EMPIRICAL EVIDENCE FOR A FOUR FACTOR … · sonality disorder scales of the test (e.g., Retzlaff &...

Journal of Personality Disorders, 24(1), 128–150, 2010 2010 The Guilford Press

EMPIRICAL EVIDENCE FOR A FOUR FACTORFRAMEWORK OF PERSONALITY DISORDERORGANIZATION: MULTIGROUP CONFIRMATORYFACTOR ANALYSIS OF THE MILLON CLINICALMULTIAXIAL INVENTORY—III PERSONALITYDISORDER SCALES ACROSS BELGIAN ANDDANISH DATA SAMPLES

Gina Rossi, PhD, Ask Elklit, MSc, and Erik Simonsen, MD

The factor structure of the Millon Clinical Multiaxial Inventory-III (Mil-lon, Millon, Davis, & Grossman, 2006) personality disorder scales wasanalyzed using multigroup confirmatory factor analysis on data ob-tained from a Danish (N = 2030) and a Belgian (N = 1210) sample. Two-,three-, and four factor models, a priori specified using structures foundby Dyce, O’Connor, Parkins, and Janzen (1997), were fitted to the data.The best fitting model was a four factor structure (RMSEA = .066, GFI =.98, CFI = .93) with partially invariant factor loadings. The robustnessof this four-factor model clearly supports the efforts to organize futurepersonality disorder description in a four-factor framework by corrobo-rating four domains that were predominant in dimensional models(Widiger & Simonsen, 2005): Factor 1, 2, 3, and 4 respectively corre-sponded to emotional dysregulation versus stability, antagonism versuscompliance, extraversion versus introversion, and constraint versusimpulsivity.

The research agenda for the Diagnostic and Statistical Manual of MentalDisorders V (DSM-V) acknowledged that personality disorders merge intoone another and into normal personality traits: “There does not appear tobe a qualitative distinction between normal personality functioning andpersonality disorder, nor does there appear to be a qualitative distinctionamong the individual personality disorders” (First et al., 2002, p. 125).Also, there is increasing agreement that the current categorical Diagnosticand Statistical Manual of Mental Disorders IV- text revision (DSM-IV-TR;

From Vrije Universiteit Brussel (G. R.); University of Southern Denmark (A. E.); and Univer-sity of Copenhagen (E. S.).

Address correspondence to Gina Rossi, Vrije Universiteit Brussel (VUB), Faculty of Psychol-ogy and Educational Sciences, Department of Clinical and Life Span Psychology, Pleinlaan2, 1050 Brussels, Belgium; E-mail: [email protected]

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MULTIGROUP CONFIRMATORY FACTOR ANALYSIS 129

American Psychiatric Association, 2000) should be replaced or integratedby or with a dimensional personality disorder configuration. DSM-IV-TR(American Psychiatric Association, 2000) still represents personality disor-ders as qualitatively distinct clinical syndromes. It remains impossible toabandon the categorical perspective into a dimensional classification aslong as a unifying structural model is lacking. Recent personality disorderresearch has accrued substantial evidence in favor of a dimensional classi-fication (Clark, 2007), latent structure modeling shows better fit for dimen-sional models (Livesley, 2007), and several empirical studies attempted totap the most fundamental dimensions that underlie pathological personal-ity functioning. Widiger and Simonsen (2005) described different propos-als and concluded that four domains seem predominant within these di-mensional models: extraversion versus introversion, antagonism versuscompliance, constraint versus impulsivity, and emotional dysregulationversus emotional stability. A minority of the models also included a fifthdomain: unconventionality versus closedness to experience, also namedopenness to experience or psychoticism. However, factor analyses of thepersonality disorder scales of the Millon Clinical Multiaxial Inventory(MCMI) produced solutions that mainly converged well with the four pre-dominant domains, and were labeled withdrawn, aggressiveness, con-straint, and neuroticism.

Factor analyses of earlier versions of the MCMI that only factored per-sonality disorder scales of the test (e.g., Retzlaff & Gibertini, 1990), or pre-sented personality disorder scale factors separately (e.g., Strack, Lorr,Campbell, & Lamin, 1992) reported somewhat inconsistent results interms of the number of factors deducted, or cutoff scores used to identifyfactor loadings (for an excellent overview of MCMI and MCMI-II studies,see Craig & Weinberg, 1993). Also, results of factor analyses could be moremisleading when the full personality disorder scales were used, since itemoverlap between the scales was much higher than in the current version.However, four major emerging factors were general maladjustment or psy-chological stress, a schizoid/asocial dimension, submission versus aggres-sion or social deviance, and a paranoid/psychotic factor (Craig & Bivens,1998; Craig & Weinberg, 1993).

Exploratory factor analytic research on the personality disorder scalesof the Millon Clinical Multiaxial Inventory-III (MCMI-III; Millon, Millon,Davis, & Grossman, 2006), the most recent version, showed two to fourfactors. Dyce, O’Connor, Parkins, and Janzen (1997) reported two-, three-,and four-factor solutions for principal components of varimax rotated non-overlapping personality disorder scales. The factors of the two-factor solu-tion also appeared as the first two factors in the three- and four-factorsolution. The authors compared their findings with the five-factor model ofpersonality disorders (Widiger, Trull, Clarkin, Sanderson, & Costa, 1994).Factor 1 resembled neuroticism and was bipolar in the two- and three-factor solution (most strongly defined by a positive loading for the avoid-ant, depressive, and masochistic, and a negative loading for the histrionic

130 ROSSI, ELKLIT, AND SIMONSEN

scale). In the four-factor solution this factor was unipolar (the histrionicscale did not have a strong negative loading). Factor 2 resembled LowAgreeableness and was identical in all solutions (most strongly defined bya high loading on the narcissistic, antisocial, aggressive, and paranoidscale). The bipolar Factor 3 in the four-factor solution resembled LowExtraversion and had a positive loading for the schizoid, and a negativeloading for the histrionic scale. Factor 4 in the four-factor solution wasidentical to Factor 3 in the three-factor solution and resembled Conscien-tiousness (strong positive loading for the compulsive scale). Haddy,Strack, and Choca (2005) concluded that the MCMI-III personality disor-der scales tap three underlying dimensions. They applied principal compo-nents analysis with varimax rotation to base rate (BR) scores, and to non-overlapping scores. Using the BR scores, three factors were retained. Thefirst factor was labeled Low Versus High Emotional Constraint, the secondSocial Detachment/Introversion Versus Extraversion, and the third HighVersus Low Neuroticism. Of more importance are the results using non-overlapping scores, since these can be compared with Dyce et al. (1997).Three factors were retained. The first factor, Social Detachment/Introver-sion Versus Extraversion, was most strongly defined by positive weightsfor the avoidant, depressive, schizotypal, masochistic, borderline, and par-anoid scale. The second factor was called Hostile Dominance, and hadpositive loadings on the narcissistic, histrionic, sadistic, paranoid, and an-tisocial scales. The third factor, Low versus High Emotional Constraint,had the antisocial scale on one end, and the compulsive scale on the otherend.

Previous studies (Dyce et al., 1997; Haddy et al., 2005; Cuevas, Garcia,Aluja, & Garcia, 2008) proposed underlying dimensions of personality dis-orders based on explorative factor analysis. One basis of their explorativeprincipal component results, Cuevas et al. (2008) used a confirmatory ap-proach to compare the fit of two-, three-, and four-factor solutions for over-lapping and nonoverlapping scales. Models designed for overlapping scalesdid not fit well to the data. The current study will be the first to apply aconfirmatory approach on basis of results from other studies (i.e., pre-viously deduced factor structures). Confirmatory factor analysis (CFA)allows to statistically test whether the previously posteriori deduced factorstructures do fit with the observed data by specifying patterns of relationsa priori and by testing them in a simultaneous analysis of the entire sys-tem of personality disorder scales. The study of Dyce et al. will be used tospecify the factor loadings of two-, three-, and four-factor solutions a pri-ori, because they explicitly tested their full-scale intercorrelations for simi-larity with the matrix reported in the MCMI-III manual (Millon & Davis,1994, p. 120). The Pearson correlation between the two sets of intercorre-lation matrices, after converting each coefficient using a Fisher’s r-to-ztransformation, was .98. This indicates similarity in the relative rank or-derings of coefficients. Dyce et al. also computed the root mean squareresidual (RMSR), an index of the average difference in sizes of the coeffi-


cients. The RMSR was only .12, which means that there were no consider-able differences in the absolute sizes of correlations.

Also, multigroup construct equivalence will be tested by examining theinvariance of estimated parameters of nested models across groups. De-gree of invariance (i.e., to which level the scales operate equivalently acrossgroups) will be explored by different measurement models (Graham, 2006;Raykov, 1997a, 1997b). The congeneric model is the least restrictive, andonly assumes the same pattern of loadings (the same set of indicators isspecified to load on the same factor). Based on this model, one can con-clude that there is no construct bias. The tau-equivalent model assumesthat all scales measure the same latent variable with the same precision(i.e., equal factor loadings), but amounts of error can differ. The parallelmodel is the most restrictive and assumes that all scales across the groupsare exactly equivalent to each other (i.e., equal factor loadings and thesame amount of error). It is highly improbable that one would find equalityof error variances (or a parallel model): This hypothesis is considered asan overly restrictive test of multigroup invariance (Bentler, 1995; Byrne,1988, 1998). Groups may be expected to differ in their variances of uniquefactors (i.e., measurement errors) even if the indicators measure the com-mon factors in comparable ways for all groups (Kline, 2005; MacCallum &Tucker, 1991). Furthermore, one can expect that the tau-equivalent modelwill possibly not be confirmed: To measure the same latent variable withthe same precision, means of all the scales should be equal over bothgroups. However, in order to exclude construct bias, the congeneric modelis a conditio sine qua non.

METHODPARTICIPANTS

The Danish sample consisted of 2,030 subjects: 841 females (41%) and1,189 males (59%). The primary language of all participants was Danish.The majority of the subjects (n = 1,825; 90%) were clinical patients: 1,566inpatients and 259 outpatients. The remainder of the subjects (n = 205,10%) came from a forensic setting; 125 were evaluated for competency tostand trial, and 80 were prisoners convicted for violent offenses. Age variedfrom 18 to 73 years (M = 35.5 years; SD = 11.3). The current sample is anextension of the sample used by Simonsen and Elklit (2008).

The Belgian sample consisted of 1,210 subjects: 471 females (39%) and739 males (61%). The primary language of all participants was Dutch. Themajority of the subjects (n = 828; 68%) were clinical patients: 643 inpa-tients and 185 outpatients. The remainder of the subjects (n = 382, 22%)came from a forensic setting and were prisoners. Age varied from 18 to 74years (M = 36.6 years; SD = 11.3). The current sample has also been usedin Rossi, van der Ark, and Sloore (2007), and Rossi, Sloore, and Derksen(2008).


INSTRUMENTS

The MCMI-III was translated into Danish (Elklit & Simonsen, 2002;Simonsen & Elklit, 2008). Elklit (2004) demonstrated the discriminativevalidity of the Danish MCMI-III in the analyses of a number of patientgroups. Scale intercorrelations were very much alike across the Danishand the US samples, and the range of Cronbach alpha values of the MCMI-III scales (.64–.93) of the Danish sample was comparable to the range ofvalues (.66–.95) in the MCMI-III manual (Millon et al., 2006).

The MCMI-III was translated into Dutch (Sloore & Derksen, 1997;Sloore, Derksen, & De Mey, 1994). Rossi, Van den Brande, Tobac, Sloore,and Hauben (2003) demonstrated the convergent validity of the DutchMCMI-III personality disorder scales with two sets of corresponding MMPI-2 personality disorder scales (set 1 of Morey, Waugh, & Blashfield, 1985;set 2 of Somwaru, 1994; Ben-Porath, 1995). The range of Cronbach alphavalues of the MCMI-III scales (.67–.94) of the Belgian sample was compa-rable to the range of values (.66–.95) in the MCMI-III manual (Millon et al.,2006).

PROCEDURE

The MCMI-III was administered by experienced psychologists/psychia-trists during psycho-diagnostic evaluation. Only valid profiles were in-cluded in the sample, on the basis of the following criteria: total numberof omitted or invalid responses (e.g., both a “yes” response and a “no” re-sponse to a single item) less than 12, V (validity index) less than 2, andraw score on scale X (disclosure) within the range 34–178 (Millon et al.,2006).

DATA ANALYSIS

Raw scale scores are more appropriate for analyses that require intervalmeasurement, such as parametric tests of significance. BR scores are an-chored to the prevalence percentages of disorders in a given populationand, therefore, they can differ across countries. So, if BR scores are used,an imbalance in subgroup composition of the contrasted groups could af-fect the results of significance tests (Holmes, 1987; Hsu, 2005). Further-more, the use of raw scale scores is mandatory for multigroup analyses(i.e., calculation of variance-covariance matrices).

The factorial structure can be estimated using the original, linearly de-pendent scale scores (i.e., overlapping scales: some items are used in morethan one scale) or using linearly independent scales scores (i.e., nonover-lapping scales: all items are used in one scale only). Although the amountof overlapping items is considerably less than in previous versions of theMCMI (Choca, 2004), from a statistical point of view factor analyzing lin-early dependent variables is clearly wrong. Rossi et al. (2007) could clearly


demonstrate a similar factor structure of linearly dependent scales andlinearly independent scales, without losing content validity of the factors:The coefficients of congruence between factors of linear dependent scalesand linear independent scales were greater than .90 for factors that shouldhave been congruent. Therefore, linear independent raw scales were calcu-lated, and used in the CFA. Linear independent raw scales are the sum ofthe scale’s so-called prototypal items (e.g., Dyce et al., 1997): For eachscale the MCMI-III manual (Millon et al., 2006) specifies a set of nonover-lapping items that are most central to the personality disorder constructand that closely correspond to DSM criteria.

Mean scale scores of the linear independent raw scales were used tocompare differences between the Danish and the Belgian sample with ttests for independent samples. Due to the large number of tests, the TypeI error rate was adjusted using a Bonferroni correction. The conventionalα = .05 was divided by the number of tests, 48 (14 scales multiplied by 2country categories = 28), yielding an adjusted α = .002. We used Cohen’sd as a measure of effect size (Cohen, 1988). The following heuristic rulesare available to interpret the effect size: r = .20 indicates a small effect, r =.50 indicates a medium effect and r = .80 indicates a large effect. Also re-ported were the standard deviation, and skewness and kurtosis values.

Maximum likelihood estimation over covariance matrices is the stan-dard method for CFA (Hoyle, 2000). It is a full-information method (i.e., allestimates of model parameters are calculated at once), and the estimatorsmaximize the likelihood of a sample that is actually observed (Winer,Brown, & Michels, 1991). For a given structural equation model, there maybe equivalent variations, so two-, three-, and four-factor solutions, pre-viously found by Dyce et al. (1997), were fitted to the largest sample (i.e.,Danish data). In first instance an oblique salient loadings model was de-fined (see appendix for a specification of the salient loadings on the basisof the results of Dyce et al.): All loadings larger than ±.40 in the study ofDyce et al. were not fixed to zero (i.e., freely estimated). However, one canexpect that a salient loadings model is too simplistic and will result inmodel rejection (Aluja, Garcia, Gracia, & Seisdedos, 2005; Katigbak,Church, & Akamine, 1996; McCrae, Zonderman, Costa, Bond, & Pauno-nen, 1996). Therefore, in a second step, modest loadings were added tothe model. Modification indices (MI) were used to decide which parameter(i.e., loading) could be set free (Joreskog & Sorbom, 1989, 1993). For eachfixed parameter the specified MI value represents the estimated drop inthe overall chi-square value if the parameter would be freely estimated.The chi-square difference statistic was used to test the statistical signifi-cance (p < .001) of the improvement in fit as paths were added. No furtherpaths were added if the improvement was not significant. If there was noapproximate fit to the data, in a third step, correlated error terms wereexamined. Correlated error terms were only allowed in the model if it madesubstantive sense: An effect exists that relates the two variables, whichwas not included in the specified CFA model. Since the chi-square value


may lead to the rejection of the model if the sample size is large, eventhough differences between observed and predicted covariances are small(Kline, 2005), information of other fit indices were used for model evalua-tion. Nowadays, the root mean square error of approximation (RMSEA) isrecognized as one of the most informative criteria in covariance modeling(Byrne, 1998). It is a parsimony-adjusted index because it includes a built-in correction for model complexity. A rule of thumb is that RMSEA values≥.10 suggest poor or unacceptable fit. Values ≤.05 suggest close model fit,and values ≤.08 suggest approximate or good model fit (Browne & Cudeck,1993; Chen, Curran, Bollen, Kirby, & Paxton, 2008; Hu & Bentler, 1999;Kline, 2005). A key advantage is that a confidence interval can be calcu-lated for the RSMEA value, which provides more information regardingmodel fit than a point estimate alone. The upper bound of this confidenceinterval should be ≤.10 (Chen et al., 2008; Nevitt & Hancock, 2000) foracceptable model fit. The comparative fit index (CFI) assesses the relativeimprovement in fit compared with the independence model (i.e., null modelwhich assumes unrelated variables). A rule of thumb is that valuesroughly greater than .90 indicate reasonable good fit (Hu & Bentler, 1999).The goodness-of-fit index (GFI) is an absolute fit index that estimates theproportion of variability in the sample covariance matrix explained by themodel. GFI = 1.0 indicates prefect model fit, and GFI > .90 indicates goodfit (Kline, 2005).

Multi-group CFA (i.e., simultaneously fitting of the model to two covari-ance matrices) was used to test for group invariance between the Danishand Belgian data. The fitting function represents a weighted combinationof model fit across groups (Byrne, 1998). Then, the restrictions of the dif-ferent measurement models (congeneric, tau-equivalent, and parallel)were implied. The congeneric model was evaluated by estimating the base-line model simultaneously in both samples. To examine the tau-equivalentand parallel model, equality constraints were defined on sets of unstan-dardized parameters (Kline, 2005). The fit of the tau-equivalent model (i.e.,equal factor loadings) was compared with the fit of the congeneric modelwith the chi-square difference statistic.1 If the fit of the tau-equivalentmodel was significantly worse than the fit of the congeneric model, onecan conclude that all the factor loadings may not be equal. If the tau-equivalent model could be applied, in a next step the fit of the parallelmodel (i.e., equal factor loadings, and equal error terms) was comparedwith the fit of the tau-equivalent model with the chi-square difference sta-tistic. If the fit of the parallel model was significantly worse than the fit ofthe tau-equivalent model, one can conclude that the error terms may notbe equal.

1. Although the use of the chi-square statistic to determine model fit can be questionable(especially in large samples), chi-square difference statistics can be used to compare the fitsof nested models in which the sample size is held constant across models (Thompson, 2004).


All CFA analyses were conducted using LISREL 8 (Joreskog & Sorbom,1993).

RESULTSDESCRIPTIVE STATISTICS AND DIFFERENCESIN MEAN SCALE SCORES

Table 1 shows the means, standard deviations, skewness and kurtosis val-ues, and the effect sizes of the linearly independent (i.e., prototypal) rawscale scores of the Danish and Belgian sample. Some mean scale scoresof the Danish sample differed significantly (p < .002) from the mean scalescores of the Belgian sample, but these differences were limited to smalleffect sizes (d > .20) for the depressive, sadistic, and compulsive linearlyindependent scales.

MULTIVARIATE NORMALITY

Since the maximum likelihood method for structural equation modelingassumes that the data follow a multivariate normal distribution, multi-variate normality tests (Joreskog & Sorbom, 1999) were performed on thelinearly independent scales of the Danish and Belgian data. There wassufficient evidence that the assumption of a multivariate normal data dis-tribution may be violated (see Table 2).

Variables had to be transformed closer to the Gaussian normal distribu-

TABLE 1. Descriptive Statistics and Differences in Mean Scale Scoresfor the Danish (N = 2030) and Belgian data (N = 1210)

Danish Data Belgian Data

Scale M SD Skew. Kurt. M SD Skew. Kurt. Cohen’s d

Schizoid 2.87 1.84 .19 −.88 2.65 1.75 .31 −.71 .12Avoidant 3.41 2.49 .27 −1.14 3.30 2.52 .28 −1.20 .04Depressive 4.18 2.49 −.02 −1.20 3.33 2.65 .26 −1.27 .33*Dependent 3.88 2.18 .14 −.94 3.55 2.32 .11 −1.06 .15*Histrionic 3.33 2.05 .03 −1.06 3.42 2.13 −.01 −1.17 .04Narcissistic 1.74 1.55 .95 .66 1.98 1.62 .88 .37 .15*Antisocial 2.15 1.80 .73 −.18 2.27 1.73 .56 −.37 .07Sadistic 2.02 1.65 .68 −.25 1.63 1.57 .87 .10 .24*Compulsive 3.99 2.03 −.01 −.85 4.64 1.98 −.27 −.73 .32*Pass.-Aggr. 3.72 2.13 .25 −.73 3.47 2.26 .28 −.838 .11Self-Def. 2.07 2.00 .72 −.54 2.01 1.97 .78 −.41 .03Schizotypal 2.77 2.39 .71 −.41 2.78 2.36 .65 −.52 .01Borderline 3.93 2.36 .21 −.86 3.95 2.47 .30 −.91 .01Paranoid 3.01 2.23 .53 −.53 3.21 2.31 .43 −.70 .09

Note: Skew. = Skewness; Kurt. = Kurtosis; Pass.-Aggr. = Passive-agressive; Self-def. = Self-defeating; an asterisk indicates that the hypothesis of equal mean scores was rejected by anindependent samples t-test (p < .002); parametric tests can be used for the data, becauseskewness and kurtosis levels were within an acceptable range (the range for skewness andkurtosis were respectively .01–.95, and .10–1.27).


TABLE 2. Test of Multivariate Normality for Continuous Variables

SkewnessSkewness Kurtosis and kurtosis

Data z- score p-value z-score p-value �2 p-value

Danish sample 26.822 <.0001 3.397 .001 730.976 <.0001Belgian sample 35.287 <.0001 14.899 <.0001 1467.125 <.0001

Note. χ2 = chi square; N Danish sample = 2030; N Belgian sample = 1210.

tion to avoid potential problems with the analysis of nonnormal variables(Curran, West, & Finch, 1996; West, Finch, & Curran, 1995). Normalscores were calculated (Joreskog & Sorbom, 1999), which is an effectiveway of normalizing a continuous variable for which the origin and unit ofmeasurement have no intrinsic meaning (such as test scores). Normalscores are a monotonic transformation of the original scale scores with thesame mean and standard deviation (rank ordering of cases are the same),but with reduced skewness and kurtosis (Joreskog, Sorbom, du Toit, & duToit, 2001).

BASELINE MODELS

A two-factor salient loadings model was defined, based on the study ofDyce et al. (1997). One modest loading was added from the linearly inde-pendent self-defeating scale to factor 2. Then, correlated error terms wereadded, if they made substantive sense according to the theory of (Millon,Millon, Meagher, Grossman, & Ramnath 2004). The first correlated errorterm was added between the linearly independent paranoid and compul-sive scale. According to Millon the puritanical compulsive subtype is char-acterized by paranoid features. A correlated error term between the lin-early independent dependent scale, and the linearly independent schizoidscale also made substantive sense. Millon describes a specific variation ofthe dependent personality with schizoid features: the ineffectual subtype.Furthermore an appeasing histrionic personality is formulated with de-pendent features, allowing a correlated error term between the linearly in-dependent histrionic and dependent scale. The correlated error term be-tween the linearly independent self-defeating and depressive scale can beexplained by the existence of the oppressed self-defeating personality withdepressive features. The abrasive passive-aggressive personality with sa-distic features justifies the correlated error term between the passive-aggressive and the sadistic linearly independent scales. At this point, thesolution reached approximate fit to the data (see Table 3), so no furthercorrelated error terms were allowed (RMSEA and upper bound of the 90%confidence interval ≤.08; CFI, and GFI ≥ .90).2

2. A rule of thumb to stop fitting a model is an adequate assessment of statistical criteriabased on information pooled from various indices of fit (Byrne, 1998).


The two-factor solution with five correlated error terms was consideredto be the baseline two-factor model (see Figure 1). Most correlated errorterms were positive (four out of five), because the linearly independentscales associated with the specific subtypes capture the essential featuresof the type. One can notice that this was not the case for the ineffectualdependent subtype. The correlated error term between the linear indepen-dent schizoid scale and the linearly independent dependent scale was neg-ative. This is because the dependent scale does not capture the essentialcharacteristics of this subtype. The ineffectual dependent type shows simi-larities to the languid schizoid pattern, and exhibits a lack of vitality, lowenergy, weakness in expressiveness, fatalism, and lack of will (Millon &Davis, 1996). These characteristics are only represented in the linearlyindependent schizoid scale.

Based on the MI, five modest loadings were added to the three-factormodel. To reach approximate fit to the data, three more correlated errorsterms were added (see Table 4).

These correlated error terms were allowed to the baseline three-factormodel, because they corresponded to Millon et al.’s (2004) appeasing his-trionic, ineffectual dependent, and oppressed self-defeating subtype (seeFigure 2).

The baseline four-factor model (see Figure 3) reached approximate fitafter adding 10 modest loadings, so no correlated error terms were added(see Table 5).

MULTIGROUP INVARIANCE

The baseline two-, three-, and four-factor models were tested for multi-group invariance. All models were invariant at a congeneric level (see Table6). However, the four-factor model clearly had the best fit to the dataacross groups. Moreover, this was the only model without measurementerror correlations, indicating that there was no other systematic source ofvariability between the indicators than that due to the underlying factors.

TABLE 3. Goodness of Fit Indices for the 2 Factor Models

Model �2 df � �2 RMSEA CI CFI GFI

SL 1493.88 71 — .099 (.095–.100) .95 .90ML (prot_8B,F2) 1348.88 70 <.0001 .095 (.091–.099) .96 .91CE (prot_P, prot_7) 1167.03 69 <.0001 .089 (.084–.093) .96 .92CE (prot_3, prot_1) 1010.56 68 <.0001 .083 (.078–.087) .97 .93CE (prot_4, prot_3) 929.47 67 <.0001 .080 (.075–.084) .97 .94CE (prot_8B, prot_2B) 857.95 66 <.0001 .077 (.072–.081) .97 .94CE (prot_8A, prot_6B) 807.16 65 <.0001 .075 (.070–.080) .97 .95

Note. N = 2030 (Danish sample); SL = salient loadings; ML = modest loading added; CE =correlated error term added; χ2 = chi-square; df = degrees of freedom; ∆ χ2 = p value of thechi-square difference test; RMSEA = root mean square error of approximation; CI = 90%confidence interval of RMSEA value; CFI = normed noncentrality fit index; GFI = good-ness-off-fit index; prot = linearly independent scale; 1 = schizoid; 2B = depressive; 3 = de-pendent; 4 = histrionic; 6B = sadistic; 7 = compulsive; 8A = passive-aggressive; 8B = self-defeating; P = paranoid.


FIGURE 1. The Two Factor Baseline Model

BEST FITTING MODEL ACROSS GROUPS

A complete tau-equivalent four-factor model resulted in a significant dif-ference in model fit (in comparison to the congeneric), however this doesnot imply that all factor loadings are different across groups. Therefore,partial invariance (Byrne, 1998) was examined: Each factor loading wasindependently tested for equality across groups, albeit cumulatively re-taining any that were found to be group-invariant (p ≥ .001). Only six outof 26 loadings were not invariant: the loading of the linear independentdepressive, and paranoid scale on factor 1, the loading of the linear inde-pendent dependent, antisocial, and paranoid scale on factor 2, and theloading of the linear independent paranoid scale on factor 3. Completelystandardized factor loadings of the partially tau-equivalent model (χ2 =1117.32, df = 140, RMSEA = 0.066, 90% confidence interval for RMSEA =0.062–0.069, CFI = 0.98, GFI = 0.93) are given in Table 7. The correlationsbetween the factors were as follows: Factor 1 correlated 0.49, −0.39, and


−0.04 with factor 2, 3 and 4, respectively. Factor 2 correlated 0.30, and0.09 with factor 3 and factor 4 respectively, and factor 3 0.01 with factor 4.

To compare the four factor solutions of the Danish and Belgian datasamples with the solution of Dyce et al. (1997), congruency coefficients(Gorsuch, 1983) were calculated by correlating the factor loadings of corre-sponding factors across sets. All corresponding factors were strongly asso-ciated with each other. The first factor of Dyce et al. was significantly re-lated with the Danish factor 1 (r = .99, p < .0001), and the Belgian factor1 (r = .96, p < .0001). The second factor of Dyce et al. was also highly simi-lar with the Danish (r = .94, p < .0001), and Belgian (r = .92, p < .0001)corresponding factor. There was a strong link between the third factorfound by Dyce et al., and the Danish (r = .98, p < .001), and the Belgianfactor 3 (r = .98, p < .001). For the fourth factor of Dyce et al., the loadingsappeared to be identical to the Belgian, and the Danish fourth factor (r =1.00, p < .0001).

DISCUSSIONWidiger & Simonsen (2005) suggested the identification of a commonground among various dimensional models of personality disorders (PD)as an important goal for future research. This is a little less ambitiousproject than O’Connor’s (2005) quest for the “true” structure of PDs. Wewere not expecting to find “true structure,” rather we searched for the bestfitting structure that captured the existing PD co-variation within the sam-ples under investigation. The (American) factor structures of Dyce et al.(1997) fitted the data across Danish and Belgian samples. The best fittingmodel identified across both groups was a model with four factors, whichwe, in analogy to Widiger and Simonsen, provided tentative names as fol-lows: Factor 1: Emotional Dysregulation versus Emotional Stability, Fac-tor 2: Antagonism versus Compliance, Factor 3: Extraversion versus Intro-version, Factor 4: Constraint versus Impulsivity. This model is also



SL 1393.05 68 — .098 (.094–.100) .96 .91ML (prot_8B,F2) 1256.02 67 <.0001 .094 (.089–.098) .96 .92ML (prot_C,F3) 1154.42 66 <.0001 .090 (.086–.095) .96 .92ML (prot_2B,F2) 1112.44 65 <.0001 .089 (.085–.094) .97 .93ML (prot_8B,F3) 1081.38 64 <.0001 .089 (.084–.093) .97 .93ML (prot_8A,F3) 1044.97 63 <.0001 .088 (.083–.092) .97 .93CE (prot_4, prot_3) 876.90 62 <.0001 .080 (.076–.085) .97 .94CE (prot_3, prot_1) 786.02 61 <.0001 .077 (.072–.081) .98 .95CE (prot_8B, prot_2B) 715.23 60 <.0001 .073 (.069–.078) .98 .95

Note. N = 2030 (Danish sample); SL = salient loadings; ML = modest loading added; CE =correlated error term added; χ2 = chi-square; df = degrees of freedom; ∆ χ2 = p value ofthe chi-square difference test; RMSEA = root mean square error of approximation; CI =90% confidence interval of RMSEA value; CFI = normed noncentrality fit index; GFI =goodness-off-fit index; prot = linearly independent scale; 1 = schizoid; 2B = depressive;3 = dependent; 4 = histrionic; 8A = passive-aggressive; 8B = self-defeating scale; C = bor-derline.


FIGURE 2. The Three Factor Baseline Model

consistent with the dimensional framework proposed by Livesley (2007)with domains labeled Emotional Dysregulation, Dissocial Behavior, Inhib-itedness, and Compulsivity, or with Markon, Krueger, and Watson’s (2005)four factor-scheme of Negative Emotionality or Neuroticism (i.e., emotionaldysregulation versus stability), Negative Agreeableness (i.e., antagonismversus compliance), Extraversion or Positive Emotionality (i.e., extraver-sion versus introversion), and Conscientiousness (i.e., constraint versusimpulsivity) that essentially represent maladaptive variants of traits in-cluded within the Five-Factor model of personality (Watson, 2008). Con-struct equivalence over both groups was clearly demonstrated, and mostfactor loadings were invariant. It was not unexpected to find a partiallytau-equivalent model, since some mean scale scores differed significantlyfrom each other. Although effect sizes were small, this gives reason to usedifferent BR scores across countries. It is important to notice that both inclinical (the studies Belgian and Danish samples), and nonclinical samples(e.g., Cuevas et al., 2008; Dyce et al. 1997), even when different popula-


tions across different countries are studied the same four-factor solutionseems to be the most plausible in confirmatory factorial analyses. The factthat Dyce et al. used a nonclinical sample of college students did not influ-ence the pattern of intercorrelations. This is not illogical since Millon sug-gested that normal and abnormal traits lie along a continuum (Millon,1969/1983; Millon & Davis 1996). Although the MCMI scales were con-structed to enhance discriminative validity in clinical samples, the factorstructure remains the same across different populations, including cross-national clinical and nonclinical samples. Nevertheless, the MCMI-III isnot a general personality instrument, since normative data (i.e., base ratescores) were developed entirely on clinical samples (Millon et al., 2006).

The currently existing hierarchical structure of DSM-IV-TR (AmericanPsychiatric Association, 2000) does not include bipolarities. Therefore it isimportant to discuss the uni- versus bipolarity of the factors. In the four-factor solution, factor 1 Emotional Dysregulation had high loadings onseveral PD scales. It is a unipolar factor and resembles general maladjust-

FIGURE 3. The Four Factor Baseline Model




SL 1022.83 65 — .085 (.081–.090) .97 .93ML (prot_C,F2) 869.19 64 <.0001 .079 (.074–.083) .97 .94ML (prot_3,F2) 817.63 63 <.0001 .077 (.072–.082) .97 .95ML (prot_C,F4) 711.49 62 <.0001 .072 (.067–.077) .98 .95ML (prot_S,F3) 648.07 61 <.0001 .069 (.064–.074) .98 .96ML (prot_2B,F2) 592.54 60 <.0001 .066 (.061–.071) .98 .96ML (prot_P,F3) 564.70 59 <.0001 .065 (.060–.070) .98 .96ML (prot_S,F4) 553.56 58 .0008 .065 (.060–.070) .98 .96ML (prot_8A,F4) 526.34 57 <.0001 .064 (.059–.069) .98 .96ML (prot_6B,F1) 513.05 56 .0003 .063 (.058–.069) .98 .97ML (prot_6B,F3) 499.61 55 .0002 .063 (058–.068) .98 .97

Note. N = 2030 (Danish sample); SL = salient loadings; ML = modest loading added;CE = correlated error term added; χ2 = chi-square; df = degrees of freedom; ∆ χ 2 =p value of the chi-square difference test; RMSEA = root mean square error of ap-proximation; CI = 90% confidence interval of RMSEA value; CFI = normed noncen-trality fit index; GFI = goodness-off-fit index; prot = linearly independent scale;2B = depressive;3 = dependent; 6B = aggressive scale; 8A = passive-aggressivescale; 8B = self-defeating scale; S = schizotypal; C = borderline; P = paranoid.

ment. Empirically and conceptually this factor is related to internalizingdisorders (Markon, Krueger, & Watson, 2005). Factor 2 Antagonismshowed a difference across groups. In the Danish sample the three highestloadings were on the narcissistic, antisocial, and sadistic scale. In the Bel-gian sample these scales showed equal loadings, but the highest loadingwas on the paranoid scale. The Belgian sample has a higher proportion ofsubjects from forensic settings, which might explain the higher loadingsof paranoid features. If one only considers the salient loadings this is aunipolar factor, however, when modest loadings are taken into consider-ation, this factor may be regarded as bipolar factor, having, at one end,the Compliant, notable dependent and depressive features and, at theother end, Antagonism. Antagonism or disinhibition has been related toexternalizing disorders (Markon et al., 2005). Factor 3 Extraversion was

TABLE 6. Multigroup Invariance (N = 3240)


Two factor models:Congeneric 1540.68 131 — .082 (.078–.085) .97 .92Tau-equivalent 1627.79 151 <.0001 .078 (.074–.081) .97 .92Parallel — — — — — — —

Three factor models:Congeneric 1375.89 123 — .079 (.076–.083) .97 .93Tau-equivalent 1486.64 148 <.0001 .075 (.071–.078) .97 .92Parallel — — — — — — —

Four factor models:Congeneric 1058.38 116 — .071 (.067–.075) .98 .94Tau-equivalent 1175.48 146 <.0001 .066 (.063–.073) .98 .93Parallel — — — — — — —

Note. Congeneric = same factor structure; tau-equivalent = equal λs (i.e., factor load-ings); parallel = equal λs and δs (i.e., error variances); χ2 = chi-square; df = degrees offreedom; ∆ χ2 = p value of the chi-square difference test; RMSEA = root mean square er-ror of approximation; CI = 90% confidence interval of RMSEA value; CFI = normednoncentrality fit index; GFI = goodness-off-fit index.


TABLE 7. Completely Standardized Maximum Likelihood Estimatesof Factor Loadings for the Partially Tau-Equivalent Four Factor

Model for the Danish (N = 2030) and Belgian Data (N = 1210)

Danish Data Belgian Data

Scale F1 F2 F3 F4 F1 F2 F3 F4

Prot_1 .49 −.72 .50 −.73Prot_2A .64 −.37 .64 −.37Prot_2B .90* −.18 .94* −.18Prot_3 .77 −.27* .75 −.15*Prot_4 .79 .77Prot_5 .63 .62Prot_6A .63* −.37 .54* −.39Prot_6B .17 .53 .11 .17 .54 .11Prot_7 .65 .67Prot_8A .59 .31 −.10 .59 .31 −.10Prot_8B .80 .81Prot_S .51 .36 −.23 −.08 .52 .36 −.24 −.08Prot_C .71 .15 −.24 .70 .14 −.24Prot_P .39* .48* −.14* .16* .69* −.27*

Note. * loadings that could not be constrained to be equal; Prot = linearly in-dependent scale; 1 = schizoid; 2A = avoidant; 2B = depressive; 3 = dependentscale; 4 = histrionic; 5 = narcissistic; 6A = antisocial; 6B = sadistic; 7 = com-pulsive scale; 8A = passive-aggressive; 8B = self-defeating scale; S = schizo-typal; C = borderline; P = paranoid.

more clearly a bipolar factor across both groups, with the histrionic scaleat one end, and the schizoid and avoidant (schizotypal and paranoid)scales at the other end. The maladaptively high positive emotionality of thehistrionic PD or the excessive euphoria, contrasts the low positive emo-tionality or anhedonia that characterizes the schizoid PD (Widiger & Lowe,2008). Finally, factor 4 Constraint had its highest loading on the compul-sive scale across both groups. This factor is also bipolar with Impulsivity(antisocial and borderline features) at one end, in contrast to obsessive-compulsive features at the other end. Fossati et al. (2006) suggested thatthe avoidant, dependent, depressive, and obsessive-compulsive PDs sharea latent dimension. In our study the obsessive-compulsive pattern clearlycompromises a separate factor, which we think is a well-established find-ing. Several studies identified this as an anankastic factor (e.g., Larstone,Jang, Livesley, Vernon, & Wolf, 2002; Leibing, Jamrozinski, Vormfelde,Stahl, & Doering, 2008). Also, the obsessive-compulsive PD does not seemto represent an extreme variant of an anxious personality trait (Fossati etal., 2007), rather it is situated on the high end of a personality dimensionranging from excessive control to lack of control. With two (or three) out offour factors being bipolar, we found a level of complexity that is currentlynot captured by DSM-IV. The bipolarity of the factors might be regarded asalso measuring extreme behavior in interpersonal conduct, and the degreeof impulse control, both aspects of the general criteria of personality disor-der. Widiger & Simonsen (2005) considered the potential bipolarity as animportant issue for future research. Our results corroborate their conclu-sion that a bipolar structure appears to be inherent to any hierarchical


organization of PD scales within the existing instruments. However, visu-ally Widiger and Simonsen excluded the bipolarity in a simplified versionof the domains. Their rationale is that a conceptual and clinical presenta-tion of personality disorders, need not to be as complex as might be im-plied out of empirical structures. This strategy of avoiding conceptual com-plexity has recently been applied by Krueger, Skodol, Livesley, Shrout, andHuang (2007, 2008) in an attempt to synthesize categorical and dimen-sional approaches for the construction of DSM-V. According to Kruegerand colleagues a future dimensional approach to personality disorders ismore likely to be successful if it does not represent a too abrupt departurefrom the categorical system in DSM-V. They suggest a set of facets or fun-damental elements to build up a comprehensive description of abnormalpersonality, and, in addition, arrange these facets into four broad groups:emotional dysregulation, dissocial behavior, inhibitedness, and compul-sivity. As an example they visually represent all four former mentioneddomains as unipolar factors. It is likely that clinicians will find it easier toemploy unipolar dimensions. The unipolar approach is closer to their wishto quantify illness by the degree of severity, while it is also in accordancewith the ideas of spectrum pathology. However, these four broad groupswere derived from research on the higher-order phenotypic structure ofthe Dimensional Assessment of Personality Pathology Disorder-BasicQuestionnaire (DAPP-BQ; Livesley & Jackson, 2002) scales in clinical andgeneral populations by conducting principal components analyses, andsome of these derived factors were actually bipolar (Livesley, Jang, & Ver-non, 1998). The unipolar versus bipolar distinction is an important se-mantic and conceptual issue for the revision of our future approach todescription of personality pathology. In our opinion it needs to be ad-dressed further, e.g., for similarities in markers of pathology in somaticmedicine or in other psychiatric domains, before more pragmatic solutionsfor a smooth transition from categorical to a dimensional system are de-cided upon.

Also, defining criteria of several PDs are multidimensional in nature, andthere is a general uncertainty about which symptoms constitute severalPDs. Fossati et al. (2006) found that several of the included cluster C crite-ria were not efficient predictors of the respective latent variables. Althoughwe have not studied the criteria set, it is interesting to compare the load-ings across the PD scales. Four of the PDs (i.e., histrionic, narcissistic,and compulsive, and self-defeating) are characterized by a high loading onjust one factor. The self-defeating PD loads only on the emotional dysregu-lation factor. The histrionic, narcissistic, and compulsive PD load only onthe factor of compliance. Interestingly, these three scales of the MCMI-IIIare, in clinical assessment, often equalized with resourcefulness and de-mand excessive scores before judged pathological. Also notable is that theextraversion dimension has a negative sign in relation to the emotionaldysregulation, and the antagonism factors (the only exception being thesadistic PD where the extraversion loading is small). This pattern of sec-


ondary relationships emphasizes that personality disorder does not con-form completely to a simple structure, and has been observed in otherstudies (e.g., Markon et al., 2005). There are also a number of PDs withsimilarities in the loading patterns on the factors, e.g., loadings of the par-anoid and the schizotypal PDs, and the loadings of the dependent and thedepressive PDs. Together there appear to be specific combinations of thefour factors involved in all of the studied PDs, some pointing to unidimen-sionality, others to combinations of several specific dimensions with vari-ous loading sizes. CFA seems to offer a solution to the redundancy prob-lems in the PD criterion sets. The four factor and similar dimensionalmodels may pave the way towards a combined examination of the impactof personality and symptoms on the outcome of common disorders and ontreating the personality component as well as the clinical symptoms.

We also want to highlight some strengths and limitations of this study.Strengths of the current study include the use of two large independentlycollected samples, the confirmatory analysis approach, and the multi-group comparisons. Also, both samples existed of clinical and nonclinical(i.e., forensic) subjects, and therefore the results provide some evidencethat a future taxonomy with a comprehensive set of dimensions can possi-bly be used for both disordered and more normal personalities. A majorlimitation is that it may not be considered as an appropriate test of Millon’stheory. Millon described a sophisticated and complex theory of disordersof personality in terms of a self-other, pleasure-pain, and active-passivepolarity model (Millon & Davis, 1996; Millon et al., 2004). This model wasnever meant to be translated into a predicted factor structure (Strack &Millon, 2007). Nevertheless, the Millon Clinical Multiaxial Inventory–IIIdoes provide a possible view on the structure of PDs. Using this MCMI-IIIview, the current study clearly corroborated the results of the review studyby Widiger & Simonsen (2005). Some authors (Tackett, Silberschmidt,Krueger, & Sponheim, 2008; Watson, 2008) argue that the “Big Four”higher order dimensions (representing maladaptive variants of the five-factor model) should be expanded with an oddity or peculiarity dimension.Widiger and Simonsen (2005) suggested that the factor is possibly toosmall to be consistently identified by factor analyses (also see Austin &Deary, 2000; Clark, Livesley, Schroeder, & Irish, 1996; Larstone et al.,2002). Another way of representing this oddity dimension would be to in-clude it into the classification of schizophrenic disorders, consistent withthe approach of the World Health Organization (World Health Organiza-tion, 1992) that defines the schizotypal personality disorder as a variantof schizophrenia (Widiger & Simonsen, 2005). This approach would implyan exclusion from this dimension from a model of personality disorderconfiguration. In our samples, we could neither refute nor confirm thisdimension, because the MCMI-III scales (like most self-report instrumentsand their respective scales) do not capture the unusual perceptual experi-ences associated with this factor.

Future research will certainly suggest a change of the criteria for several


PDs. Some criteria or personality disorders might even vanish, or newmight emerge, as our understanding of the involved dimensions will in-crease, and will be tested in clinical and general population samples. Atthis point, an integrated model compromised of the four factors convinc-ingly demonstrated its validity by CFA. There is a clear need for futurestudies that test its clinical utility in cross-national studies, although sev-eral authors pointed out that a dimensional classification would help todirect the general therapeutic approach. It could be more consistent withtreatment planning, and goal setting than categorical classification (Ver-heul, 2005), and the diagnostic process could be simplified by a globalassessment of the four domains and their salient features (Livesley, 2007).

APPENDIXSpecification of Salient Loadings on the basis of the Study of Dyce et al. (1997)

Two-Factor Three-Factor Four-FactorSolution Solution Solution

Scale F1 F2 F1 F2 F3 F1 F2 F3 F4

Prot_1 +SL _SL SL +SLProt_2A +SL +SL SL +SLProt_2B +SL +SL SLProt_3 +SL +SL SLProt_4 −SL +SL −SL SL −SLProt_5 +SL SL SLProt_6A +SL SL −SL SL −SLProt_6B +SL +SL SL SLProt_7 −SL +SL +SLProt_8A +SL +SL +SL SL SL SLProt_8B +SL +SL SLProt_S +SL +SL +SL SL SL SLProt_C +SL +SL +SL SL SLProt_P +SL +SL +SL SL SL SLNote. Prot = linearly independent scale; 1 = schizoid; 2A = avoidant; 2B = depres-sive; 3 = dependent scale; 4 = histrionic; 5 = narcissistic; 6A = antisocial; 6B = sa-distic; 7 = compulsive scale; 8A = passive-aggressive; 8B = self-defeating scale; S =schizotypal; C = borderline; P = paranoid; SL = salient loading; scales that shouldload on opposite ends are differentiated by + and −.

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