler & Bonett, 1980; Tucker & Lewis, 1973).We have chosen to report these particular measures because they have more desirable psycho-metric properties than other measures of relative t (Bentler, 1990; Hu & Bentler, 1998; Marsh,Balla, & Hau, 1996; McDonald & Marsh, 1990). Each of these two relative t measures usesa different formula to contrast the goodness-of-t chi-square of a given model with that of anull model, which assumes sampling error alone explains the covariation among observedmeasures (i.e., that there is no common variance among the AQ items). For each relative t

index, larger values represent better t, with values of .90 or higher considered acceptable(Bentler & Bonett, 1980).Stage Two. Given the poor t of the unidimensional and multidimensional models, we

sought to develop a better-tting, rened measurement model in Stage Two of the analysis.Stage Two consisted of four phases. In the rst phase (model renement), we subjected thedata of Sample 1 to a principal components analysis (PCA) with oblique rotation in order toexplore the structure underlying the AQ. Extracting four factors, we looked for items withlow communalities or multiple loadings across factors to identify questions that are unreliableindicators of aggression or that reect more than one dimension of aggression. We also decided

to omit items that are reverse-scored because we wanted the rened measurement model touse only indicators that reect the endorsement of aggression rather than the rejection of


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nonaggression. This latter approach has been useful in rening measurement models for otherconstructs, such as affect intensity (Bryant et al., 1996).

In the second phase of Stage Two (model evaluation), we used CFA to impose a parsimoni-ous conrmatory version of this new measurement model on the data of Samples 13, usingthe rened subset of AQ items. We also evaluated a hierarchical form of this model in which

a single, second-order factor explained the relationships among the four rst-order factors. Inaddition, we used multigroup CFA to evaluate the generalizability of these rened measure-ment models across Samples 13. In these multigroup analyses, we contrasted the goodness-of-t chi-squares of two nested CFA models: one constraining the magnitudes of the factorloadings to be equal for all three samples and the other omitting this invariance constraint.A statistically signicant difference in the chi-square values of these two models ( 2) indi-cates that the given model yields different factor loadings across samples (cf. Bryant & Baxter,1997; Bryant & Yarnold, 1995). Given a signicant overall structural difference, we usedmultigroup CFA with equality constraints to pinpoint the specic items responsible for cross-

sample differences. In accordance with standard practice in the structural equation modelingliterature, all multigroup analyses were performed using covariance matrices as input (cf.Joreskog & Sorbom, 1996).

In the third phase of Stage Two, for comparison purposes we tested a condensed, alternativeform of Buss and Perrys (1992) original four-factor that preserved the full range of itemcontent while reducing the number of indicators per factor. Here we used a partial disaggrega-tion approach (Bagozzi & Edwards, 1998; Bagozzi & Heatherton, 1994; Hull, Lehn, & Ted-lie, 1991) to recongure Buss and Perrys (1992) original total disaggregation model (whichhad nine indicators for PA, ve indicators for VA, seven indicators for ANG, and eight indica-

tors for HO) in terms of three indicators for each latent variable. This entailed parceling indi-vidual items into composite indicators for each factor, so as to modify the atomistic originalmodel into a more molecular form. As Bagozzi and Heatherton (1994) have noted, CFAmodels containing more than about ve measures per factor are unlikely to t the data satisfac-torily. For this reason, we sought to test the goodness-of-t of a condensed form of Buss andPerrys original four-factor model and to evaluate its cross-sample generalizability.

In the fourth phase of Stage Two (testing gender invariance), we used multigroup CFA todetermine whether the rened measurement models provided an equivalent goodness-of-t tothe data of males and females in Samples 1 and 2. This involved contrasting the goodness-

of-t chi-squares of two nested CFA models: one constraining the magnitudes of the factorloadings to be equal for males and females and the other omitting this invariance constraint.A statistically signicant difference in the chi-square values of these two models ( 2) indi-cates that the given model yields different factor loadings for men and women (cf. Bryant &Baxter, 1997; Bryant & Yarnold, 1995). Given a signicant overall structural difference, weused multigroup CFA with equality constraints to pinpoint the specic items responsible forgender differences. Again, all multigroup analyses were performed on covariance matrices(cf. Joreskog & Sorbom, 1996).

Stage Three. In Stage Three of the analysis, we evaluated and compared the convergent

and discriminant validity of the rened and original versions of the four-factor model. Herewe used CFA with equality constraints to determine whether each of the four AQ factorsshowed a stronger relationship with the criterion measure to which it is presumed to correspondthan with the other criterion measures.

Stage Four. Having established the cross-sample generalizability of the rened measurementmodel, we sought to reconrm it in the nal stage of the analysis using a new short formof the AQ, which contains only the rened subset of 12 items. Here we used CFA to imposethe rened measurement model on the data of Samples 4 and 5, who completed this new,short form of the AQ. We also used multigroup CFA to assess the generalizability of the

rened measurement model across Samples 4 and 5 as well as the models invariance withrespect to gender in both of these samples.


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RESULTS AND DISCUSSIONStage One: Assessing Current Measurement Models

We used CFA rst to evaluate the goodness-of-t of the four alternative

measurement models currently in the literature, using the AQ data of Sam-ples 13. Which model, if any, provides the most reasonable representationof responses to this instrument? Table 1 presents the results of these analyses.Across all three samples, the explanatory power of existing measurementmodels fell short of accepted standards. First, a single AQ total scoreprovided an inadequate measurement model for Samples 13, leaving toomuch common variance unexplained in both an absolute (GFIs .65 .70)and relative (t indices .59 .66) sense. For all three samples, this one-factor model also had a relatively high ratio of chi-square to degrees of free-dom ( 2 / dfs 3.4 4.2) and an unacceptably large, root-mean-square errorof approximation (RMSEAs .098 .109). These ndings support theAQs multidimensionality.

Yet, none of the multidimensional models currently available provides anacceptable measurement model for the AQ. Both Buss and Perrys (1992)original four-factor model and its hierarchical counterpart t the data of all

three samples better than the unidimensional model, all 2

s(6) 379.2, ps.0001. However, for all three samples, each of these multifactor structuresfails to achieve sufcient goodness-of-t to be an acceptable measurementmodel in both absolute (GFIs .76 .81) and relative (t indices .76.82) terms. Furthermore, the chi-square to degrees of freedom ratios for thesemodels ( 2 / dfs 2.4 2.8) show a poor t (Buss & Perry, 1992, p. 454),and their RMSEAs show room for improvement (RMSEAs .072 .084).Evidently, current measurement models of the AQ operationalize underlyingsubtraits of aggression in ways that do not correspond closely enough to theconceptual framework that Buss and Perry (1995) intended. This conclusionis consistent with those of previous researchers (e.g., Archer, Kilpatrick, &Bramwell, 1995; Harris, 1995; Williams et al., 1996) who have noted theinadequacy of existing factor models for the AQ.

Imposed on the data of Samples 13, the four-factor model containingHarriss (1995) condensed Hostility factor fared little better (see Table 1).

Although this modied model was a signicant improvement in t over theoriginal four-factor model for all three samples, all 2(53)s 143.6, p.0001, it nevertheless fell short of accepted standards for a formal measure-ment in both an absolute (GFIs .78 .83) and relative (t indices .79 .83) sense. Taken as a whole, this evidence underscores the need fora better tting measurement model for the AQ.

Stage Two: Developing a Better Fitting Measurement Model

What might a more appropriate measurement model look like, and howshould we best go about developing it? In answering these questions, we


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T A B L E 1

G o o d n e s s - o

f - F i t S t a t i s t i c s f o r V a r i o u s M e a s u r e m e n t M o d e l s o f t h e A Q I m p o s e d

o n S a m p l e s 1 3

R e l a t i v e

A b s o l u t e t m e a s u r e s

t m e a s u r e s

M o d e l

N o . i t e m s

S a m p l e

2

d f

2

/ d f

G F I

R M S E A

C F I

N N F I

O n e - f a c t o r

2 9

1

1 5 6 7

. 9

3 7 7

4 . 2

. 7 0

. 1 0 2

. 6 6

. 6 4

( t o t a l s c o r e )

2

1 2 6 7

. 8

3 7 7

3 . 4

. 6 5

. 1 0 9

. 6 2

. 5 9

3

1 4 6 9

. 1

3 7 7

3 . 9

. 6 8

. 0 9 8

. 6 6

. 6 3

B u s s & P e r r y s

2 9

1

1 0 4 2

. 8

3 7 1

2 . 8

. 8 1

. 0 7 7

. 8 1

. 7 9

f o u r f a c t o r s :

2

8 8 6 . 4

3 7 1

2 . 4

. 7 6

. 0 8 4

. 7 8

. 7 6

P A , V

A , A

N G

, H O

3

9 5 0 . 3

3 7 1

2 . 6

. 8 1

. 0 7 2

. 8 2

. 8 0


2 9

1

1 0 4 6

. 4

3 7 3

2 . 8

. 8 1

. 0 7 7

. 8 1

. 7 9

h i e r a r c h i c a l m o d e l :

2

8 8 8 . 5

3 7 3

2 . 4

. 7 6

. 0 8 3

. 7 8

. 7 6

o n e s e c o n d - o r d e r f a c t o r

3

9 6 9 . 6

3 7 3

2 . 6

. 8 1

. 0 7 2

. 8 1

. 8 0


2 7

1

8 8 1 . 9

3 1 8

2 . 9

. 8 2

. 0 7 6

. 8 3

. 8 2

P A , V

A , A

N G

, &

2

7 3 4 . 2

3 1 8

2 . 3

. 7 8

. 0 8 1

. 8 1

. 7 9

H a r r i s s H O f a c t o r

3

8 0 6 . 6

3 1 8

2 . 5

. 8 3

. 0 7 1

. 8 3

. 8 1

F o u r r e n e d f a c t o r s :

1 2

1

1 0 5 . 7

4 8

2 . 2

. 9 4

. 0 6 3

. 9 6

. 9 4

P A , V

A , A

N G

, H O

2

9 2 . 4

4 8

1 . 9

. 9 3

. 0 6 8

. 9 5

. 9 3

3

1 2 1 . 7

4 8

2 . 5

. 9 4

. 0 7 1

. 9 1

. 8 7

R e n e d h i e r a r c h i c a l

1 2

1

1 0 8 . 5

5 0

2 . 2

. 9 4

. 0 6 2

. 9 6

. 9 4

m o d e l :

2

9 4 . 4

5 0

1 . 9

. 9 3

. 0 6 7

. 9 5

. 9 3

o n e s e c o n d - o r d e r f a c t o r

3

1 3 3 . 6

5 0

2 . 7

. 9 3

. 0 7 4

. 9 0

. 8 6

N o t e .

P A

P h y s i c a l A g g r e s s i o n ; V A

V e r b a l A g g r e s s i o n ; A N G

A n g e r ; H O

H o s t i l i t y ; G F I

g o o d n e s s - o f - t i n d e x ( J o r e s k o g & S o r b o m ,

1 9 9 6 ) ; R M S E A

r o o t - m e a n - s q u a r e e r r o r o f a p p r o x i m a t i o n ( S t e i g e r , 1

9 8 9 ) ; C F I

c o m p a r a t i v e t i n d e x ( B e n t l e r , 1 9 9 0 ) ; N N F I

n o n n o r m e d

t i n d e x ( B e n t l e r & B o n e t t , 1 9 8 0 ) . S a m p l e 1

3 0 7 A m e r i c a n u n d e r g r a d u a t e s ; S a m p l e 2

2 0 0 B r i t i s h u n d e r g r a d u a t e s ( A r c h e r , H o l l o w a y , &

M c L o u g h l i n

, 1 9 9 5 ) ; S a m p l e 3

3 0 6 C a n a d i a n u n d e r g r a d u a t e s ( H a r r i s , 1

9 9 5 ) . T h e a b o v e g o o d n e s s - o f - t s t a t i s t i c s a r e f r o m a n a l y s e s c o n d u c t e d

v i a L I S R E L 8 ( J o r e s k o g &

S o r b o m , 1

9 9 6 )

.


12/30


sought rst to preserve the solid theoretical foundation underlying Buss andPerrys (1992) original four-factor model, while at the same time sharpeningits measurement focus. Accordingly, we set out not only to maintain theconceptual denitions of the original factors, but also to improve the four-

factor models goodness-of-t by eliminating AQ items that were relativelyunreliable indicators of the dimensions they were intended to reect.

Model renement. With these goals in mind, we inspected the results fromprincipal components analysis (PCA) of Sample 1 data and decided to ex-clude AQ items according to three criteria. First, we eliminated items withlow loadings ( .40) in order to increase the proportion of variance thatfactors explained in their constituent indicators. Second, to enhance the con-ceptual clarity of the model, we excluded items that loaded at least moder-ately ( .40) on two or more scales, based on CFA modication indicesand PCA results. Third, to improve conceptual precision, we omitted itemsthat did not reect the direct endorsement of aggressive traits. The AQ in-cludes two reverse-scored itemsa Physical Aggression item (I can think of no good reason for ever hitting a person) and an Anger item (I am aneven-tempered person)which entail the rejection of nonaggressive traitsrather than the acceptance of aggressive characteristics. These three exclu-

sion criteria yielded a rened 12-item, four-factor model that reects thesame underlying constructs (Physical Aggression, Verbal Aggression,Anger, and Hostility) as Buss and Perrys (1992) original model, but withan equal number of items for each factor. Table 2 presents the items compris-ing both the original and rened versions of the four-factor model of theAQ.

Model evaluation. How well does this rened four-factor model explainresponses to the AQ? To address this question, we used CFA to impose therened measurement model on the data of Samples 13. In doing this, wehave used Sample 1 to modify the model post hoc and used Samples 2 and3 to cross-validate the model a priori. This strategy enabled us to assess thedegree to which model respecications based on Sample 1 generalized acrossindependent samples, so as to avoid being misled by the unique characteris-tics of a single sample (cf. MacCallum, 1986; MacCallum, Roznowski, &Necowitz, 1992).

Table 1 also presents the results of these analyses. As seen in this table,across all three samples, the rened four-factor model explains an acceptableproportion of common variance in both absolute (GFIs .93 .94) andrelative (t indices .87 .96) terms. Although its ratio of chi-square todegrees of freedom shows cross-sample inconsistency ( 2 / dfs 1.9 2.5),the rened models RMSEA reects reasonably close t across all three sam-ples (RMSEAs .063 .071). Considered together, these ndings suggestthat the modied four-factor model is an appropriate measurement modelfor the AQ.


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TABLE 2Items Constituting the Original and Rened Measurement Models of the AQ

Factor Constituent items

Physical Aggression 1. Once in a while I cant control the urge to hit another person.2. Given enough provocation, I may hit another person.3. If somebody hits me, I hit back.4. I get into ghts a little more than the average person.5. If I have to resort to violence to protect my rights, I will.6. There are people who pushed me so far that we came to

blows.7. I can think of no good reason for ever hitting a person.

[reverse-scored]

8. I have threatened people I know.9. I have become so mad that I have broken things.

Verbal Aggression 10. I tell my friends openly when I disagree with them.11. I often nd myself disagreeing with people.12. When people annoy me, I may tell them what I think of them.13. I cant help getting into arguments when people disagree

with me.14. My friends say that Im somewhat argumentative.

Anger 15. I are up quickly but get over it quickly.16. When frustrated, I let my irritation show.17. I sometimes feel like a powder keg ready to explode.18. I am an even-tempered person. [reverse-scored]19. Some of my friends think Im a hothead.20. Sometimes I y off the handle for no good reason.21. I have trouble controlling my temper.

Hostility 22. I am sometimes eaten up with jealousy.23. At times I feel I have gotten a raw deal out of life.24. Other people always seem to get the breaks.25. I wonder why sometimes I feel so bitter about things.26. I know that friends talk about me behind my back.27. I am suspicious of overly friendly strangers.28. I sometimes feel that people are laughing at me behind my

back.29. When people are especially nice, I wonder what they want.

Note: The 29 items constituting the original four-factor model for the Aggression Question-

naire (AQ) are listed in the order presented by Buss and Perry (1992, Table 1, p. 454). Bussand Perry (1992) instructed researchers to randomly order the above items when administeringthe AQ. The order of the 29 AQ items for Sample 1 was 26, 15, 11, 10, 16, 27, 2, 4, 29, 12,21, 13, 14, 8, 5, 22, 28, 7, 20, 6, 25, 19, 23, 3, 24, 1, 9, 17, and 18. Items in bold comprisethe rened four-factor measurement model. The randomized order of these questions in the12-item short form of the AQ is 11, 23, 8, 25, 21, 14, 15, 2, 13, 24, 6, and 20. From TheAggression Questionnaire, by A. H. Buss and M. Perry, 1992, Journal of Personality and Social Psychology, 63, p. 454 (Table 1). Copyright by the American Psychological Associa-tion. Adapted with permission.


14/30


Results converge on an identical conclusion concerning the hierarchicalversion of this rened model. Specically, a model specifying a single, over-arching second-order aggression trait that explains the covariation amongthe four rst-order factors t the data of all three samples reasonably well,

both absolutely (GFIs .93 .94) and relatively (t indices .86 .96).This hierarchical model also showed chi-square to degrees of freedom ratios( 2 / dfs 1.9 2.7) and RMSEAs ( .062 .074) comparable to thoseof the rened four-factor model across the three samples. Thus, both therened four-factor model and its hierarchical counterpart represent accept-able measurement models for the AQ.

Testing cross-sample generalizability. Having identied an appropriatemeasurement structure, we next used multigroup CFA to evaluate the cross-sample generalizability of the four-factor model more systematically. Weconsidered rst the question of whether the rened four-factor model pro-duces the same factor loadings across the three samples. In other words, doPhysical Aggression, Verbal Aggression, Anger, and Hostility have the samemeanings for American (Sample 1), British (Sample 2), and Canadian (Sam-ple 3) undergraduates?

Table 3 presents the loadings for the four-factor model imposed on the

data of each sample. An initial omnibus test revealed that the magnitudesof these factor loadings varied across samples, 2(16, n 813) 29.3, p .022. Following up the omnibus test, only Samples 1 and 3 showedsignicant differences in factor loadings, 2(8, n 613) 24.3, p .003,whereas loadings were equivalent for Samples 1 and 2, 2(8, n 507)11.1, p .19; and Samples 2 and 3, 2(8, n 506) 7.7, p .46. Addi-tional multigroup CFAs disclosed that only one factor loading actually dif-fered signicantly for Samples 1 and 3the loading for Anger item 1 (Iare up quickly but get over it quickly) was stronger for the Canadiansample, 2(1, n 613) 13.8, p .0003and all other loadings for thefour-factor model were statistically comparable, 2(7, n 613) 12.5, p .09. Supporting this conclusion, a model that constrains (a) all factorloadings except Anger item 1 to be equal across Samples 13 and (b) Angeritem 1 to load equally for Samples 1 and 2 but not for Sample 3 t the dataof the three samples no worse than a multigroup model with no equality

constraints, 2(15, n 813) 19.5, p .19. These results indicate thatthe loadings of the four-factor model are largely (11/12 92%) invariantacross the three samples; they also suggest that the meaning of aggression,as dened by the rened measurement model, holds across culture.

The same cannot be said of Buss and Perrys (1992) original four-factormodel, which produced nonequivalent loadings for all three samples, 2(50,n 813) 554.8, p .0001. Indeed, the original four-factor model yieldedstrong differences in loadings when comparing Samples 1 and 2, 2(25,n 507) 67.6, p .0001; Samples 2 and 3, 2(25, n 506) 634.4,


15/30


T A B L E 3

C F A F a c t o r L o a d i n g s f o r t h e R e n e d 1 2 - I t e m , F

o u r - F a c t o r M e a s u r e m e n t M o d e l o f t h e A Q

P A

V A

A N G

H O

s a m p l e

s a m p l e

s a m p l e

s a m p l e

A Q i t e m s

1

2

3

1

2

3

1

2

3

1

2

3

2 . G i v e n e n o u g h p r o v o c a t i o n , I m a y h i t a n o t h e r p e r s o n .

7 6

7 0

5 8

6 . T h e r e a r e p e o p l e w h o p u s h e d m e s o f a r t h a t w e c a m e t o b l o w s .

7 2

7 3

6 5

8 . I h a v e t h r e a t e n e d p e o p l e I k n o w .

8 0

8 2

6 8

1 1 . I o f t e n n d m y s e l f d i s a g r e e i n g w i t h p e o p l e

.

8 0

7 5

7 0

1 3 . I c a n t h e l p g e t t i n g i n t o a r g u m e n t s w h e n p e o p l e d i s a g r e e w i t h m e .

8 2

7 1

6 8

1 4 . M y f r i e n d s s a y t h a t I m

s o m e w h a t a r g u m e n t a t i v e .

5 8

6 1

7 6

1 5 . I a r e u p q u i c k l y b u t g e t o v e r i t q u i c k l y .

5 0

6 2

6 9

2 0 . S o m e t i m e s I y o f f t h e h a n d l e f o r n o g o o d r e a s o n

8 1

8 3

5 7

2 1 . I h a v e t r o u b l e c o u n t r o l l i n g m y t e m p e r .

7 1

7 1

3 4

2 3 . A t t i m e s I f e e l I h a v e g o t t e n a r a w d e a l o u t o f l i f e

.

6 5

7 6

4 5

2 4 . O t h e r p e o p l e a l w a y s s e e m t o g e t t h e b r e a k s

.

7 7

7 5

6 4

2 5 . I w o n d e r w h y s o m e t i m e s I f e e l s o b i t t e r a b o u t t h i n g s .

6 8

6 8

5 2

N o t e .

P A



A n g e r ; H O

H o s t i l i t y

. D e c i m a l p o i n t s a r e o m i t t e d . I

t e m n u m b e r s i n

p a r e n t h e s e s r e f e r t o t h e o r i g i n a l o r d e r i n g o f i t e m s i n B u s s a n d P e r r y s ( 1 9 9 2 , p . 4 5 4 ) T a b l e 1 . B l a n k l o a d i n g s w e r e x e d a t z e r o . T h e l o a d i n g s o f

i t e m s 2 , 1 4

, 2 0 , a n d 2 3 w e r e x e d a t u n s t a n d a r d i z e d

v a l u e s o f 1 . 0 t o s c a l e t h e l a t e n t v a r i a b l e s i n m u l t i g r o u p c o n r m a t o r y a n a l y s e s .


16/30


p .0001; and Samples 1 and 3, 2(25, n 613) 126.9, p .0001.Clearly, the rened measurement model is superior to the original in termsof both its goodness-of-t and its cross-cultural generalizability.

Comparing the rened hierarchical model across samples, the second-

order Aggression factor had the same relationships with the four rst-orderfactors in Samples 1 and 2, 2(3, n 507) 0.6, p .89; but the Aggressionsuper factor had less to do with Anger in Canadian Sample 3 comparedto American Sample 1, 2(1, n 613) 25.5, p .0001; and British Sample2, 2(1, n 506) 24.6, p .0001 (see Table 4). These results are consis-tent with the earlier nding that the four-factor model ts the data of Sample3 better than the hierarchical model.

Comparing the original hierarchical model across samples, the second-order Aggression factor had the same relationships with the four rst-orderfactors in Samples 1 and 2, 2(3, n 507) 1.9, p .59; but the Aggressionsuper factor had less to do with Anger in Canadian Sample 3 comparedto American Sample 1, 2(1, n 613) 22.6, p .00005; and BritishSample 2, 2(1, n 506) 28.8, p .00001 (see Table 4). Unlike therened hierarchical model, however, second-order Aggression also had moreto do with Hostility in Canadian Sample 3 compared to the American Sample

1, 2(1, n 613) 34.0, p .00001; and British Sample 2, 2(1, n 506)16.6, p .0009 (see Table 4). Thus, the rened second-order CFA model

showed stronger cross-cultural generalizability than did the original second-order CFA model.

We also addressed the question of whether the four factors comprisingthe rened model interrelate in the same ways for the American, British, andCanadian samples. Table 5 presents the reliabilities and factor intercorrela-tions for this model imposed on the data of Samples 13. Using the modelwith partially invariant loadings as a baseline (cf. Byrne, Shavelson, & Mu-then, 1989), the rened four-factor model produced different factor correla-tions for the three samples, 2(12, n 813) 65.3, p .0001. AlthoughSamples 1 and 2 had equivalent factor intercorrelations, 2(6, n 507)3.1, p .79; Sample 3 had different factor intercorrelations compared toSample 1, 2(6, n 613) 53.1, p .0001; and Sample 2, 2(6, n506) 46.3, p .0001. Thus, the four rened AQ factors interrelated differ-

ently among the Canadian sample than among the American and Britishsamples.

Although the correlation between Physical and Verbal Aggression wasthe same in all three samples, 2(2) 4.2, p .12, Physical Aggressioncorrelated more strongly with Anger in the Canadian sample than in the othertwo samples, both 2(1)s 5.1, ps .025. For the Canadian sample, Ver-bal Aggression also correlated more strongly with Anger, both 2(1)s 14.0, ps .002; but Hostility correlated less strongly with Physical Ag-gression, both 2(1)s 9.2, ps .0025, with Verbal Aggression, both


17/30


T A B L E 4

S e c o n d - O r d e r F a c t o r L o a d i n g s a n d R e s i d u a l V a r i a n c e s o f t h e F i r s t - O r d e r F a c t o r s f o r t h e O r i g i n a l a n d R e n e d H i e r a r c h i c a l C

F A M o d e l

I m p o s e d o n t h e A Q D a t a o f S a m p l e s 1 3

S a m p l e 1

S a m p l e 2

S a m p l e 3

A Q f a c t o r s

M o d e l

P A

V A

A N G

H O

P A

V A

A N G

H O

P A

V A

A N G

H O

F a c t o r l o a d i n g

O r i g i n a l

1 . 0 0 *

. 9 9

1 . 0 1

. 5 4

1 . 0 0 *

1 . 1 8

1 . 3 3

. 6 3

1 . 0 0 *

. 9 3

. 4 2

1 . 4 4

( )

R e n e d

1 . 0 0 *

. 8 0

1 . 2 1

. 7 7

1 . 0 0 *

. 7 5

1 . 2 3

. 8 1

1 . 0 0 *

. 9 6

. 4 7

1 . 0 1

S t a n d a r d e r r o r o f

O r i g i n a l

. 1 0

. 1 1

. 0 7

. 1 6

. 1 7

. 1 1

. 1 2

. 0 8

. 1 7

f a c t o r l o a d i n g

R e n e d

. 1 2

. 1 6

. 1 2

. 1 3

. 2 0

. 1 6

. 1 6

. 1 1

. 1 8

S t a n d a r d i z e d

O r i g i n a l

. 7 6

. 8 0

. 9 9

. 6 4

. 7 6

. 8 6

. 9 5

. 6 1

. 7 5

. 6 5

. 6 3

. 9 9

f a c t o r l o a d i n g

R e n e d

. 7 1

. 8 3

. 9 0

. 6 6

. 7 7

. 8 4

. 8 6

. 5 4

. 7 1

. 6 2

. 7 0

. 9 9

S q u a r e d m u l t i p l e

O r i g i n a l

. 5 7

. 6 4

. 9 9

. 4 1

. 5 8

. 7 3

. 9 0

. 3 7

. 5 6

. 4 3

. 4 0

. 9 9

c o r r e l a t i o n

R e n e d

. 5 0

. 6 8

. 8 1

. 4 3

. 5 9

. 7 0

. 7 4

. 2 9

. 5 1

. 3 8

. 4 8

. 9 9

R e s i d u a l v a r i a n c e

O r i g i n a l

. 5 5

. 4 0

. 0 1

. 3 1

. 3 5

. 2 5

. 1 0

. 3 3

. 3 3

. 4 8

. 1 1

. 0 1

( )

R e n e d

. 3 8

. 1 1

. 1 3

. 3 0

. 3 0

. 1 0

. 2 2

. 7 0

. 3 2

. 5 1

. 0 8

. 0 1

S t a n d a r d e r r o r o f

O r i g i n a l

. 0 8

. 0 7

. 0 4

. 0 6

. 0 7

. 0 8

. 0 6

. 0 7

. 0 6

. 0 8

. 0 3

. 0 6

r e s i d u a l v a r i a n c e

R e n e d

. 0 7

. 1 1

. 0 5

. 0 6

. 0 8

. 0 4

. 0 8

. 1 4

. 0 8

. 0 9

. 0 3

. 0 4

S t a n d a r d i z e d

O r i g i n a l

. 4 3

. 3 6

. 0 1

. 5 9

. 4 2

. 2 7

. 1 0

. 6 3

. 4 4

. 5 7

. 6 0

. 0 1

r e s i d u a l v a r i a n c e

R e n e d

. 5 0

. 3 2

. 1 9

. 5 7

. 4 1

. 3 0

. 2 6

. 7 1

. 4 9

. 6 2

. 5 2

. 0 1

N o t e :

P A



A n g e r ; H O

H o s t i l i t y

. S a m

p l e 1

3 0 7 A m e r i c a n u n d e r g r a d u a t e s ;

S a m p l e 2


M c L o u g h l i n , 1 9 9 5 ) ; S a m p l e 3


9 9 5 )

.

T a b l e d a r e r e s u l t s f r o m s e c o n d - o r d e r C F A m o d e l s i m p o s e d s e p a r a t e l y o n t h e d a t a o f e a c h s a m p l e . S e c o n d - o r d e r f a c t o r l o a d i n g s ( s ) a r e u n s t a n d a r d -

i z e d r e g r e s s i o n c o e f c i e n t s

r e p r e s e n t i n g t h e a m o u n t o f c h a n g e i n r s t - o r d e r f a c t o r s c o r e s r e s u l t i n g f r o m a o n e - u n i t c h a n g e i n t h e s e c o n d - o r d e r

l a t e n t v a r i a b l e . S t a n d a r d i z e d s e c o n d - o r d e r f a c t o r l o a d i n g s a r e s t a n d a r d i z e d r e g r e s s i o n c o e f c i e n t s r e p r e s e n t i n g t h e c h a n g e i n s t a n d a r d d e v i a t i o n s

i n

r s t - o r d e r f a c t o r s c o r e s r e s u l t i n g f r o m a 1 - s t a n d a r d - d e v i a t i o n c h a n g e i n t h e s e c o n d - o r d e r f a c t o r . S q

u a r e d m u l t i p l e c o r r e l a t i o n s r e p r e s e n t t h e

p r o p o r t i o n o f t o t a l v a r i a n c e i n e a c h r s t - o r d e r f a c t o r t h a t i s a s s o c i a t e d w i t h t h e s e c o n d - o r d e r f a c t o r , a n a l o g o u s t o R

2

i n m u l t i p l e r e g r e s s i o n . R

e s i d u a l

v a r i a n c e s ( s ) r e p r e s e n t t h e

a m o u n t o f v a r i a n c e i n r s t - o r d e r f a c t o r s t h a t i s u n e x p l a i n e d b y t h e s e c o n d - o r d e r f a c t o r . S

t a n d a r d i z e d r e s i d u a l v a r i a n c e s

r e p r e s e n t t h e p r o p o r t i o n o f t o t a l v a r i a n c e i n e a c h r s t - o r d e r f a c t o r t h a t i s u n r e l a t e d t o t h e s e c o n d - o r d e r f a c t o r a n d t h a t i s s p e c i c t o

t h a t r s t - o r d e r

f a c t o r . S t a n d a r d e r r o r s o f s e c o n d - o r d e r f a c t o r l o a d i n g s ( a n d o f r e s i d u a l v a r i a n c e s ) r e p r e s e n t t h e s t a n d a r d

d e v i a t i o n o f c h a n g e s i n l o a d i n g s ( a n d i n

r e s i d u a l v a r i a n c e s ) t h a t w o u l d b e e x p e c t e d t o o c c u r f r o m s a m p l e t o s a m p l e .

* F i x e d a t v a l u e o f 1 . 0 t o d e n e t h e m e t r i c o f t h e s e c o n d - o r d e r l a t e n t v a r i a b l e i n t h e u n s t a n d a r d i z e d s o l u t i o n .


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T A B L E 5

R e l i a b i l i t i e s a n d C F A F a c t o r I n t e r c o r r e l a t i o n s f o r t h e O r i g i n a l a n d R e n e d F o u r - F a c t o r M o d e l s

S a m p l e 1

S a m p l e 2

S a m p l e 3

A Q f a c t o r s

M o d e l

P A

V A

A N

G

H O

P A

V A

A N G

H O

P A

V A

A N G

H O

P A

O r i g i n a l

8 6 a

8 4 a

8 4 b

R e n e d

8 0 a

8 0 a

V A

O r i g i n a l

6 0

7 4 a

6 4

6 8 a

6 2

7 5 b

R e n e d

5 7

7 7 a

6 3

7 3 a

5 8

A N G

O r i g i n a l

7 4

8 1

8 2 a

7 2

8 2

8 3 a

3 7

3 7

8 0 b

R e n e d

6 3

7 6

7 1 a

6 6

7 4

7 3 a

3 9

3 5

H O

O r i g i n a l

5 4

4 7

6 3

7 6 a

5 2

4 8

5 7

8 1 a

7 5

6 4

6 7

8 3 b

R e n e d

5 3

5 3

5 7

7 3 a

4 7

4 3

4 3

7 7 a

8 0

6 6

8 5

N o t e :

P A



A n g e r ; H O

H o s t i l i t y

. S a m

p l e 1

3 0 7 A m e r i c a n u n d e r g r a d u a t e s ;

S a m p l e 2


M c L o u g h l i n , 1 9 9 5 ) ; S a m p l e 3


9 9 5 )

.

T a b l e d b e l o w t h e r e l i a b i l i t y c o e f c i e n t s a r e f a c t o r c o r r e l a t i o n s f r o m c o n r m a t o r y f a c t o r a n a l y s e s i n w h i c h l a t e n t f a c t o r s a n d m e a s u r e d v a r i a b l e s

h a v e b e e n s t a n d a r d i z e d s e p a r a t e l y w i t h i n e a c h s a m p l e

. D e c i m a l p o i n t s a r e o m i t t e d .

a

C r o n b a c h s a l p h a ( a n i n d e x o f i n t e r n a l c o n s i s t e n c y ) f o r u n i t - w e i g h t e d o r i g i n a l a n d r e n e d f a c t o r s c o r e s .

b

R e l i a b i l i t y c o e f c i e n t s o r i g i n a l l y r e p o r t e d b y H a r r i s ( 1 9 9 5 , T a b l e 2 , p . 9 9 3 )

. W e c o u l d n o t c o m p u t e r e l i a b i l i t y c o e f c i e n t s f o r t h e r e n e d f a c t o r s

i n

S a m p l e 3 b e c a u s e o n l y t h e c o v a r i a n c e m a t r i x ( b u t n o t t h e n e c e s s a r y r a w d a t a ) w a s a v a i l a b l e f o r r e a n a l y s i s o f t h i s d a t a s e t .


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2(1)s 3.8, ps .05, and with Anger, both 2(1)s 7.5, ps .006,compared to the American and British samples. Although interesting froma cross-cultural perspective, these differences in factor interrelationships donot alter the conclusion that the 12 AQ indicators measure the latent factors

in comparable ways for all three samples (cf. Kline, 1998).Comparing the original and rened factors. For purposes of comparison,

Table 5 also displays the correlations among Buss and Perrys (1992) originalfour factors in these same three samples. As evident in this table, the patternof correlations among the rened factors is strikingly similar to the patternof correlations among the original BussPerry factors. Indeed, the renedfactors have only slightly lower internal consistency reliabilities than theiroriginal counterparts. This is important because it suggests that rening thefactors improved the models overall goodness-of-t, but did not substan-tially reduce the reliabilities of the individual factors. 1

Testing a Partially Disaggregated form of Buss and Perrys originalmodel. Before abandoning Buss and Perrys (1992) original four-factormodel, we recongured it into a partially disaggregated measurementmodel that preserved the full range of totally disaggregated item contentwhile reducing the number of indicators per factor (cf. Bagozzi & Edwards,

1998; Bagozzi & Heatherton, 1994; Hull et al., 1991). To do this, we modi-ed the nine single-item indicators for PA into three composite measures,using as indicators (a) the mean of the three PA items from the rened mea-surement model; (b) the mean of original AQ items 1, 3, and 4; and (c) themean of original AQ items 5, 7, and 9. We modied the ve single-itemindicators for VA into three measures, using as indicators (a) the mean of the three VA items from the rened measurement model, (b) original AQitem 10, and (c) original AQ item 12. We modied the seven single-itemindicators for ANG into three composite measures, using as indicators (a)the mean of the three ANG items from the rened measurement model, (b)the mean of original AQ items 16 and 17, and (c) the mean of original AQitems 18 and 19. Finally, we modied the eight single-item indicators forHO into three composite measures, using as indicators (a) the mean of thethree HO items from the rened measurement model; (b) the mean of originalAQ items 22, 26, and 27; and (c) the mean of original AQ items 28 and 29.

We then imposed this partially disaggregated four-factor model on the

1 As further evidence concerning the degree of conceptual overlap between the rened andoriginal BussPerry factors, we correlated unit-weighted factor scores for the former and thelatter within Samples 1 and 2. (We were unable to correlate factor scores in Sample 3 becauseonly the covariance matrix, and not the necessary raw data, was available for reanalysis.)For Samples 1 and 2, respectively, these intercorrelations were uniformly high: (a) PhysicalAggression (.91 and .86), (b) Verbal Aggression (.90 in both samples), (c) Anger (.90 and

.85), and (d) Hostility (.83 and .85). These ndings suggest that the rened AQ factors basicallymeasure the same latent constructs as the original factors.


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data of Samples 1 and 2 to evaluate its goodness-of-t and cross-samplegeneralizability. (We could not construct partially disaggregated indicatorsfor Sample 3 because only the covariance matrix was available for reanalysisof this sample.) Although the partial disaggregation model provided a satis-

factory t to the data of Sample 1, 2(48, n 307) 157.6,

2 / df 3.3,

GFI .93, RMSEA .083, CFI .93, NNFI .91; it did not adequatelyt the data of Sample 2, 2(48, n 200) 197.4, 2 / df 4.1, GFI .87, RMSEA .120, CFI .88, NNFI .83. Multigroup analyses furtherdemonstrated that neither the factor loadings, 2(8, n 507) 32.2, p.0001, nor the factor variancescovariances, 2(10, n 507) 115.8, p .00001, of this partially disaggregated model were invariant across thetwo samples. Thus, even in a partially disaggregated form, Buss and Per-rys (1992) original four-factor model does not provide an acceptable mea-surement model for the AQ.

Testing the Gender Invariance of the Rened Model. Does aggressionmean the same thing to men and women? Is the rened measurement modelfor the AQ equally applicable to the data of males and females? This is acritical question for researchers interested in using the AQ to compare levelsof aggression in men and women. With respect to this question, Buss and

Perry (1992) reported that mens and womens loadings differed in separatefour-factor PCA solutions, though they did not directly test the gender invari-ance of the four-factor model.

The rened four-factor model generated gender-equivalent loadings forthe British Sample 2, 2(8, n 200) 6.0, p .64, but not for the Ameri-can Sample 1, 2(8, n 304) 21.4, p .007. (Because only the pooledcovariance matrix was available for reanalysis of Harriss data, we could nottest for gender invariance in Sample 3.) Follow-up multigroup CFAs re-vealed that only one factor loading actually differed signicantly for malesand females in Sample 1the loading for Physical Aggression item 3(There are people who have pushed me so hard that we came to blows)was stronger for men than women, 2(8, n 304) 12.3, p .0005andall other loadings for the four-factor model were gender-equivalent, 2(7,n 304) 2.9, p .89. These ndings suggest that the loadings of therened four-factor model are largely invariant with respect to gender. Like-

wise for the hierarchical model, the overarching second-order Aggressionfactor showed comparable relationships with the four rst-order factors formales and females in both Sample 1, 2(4, n 304) 1.5, p .82, andSample 2, 2(4, n 200) 5.9, p .20. Thus, the rened factors appearto have substantially the same meaning for men and women.

Stage Three: Assessing Construct Validity

What evidence of convergent or discriminant validity is there for the re-ned AQ factors? And how does this validity evidence compare to that for


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Buss and Perrys original AQ factors? To address these questions, we usedCFA with equality constraints in Sample 1 data to test hypotheses aboutrelationships between (a) the four AQ factors in both their rened and origi-nal forms; and (b) the four criterion measures of physical assault, verbal

hostility, anger arousal, and global hostility. We used CFA rather than tradi-tional correlational methods because it allowed us to estimate the relationshipbetween aggression subtraits and criterion measures, partialing out measure-ment error, and also provided a way to systematically test hypotheses aboutthe strength of associations across measures.

Because measurement error attenuates relationships, different measuresmay demonstrate different interrelationships due to differences in reliability.For this reason, it is important to control for differential reliability whenassessing the strength of relationships between observed measures. Tradi-tional correlational methods assume that all analyzed variables are measuredperfectly and therefore do not allow researchers to adjust for differentialreliability (Kline, 1998; Maruyama, 1998). Using CFA, in contrast, enabledus to control for differences in the reliabilities of the AQ factors and thecriterion measures, which might otherwise inuence the strength of the ob-served associations (Bagozzi, 1993; Judd, Jessor, & Donovan, 1986).

Another advantage of CFA over the traditional correlational approach isthat it allowed us to use equality constraints to systematically test hypothesesabout the strength of the relationships among the latent constructs. Typically,researchers have simply eyeballed differences in correlation coefcients todetermine the degree to which measures show convergent or discriminantvalidity. Using CFA, in contrast, enabled us to test the statistical signicanceof differences in the magnitude of validity coefcients by contrasting thegoodness-of-t chi-square values (and degrees of freedom) of two nestedmodels: one that constrained the correlations in question to have equal valueand one that contained no equality constraint. A signicant difference inthese two nested chi-square values signies that the correlations differ inmagnitude (cf. Bryant & Baxter, 1997; Bryant & Yarnold, 1995).

To obtain the multiple indicators required for CFA while also minimizingthe number of measured variables in the model, we used the partial disag-gregation approach to parcel each of the four criterion measures into two

composite indicators. For the BussDurkee Physical Assault scale, wesummed responses to the odd-numbered items (1, 3, and 5) to create oneindicator and summed responses to the even-numbered items (2 and 4) tocreate a second indicator. For the BussDurkee Verbal Hostility scale, wesummed responses to items 14 to create one indicator and summed re-sponses to items 58 to create a second indicator. For the MAI AngerArousal scale, we summed responses to items 1 and 2 to create one indicatorand summed responses to items 3 and 4 to create a second indicator. Totalscores on split-halves of the CookMedley Hostility Scale served as indica-


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factor, levels of this AQ factor were more strongly correlated with the AngerArousal criterion than with the criteria of Verbal Hostility, 2(1, n 180)

9.2, p .025; Anger Arousal, 2(1, n 180) 6.8, p .009; andGlobal Hostility, 2(1, n 180) 20.7, p .0001. And supporting the

construct validity of the Hostility factor, levels of this AQ factor were morestrongly correlated with the Global Hostility criterion than with the criteriaof Physical Aggression, 2(1, n 180) 13.3, p .003; Verbal Aggres-sion, 2(1, n 180) 14.0, p .0002; and Anger Arousal, 2(1, n180) 6.0, p .015. Thus, three of the four rened AQ factors showedevidence of convergent and discriminant validity. 2

Original AQ Factors. We next analyzed the 29 items constituting Bussand Perrys (1992) original four-factor measurement model together withthe eight criterion measures and examined the factor intercorrelations. Table6 also presents the correlations between the four original AQ factors and thefour criterion constructs for this CFA model. As with the rened measure-ment model, we rst examined these correlations separately within factors,conducting an initial omnibus test of the homogeneity of correlations foreach column in the table. Paralleling results for the rened AQ factors, thehypothesis of equality in correlations across criteria (i.e., no discriminant

validity) was rejected for the original AQ factors of Physical Aggression, 2(3, n 180) 27.4, p .0001; Anger, 2(3, n 180) 31.1, p.0001; and Hostility, 2(3, n 180) 50.6, p .0001; but not for VerbalAggression, 2(3, n 180) 1.5, p .68. Thus, in both rened andoriginal forms, Verbal Aggression lacked discriminant validity.

Supporting the construct validity of the original Physical Aggression fac-tor, follow-up CFA tests using equality constraints revealed that levels of

Bryant and Smith 2001 - Refining the Architecture of Aggression

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