Person-factors in the California Adult Q-Set: Closing the Door on Personality Trait Types? y

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1 European Journal of Personality Eur. J. Pers. 20: (2006) Published online 31 January 2006 in Wiley InterScience ( DOI: /per.553 Person-factors in the California Adult Q-Set: Closing the Door on Personality Trait Types? y ROBERT R. McCRAE, 1 * ANTONIO TERRACCIANO, 1 PAUL T. COSTA, JR. 1 and DANIEL J. OZER 2 1 National Institute on Aging, NIH, DHHS, Baltimore, MD, USA 2 University of California, Riverside, CA, USA Abstract To investigate recent hypotheses of replicable personality types, we examined data from 1540 self-sorts on the California Adult Q-Set (CAQ). Conventional factor analysis of the items showed the expected Five-Factor Model (FFM). Inverse factor analysis across random subsamples showed that none of the previously reported person-factors were replicated. Only two factors were replicable, and, most importantly, these factors were contaminated by mean level differences in item endorsement. Results were not due to sample size or age heterogeneity. Subsequent inverse factor analysis of standardized items revealed at least three replicable factors; when five person-factors were extracted, they could be aligned precisely with the dimensions of the FFM. The major factors of person similarity can be accounted for entirely in terms of the FFM, consistent with the hypothesis that there are no replicable personality types in the CAQ. Published in 2006 by John Wiley & Sons, Ltd. Personality types succinctly convey information about individual differences, but their empirical status is questionable. Claims for discrete personality types, characterized by a distinctive profile of personality traits, have appeared repeatedly in the history of personality psychology (Myers, 1962; Robins, John, Caspi, Moffitt, & Stouthamer-Loeber, 1996; York & John, 1992). Most recently, a special issue of the European Journal of Personality (Asendorpf, Caspi, & Hofstee, 2002) found mixed support for three types (Resilient, Overcontrolled, and Undercontolled) derived from cluster analyses of measures of the Five-Factor Model (FFM; McCrae & John, 1992). In these analyses persons were grouped on the basis of their similarity on the five personality factors, Neuroticism (N), Extraversion (E), Openness (O), Agreeableness (A), and Conscientiousness (C); the typological approach presumes that there are regions of the five-factor space in which *Correspondence to: Robert R. McCrae, Box No. 03, Gerontology Research Center, 5600 Nathan Shock Drive, Baltimore, MD , USA. mccraej@grc.nia.nih.gov y This article is U.S. Government work and is in the public domain in the USA. Received 8 October 2004 Published in 2006 by John Wiley & Sons, Ltd. Accepted 25 January 2005

2 30 R. R. McCrae et al. persons are more densely clustered than would be predicted from a multivariate normal distribution. Psychologically, such clusters might result from the operation of some intrapsychic mechanism that affects a wide range of personality traits. However, the three clusters were replicated only in a minority of cross-sample comparisons, and further research is needed before accepting or rejecting this typology. The three types were named after constructs proposed by J. H. Block and J. Block (1980), and identified empirically (Robins et al., 1996; see also Asendorpf & van Aken, 1999; Hart, Hofmann, Edelstein, & Keller, 1997) in analyses of a version of the California Child Q-Set (CCQ; Caspi et al., 1992). The CCQ is a set of 100 items that are sorted in a fixed distribution from extremely uncharacteristic to extremely characteristic. The content of the CCQ and the related California Adult Q-Set (CAQ; Block, 1961) is intended to allow a comprehensive description of personality characteristics, and previous studies have shown that these items cover the full range of the FFM (John, Caspi, Robins, Moffitt, & Stouthamer-Loeber, 1994; McCrae, Costa, & Busch, 1986). In the study by Robins et al., ratings of year-old boys were provided by 300 of their caregivers; the present study includes an attempted replication in self-sorts by adults. Instead of cluster analysis, Robins et al. (1996) used inverse factor analysis, a method previously used by York and John (1992) in a study of midlife women. In this procedure, similarity between persons is quantified as the correlation for each pair of individuals across the 100 items of the CAQ. These correlations are then factored, and varimax-rotated person-factors are derived. The person-factors are interpreted by examining the associated factor scores for CAQ items, either rationally or by correlations with established criteria. Typically these criteria have included conventional factor loadings for CAQ items (which yield measures of the FFM) and expert CAQ prototype ratings of constructs, including Ego Resiliency and Ego Under- and Overcontrol. Such correlations allow one to characterize members of the type as, for example, high in Extraversion and low in Overcontrol. People can be assigned to a single type on the basis of factor loadings. It should be noted that cluster analysis and inverse factor analysis are entirely different statistical approaches to the problem of classifying people into types, and criticisms of one method need not reflect on the other. However, much of the recent enthusiasm for types has been based on the apparent convergence of these two separate methods on three theoretically interesting types, so a further examination of their convergence is useful. York and John (1992) and Robins et al. (1996) identified the number of factors (and thus types) using a criterion of factor replicability. Following Everett (1983), they considered the correct number of factors to be the solution that could be replicated after varimax rotation across random subsamples. Their procedure differed from Everett s in two respects. First, they sought similar factors in different subsamples of persons, whereas Everett s technique, applied to an inverse factor analysis, would have examined the same subjects using different random subsamples of Q-set items. Both seem to be reasonable ways to seek replicable factors. Second, and perhaps more importantly, they evaluated each solution on the basis of the mean correlation of factor scores across subsamples, whereas Everett required that all factor comparabilities in the solution selected be above This is problematic because the use of mean values makes it possible to include a relatively weak and perhaps unreplicable factor along with other strongly replicated factors. Varimax factor rotation is an essential part of this strategy. The hypothesis of discrete types implies that there should be relatively tight clusters of individuals with common personality characteristics, and varimax rotation will tend to align person-factors with

3 Person-factors 31 these clusters. If the hypothesis of types is wrong, however, persons will still vary in how much they resemble others, but in a continuous fashion. The position of factor axes will be arbitrary, and varimax rotations cannot be expected to replicate across samples. Instead, the similarity of person-factors would be better assessed by targeted rotation in which the optimal alignment of factor solutions can be evaluated. In this article we first replicate the FFM structure of the CAQ in order to provide a reference for interpreting person-factors. We then seek replicable solutions from inverse factor analyses and compare the present solutions to previous types from Schnabel, Asendorpf, and Ostendorf (2002), Robins et al. (1996), York and John (1992), and Gramzow et al. (2004). We also interpret person-factors in terms of CAQ prototypes of Ego Resiliency and Under- and Overcontrol. Finally, because Q-correlations are dramatically affected by mean item endorsements, we argue that in sharp contrast to traditional Q-factor analyses type analyses should be performed on standardized variables, and these analyses show that the structure of person-factors mirrors the structure of personality variables. METHOD Participants Data were obtained from volunteers in the Baltimore Longitudinal Study of Aging (BLSA; Shock et al., 1984) who completed the CAQ at their regularly scheduled visits to the Gerontology Research Center. BLSA participants are generally healthy, well educated volunteers. Participants were retested every six years (total N ¼ 2289 administrations), but the present study focuses on first administration data. Between August 1981 and July 2001 a total of 1540 individuals completed a valid first CAQ; they ranged in age from 17 to 93 (M ¼ 53.0 years, SD ¼ 16.7); 83.4% were White, 12.9% Black, and 3.7% other; 54% were male. Data from the first 403 administrations were reported earlier (McCrae et al., 1986). Instrument The CAQ consists of 100 items designed for use by expert raters but modified for self-sorts (Bem & Funder, 1978). Each item is printed on a card, and participants are asked to describe themselves by sorting the cards from least to most characteristic of them, using a fixed, normal distribution. In previous studies in the BLSA (Costa & McCrae, 1995; Costa, McCrae, & Siegler, 1999; McCrae et al., 1986), responses have shown longitudinal stability and convergent correlations with self-reports and observer ratings on the Revised NEO Personality Inventory (NEO-PI-R; Costa & McCrae, 1992). The sorting procedure is cognitively challenging, especially for older participants, who sometimes required as much as two hours to complete the task. Rarely, respondents become confused about the direction of the sort, and list their least characteristic traits as their most characteristic. To minimize this possibility, participants were asked at the end of the sort if the most characteristic items were in fact most characteristic. However, a check on the data was still deemed advisable. One such check relies on the fact that CAQ items have predictable mean values: in the full set of 2289 administrations, the mean (on a scale from 1 to 9) for Item 37, is guileful, deceitful, was 1.98; the mean for Item 2, is genuinely dependable, was We converted these means into the fixed distribution of the CAQ and correlated that normative Q-sort with each individual sort. These

4 32 R. R. McCrae et al. Q-correlations ranged from 0.82 to 0.88 with a mean of There were 31 negative Q- correlations (1.4% of 2289), suggesting a reversal of the sort direction, and these cases were eliminated from the sample. Jack Block (personal communication, 27 April 1993) has endorsed this kind of screening procedure. CAQ prototypes A number of CAQ prototypes have been developed to operationalize psychological constructs. A panel of experts is asked to sort the items of the CAQ to describe a hypothetical individual who is prototypical of the construct; ratings are averaged to yield a consensus description. In the present study we use CAQ prototypes for Ego Resiliency (e.g. is productive, is calm, relaxed ), Undercontrol (e.g. rapid personal tempo, unable to delay gratification ), and Overcontrol (e.g. is fastidious, tends toward overcontrol of impulses ; Block & Block, 1980; Kremen & Block, 2002) to help interpret the observed person-factors. RESULTS AND DISCUSSION Conventional factor analysis The 100 CAQ items were subjected to principal components analysis with varimax rotation. The first eight eigenvalues were 7.95, 4.84, 4.61, 3.32, 2.76, 2.24, 1.99, and 1.84, but we selected a five-factor solution 1 on theoretical grounds (McCrae & John, 1992). These factors could be clearly identified as N ( basically anxious, concerned with adequacy versus satisfied with self, interesting person ), E ( talkative, expressive versus emotionally bland, keeps people at a distance ), O ( values intellectual matters, unconventional thoughts versus conservative values, judges in conventional terms ), A ( behaves in sympathetic manner, compassionate versus critical, skeptical, has hostility ), and C ( genuinely dependable, productive versus eroticizes situations, enjoys sensuous experiences ). 2 These factors closely replicate those found in an earlier analysis (McCrae et al., 1986); when factor scores are generated using factor scoring weights from the present and earlier studies, correlations between old and new factors ranged from 0.89 for C to 0.95 for A. (Incidentally, the varimax results in the present, much larger study provide justification for the 1986 decision to rotate E and A factors through 30 degrees from their varimax position.) The present factor loadings can be used to interpret person-factors. The replicable and meaningful results of this conventional factor analysis and previous analyses in this sample (e.g. Costa et al., 1999) demonstrate that CAQ data obtained from self-sorts at least in the well educated BLSA sample are reliable and valid, and should be appropriate for use in inverse factor analyses. 1 Parallel analysis (Cota, Longman, Stewart, Holden, & Fekken, 1993) suggested that 15 factors be retained, the same number that Lanning (1994) found by the minimum average partial criterion in his analysis of expert ratings on CAQ data. The additional factors in his data concerned narrow topics such as somatization, social acuity, and hostile candour. 2 The CAQ Conscientiousness factor is somewhat atypical at the low pole, emphasizing hedonism instead of sloth and disorganization. However, it does show convergent validity with other measures of this factor, although at a lower level than the other factors (McCrae et al., 1986).

5 Table 1. Correlations of matching person-factor scores after varimax rotation in two random subsamples for two- to seven-factor solutions No. of factors extracted Correlations of factor scores for factor LADC a Two Three Four Five Six Seven a LADC ¼ largest absolute discriminant correlation. Person-factors 33 Inverse factor analyses of CAQ items Following York and John (1992), to identify replicable person-factors in CAQ data we randomly divided the sample into two subsamples, transposed the data matrices so that persons became variables, and extracted from two to seven factors in each subsample. After varimax rotation, inverse factor scores were calculated for each solution in each subsample, and these scores were correlated across the 100 CAQ items. These correlations quantify resemblance of person-factors across subsamples, and Table 1 reports the optimal matching of factors across the six pairs of solutions. The last column of the table lists the largest absolute discriminant correlation, that is, the largest correlation between a factor and another factor with which it is not matched. These values may be interpreted as factor comparabilities, because they are correlations between factor scores. By Everett s (1983) criterion of factor comparabilities greater than 0.90, only the twofactor solution is replicable. By any criterion, the three-factor solution that might have corresponded to Resilient, Overcontrolled, and Undercontrolled types is not replicable. The remaining solutions show some resemblance across factors, but not clear one-to-one matches: the largest discriminant correlation is not much lower than the smallest convergent correlation (cf. Campbell & Fiske, 1959). Table 1 reports results of attempts to replicate across subsamples, but it is also possible to attempt replications across studies. To determine if a three person-factor solution would replicate previous findings, we extracted three inverse factors from the total sample, calculated factor scores after varimax rotation, and correlated inverse factor scores with factor loadings from the conventional factor analysis across the 100 CAQ items (cf. York & John, 1992). Results are shown in the top panel of Table 2. A word of explanation on the values in Table 2 may be helpful. The first correlation, 0.75, is derived by correlating loadings on the N factor in the conventional factor analysis for the 100 CAQ items with the person-factor scores for the 100 CAQ items for the first person-factor. For example, Item 45, Has a brittle ego-defense system, loads 0.46 on the CAQ N factor, and has a person-factor score of 1.49 on the first person-factor, implying that this item is very uncharacteristic of people of this type. High positive loadings on N and low Person-Factor I scores for many items lead to the listed correlation of Schnabel et al. (2002), in analyses of NEO-PI-R data in a sample of young adult Germans, found three types. The Resilient type was characterized by low N, high E, and high C. The closest approximation in the present data is found with Factor I, characterized by low N and high E. However, Factor I fails to show high C. Factor II has high C, but low

6 34 R. R. McCrae et al. Table 2. Correlations of factor scores from the inverse factor analyses with factor loadings from conventional factor analyses and CAQ prototypes Person-factor Conventional factor loading for factor CAQ prototype N E O A C Resil Under Over Total sample I 0.75** 0.62** 0.35** 0.35** ** 0.46** 0.43** II 0.34** 0.63** ** 0.32** 0.50** 0.56** III 0.45** ** * 0.17 Men only M-I 0.73** 0.49** ** ** 0.28** 0.31** M-II 0.36** 0.47** ** 0.28** ** 0.48** M-III 0.36** 0.22* 0.50** 0.51** 0.44** 0.39** * Women only W-I 0.83** 0.31** 0.48** ** 0.83** 0.30** 0.20* W-II 0.21* 0.42** 0.39** 0.71** 0.35** 0.25* 0.52** 0.40** W-III ** * 0.39** 0.22* 0.41** 0.45** W-IV 0.48** 0.21* 0.46** ** * 0.32* Both conventional and inverse factor analyses used Varimax rotation. N ¼ 100 items. For the total sample, k ¼ 1540; for men only, k ¼ 831; for women only, k ¼ 709. N ¼ Neuroticism. E ¼ Extraversion. O ¼ Openness to Experience. A ¼ Agreeableness. C ¼ Conscientiousness. Resil ¼ Ego Resiliency. Under ¼ Ego Undercontrol. Over ¼ Ego Overcontrol. *p < **p < rather than high E, and thus cannot be the Resilient type. Factor III shows no resemblance to the Resilient type. The overcontrolled type of Schnabel et al. showed high N, low E, and low O; their Undercontrolled type had high N, E, and O and low C. Neither of these patterns can be found in Table 2, so it appears that none of the types of Schnabel et al. are clearly replicated here. A more direct comparison might be to the types of Robins et al. (1996), which were based on an analysis of California Q-set data (although in a different version and with observer sorts instead of self-sorts). Their Resilient type was low average in N and high average in E, O, A, and C, which shows some resemblance to the present Factor I. Their Overcontrolled type is marked chiefly by high N and low E, which is not found in the present results. Finally, the Undercontrolled type is defined by high N, and low O, A, and C. Again, that pattern is not seen here. The results of Robins et al. (1996) were found in adolescent boys, whereas adults of both sexes constitute the present sample. We therefore examined person-factors in men only (middle panel, Table 2), to test the hypothesis that types vary across sexes. Factor M-I shows some similarity to the Resilient type of Robins et al., but neither M-II nor M-III resembles any of their types. It is, of course, possible that the types of Robins et al. are replicable within ratings of adolescent boys, but they do not appear to be generalizable to adult self-report data. We also sought to replicate the four person-factors reported by York and John (1992) in a sample of women. Correlations of inverse factor scores with conventional factor loadings are reported in the bottom panel of Table 2 for the women in our sample. The four types of York and John were described as Individuated (high E, O, and A), Traditional (low E, high A and C), Conflicted (high N and low A), and Assured (low N, high E, low A, and high C). Probably the closet match-up would pair these factors with W-III, W-II, W-IV, and W-I, respectively, but none of these is really a close match. For example, the Individuated type

7 has high O, but O is not related to W-III. Again, the Traditional type, like W-II, has low E and high A and C, but W-II also has low N and O, which the Traditional type does not. Finally, the four-factor solution can be compared with results reported by Gramzow et al. (2004), who found a four-cluster solution based on Ego Resiliency and Ego Undercontrol in a predominantly female sample. Their first and second clusters have similar correlates with FFM dimensions as do W-I and W-II, respectively, but their third and fourth clusters do not resemble any of the women s factors in Table 2. The person-factors in Table 2 can also be interpreted with respect to the theoretical constructs of Ego Resiliency and Under- and Overcontrol operationalized as CAQ prototypes (Kremen & Block, 2002). An immediate issue arises from the fact that prototypes for Ego Under- and Overcontrol, although conceptually distinct, are empirically virtual mirror images (r ¼ 0.90), and show directly opposite patterns of correlations with person-factor scores. If, like Robins et al. (1996), we focus on Ego Resiliency and Undercontrol, it appears that the first person-factor is related to Resiliency and, to a lesser extent, to Undercontrol, whereas the second factor is moderately related to low Undercontrol. The third person-factor is essentially unrelated to these constructs. Results for the three-factor solution in men are similar; results for the four-factor solution in women show two factors related to Undercontrol. Clearly, none of these solutions shows a clear match to three separate constructs of Ego Resiliency and Under- and Overcontrol. Because there are no replications across studies, it appears that there are only two replicable factors in the present data (see Table 1). Table 3 presents the CAQ items that are most strongly related to each pole of the two factors. A reading of item content suggests that the first factor is akin to self-esteem, whereas the second factor contrasts nice but weak characteristics with undesirable but strong characteristics. Factor I is strongly correlated Table 3. CAQ items most and least descriptive of two personfactors Factor score CAQ item Factor I Assertive Verbally fluent High aspiration level Has social poise Is productive Feels victimized Has brittle defenses Genuinely submissive Self-defeating Basically anxious Factor II Concerned with adequacy Genuinely dependable Considerate Ethically consistent Responds to humor Guileful and deceitful Tries to stretch limits Assertive Power oriented Expresses hostility Person-factors 35

8 36 R. R. McCrae et al. with N (r ¼ 0.86, p < 0.01), and has smaller positive correlations with the other factors (E, 0.40; O, 0.34; A, 0.26; C, 0.25; all p values < 0.05). Factor II is most strongly related to A(r ¼ 0.50, p < 0.01) and significantly related to N (r ¼ 0.31), E (r ¼ 0.37), and C (r ¼ 0.34). It is unrelated to O (r ¼ 0.03). Incidentally, these two person-factors differ from the two higher-order variable factors that Digman (1997) proposed for the FFM. In Digman s model, the first factor contrasts N with A and C, and the second combines E and O a completely different assortment of the five factors. Correlations of the two person-factors with prototype scores show a close correspondence of Factor I with Resiliency (r ¼ 0.89, p < 0.01), but only a moderate match of Factor II with Undercontrol (r ¼ 0.45, p < 0.01). Conceptually, perhaps a closer match is with the dimensions of meaning identified by Osgood (1976) in semantic differential studies: Factor I is close to Evaluation, Factor II to Potency (reflected). Item endorsement artifacts Because Osgood s factors refer to connotative rather than denotative meaning, we may begin to suspect that artifact may be involved. As noted earlier, items on the CAQ have normative values. When the mean endorsement for each item is correlated with factor scores on the two replicable person-factors, the correlations are 0.82 for Factor I and 0.58 for Factor II. When mean endorsement values are correlated with the unrotated first factor, the correlation is Thus, in the present sample, person-factors derived from raw CAQ items are chiefly determined by properties of the items, not the persons. This is understandable. Because almost all people rate the same items high and low in their sorts, Q-correlations between individuals are almost all positive (cf. Ozer & Gjerde, 1989), and a single general factor is created on which almost everyone has a positive loading. In the present sample, loadings on the first unrotated factor ranged from 0.01 to 0.89, with 92.7% of the sample loading above 0.40, the criterion for type membership used by Robins et al. (1996). Note that such a factor would emerge regardless of item content. For example, the items is over 7 feet tall and is an Odinist (i.e. worships Odin) would be uncharacteristic of almost everyone, and would have strongly negative factor scores on the first factor, although these two items presumably have little or no personological significance. 3 Differing item endorsement levels thus introduce systematic error into the first factor from Q-correlations computed on raw scores. Because the first unrotated factor contributes so heavily to rotated Factors I and II (r ¼ 0.82 and 0.58, respectively), the replicated solution examined in Table 3 is uninterpretable in typological terms. This interpretive problem is compounded by the fact that the Ego Resiliency prototype, which has consistently been related to the first person-factor in analyses in the present study, is itself strongly correlated with mean endorsement (r ¼ 0.81, p < 0.01). 4 The variables-to-persons ratio and age heterogeneity Before addressing the problem of item endorsement, we consider two different issues that may account for our failure to replicate previously reported person-factors. Traditionally, 3 Because the item content of the CAQ concerns personality characteristics, it might seem of interest to examine what characteristics are commonly endorsed what the modal human personality is like. But the answer is not news. We have known for half a century (Edwards, 1957) that people tend to endorse socially desirable items (whether honestly or otherwise), and that there is great consensus on which items are in fact desirable. 4 Correlations of mean endorsements with conventional factor scores for N, E, O, A, and C were lower: 0.51, 0.12, 0.30, 0.49, and 0.39, respectively.

9 Person-factors 37 factor analysts have argued that the number of subjects in a factor analysis should be much larger than the number of variables (e.g. Nunnally, 1978); by analogy, the number of variables in an inverse factor analysis should be large compared with the number of persons. In most previous studies of CAQ clusters, the number of subjects has been about equal to the number of variables (e.g. York & John, 1992; N ¼ 103). Our study has 15 persons for each variable, and that disproportion may perhaps lead to unstable results. If the same well defined structure were found in all groups of people, then the sheer number of people in the analysis would probably not matter much. But the BLSA sample includes a far broader age range (17 93 years) than any previous study of CAQ clusters; if there are age variations in the composition of clusters, the structure may be obscured by the analysis of the full sample. Both of these objections are debatable. Guadagnoli and Velicer (1988) showed that it is the sheer number of subjects, not the ratio of subjects to variables, that is crucial to the stability of factor solutions. With its 100 items, CAQ results should be equally stable with inverse analyses of 100 people or Similarly, the argument that cluster composition might be affected by age is weakened by the fact that similar factors have been reported in adolescent boys (Robins et al., 1996) and middle-aged men and women (Costa, Herbst, McCrae, Samuels, & Ozer, 2002). Nevertheless, to examine these possibilities, we sorted the sample on age at first CAQ and divided the distribution into 16 successively older subsamples of 96 subjects each (four subjects were dropped in this analysis). With the exception of the youngest ( years) and the oldest ( years) groups, the age range of each subsample was 5 years or less. Within each subsample, we conducted an inverse factor analysis, extracting three factors and saving the 100 factor scores after varimax rotation. These factor scores could be correlated with conventional factor loadings and with CAQ prototype scores, just as in Table 2. The task of interpreting all these person-factors was simplified by the fact that rather similar factors occurred in each of the subsamples. For example, the first person-factor in each subsample was strongly negatively correlated with N. To facilitate grouping the factors, we factored the 16 subsamples 3 factors ¼ 48 columns of person-factor scores, extracting and rotating three factors. The first factor was defined by the first person-factor in each subsample, whereas the second and third overall factors were sometimes defined by the second and sometimes by the third subsample person-factor. These factor results allowed us to arrange the 48 factors into three groups of loosely replicated factors. Table 4 reports correlations for these 48 factors, and suggests several conclusions. First, the general similarity of the three factors across subsamples suggests that there is a replicable structure, and that it generalizes across age groups from 17 to 93. This is especially true for the first and third factors; some of the subsamples (such as A3) do not follow the general pattern for the second factor. Second, as Guadagnoli and Velicer might have predicted, these subsamples yield person-factors that are similar to Factors I, II, and III, respectively, in Table 2, which were derived from the total group. In fact, factor scores from the analysis of 48 subsamples correlate 0.94, 0.73, and 0.92 with Factor Scores I, II, and III from the total group. Thus, the use of a single large sample does not seem seriously to distort inverse factor analysis results. Third, as in Table 2, there is no one-to-one correspondence between these clusters and the CAQ Prototypes. The first factor does resemble Ego Resiliency, but the second factor is only weakly related to Ego Overcontrol, and the third factor is essentially unrelated to the CAQ Prototypes, and is defined by Agreeableness. Finally, as the last column of Table 4 shows, all three person-factors are strongly related to the mean endorsement level of items, and thus all are contaminated by

10 38 R. R. McCrae et al. Table 4. Correlations of factor scores from inverse factor analyses with factor loadings from conventional factor analysis, CAQ prototypes, and mean item endorsement within age-graded subsamples Subsample/ Conventional factor loading for factor CAQ prototype factor N E O A C Resil Under Over Endorse First factor A B C D E F G H I J K L M N O P Mdn Second factor A B C D E F G H I J K L M N O P Mdn Third factor A B C D E F G H I J K Continues

11 Table 4. Continued Subsample/ Conventional factor loading for factor CAQ prototype factor N E O A C Resil Under Over Endorse L M N O P Mdn Both conventional and inverse factor analyses used Varimax rotation. N ¼ 100 items. For each subsample, k ¼ 96. N ¼ Neuroticism. E ¼ Extraversion. O ¼ Openness to Experience. A ¼ Agreeableness. C ¼ Conscientiousness. Resil ¼ Ego Resiliency. Under ¼ Ego Undercontrol. Over ¼ Ego Overcontrol. Endorse ¼ mean item endorsement. For correlations greater than 0.21 in absolute magnitude, p < 0.05; for correlations greater than 0.25 in absolute magnitude, p < irrelevant item difficulty variance. The replicable structure of the CAQ in these analyses is likely to be due in part to the similarity of endorsement artifacts across subsamples. Inverse factor analysis of standardized CAQ items There is a straightforward solution to the problem of item endorsement artifacts: the 100 CAQ item responses can be standardized across the full sample as z-scores, with means of 0 and standard deviations of 1. This linear transformation eliminates differences in item endorsement by scaling all means to 0, and thus eliminates the artifactually inflated Q- correlations. Inverse factor analysis of standardized CAQ items yields person-factors based solely on individual differences around each item s mean. 5 It should be noted that this is not the usual practice in the analysis of Q-sort data, and that the person correlations we analyse are not, strictly speaking, Q-correlations as defined by Stephenson (1953). They are, however, perfectly appropriate data for an inverse factor analysis, just as standardized variables are appropriate for use in conventional factor analysis. Person-factors from these analyses will be defined by people who are similar by virtue of the fact that they are above average on one set of items and below average on another. The analysis simply disregards where the average of an item is located with respect to other items, information relevant to the item, not to the people who are being clustered. Table 5. Correlations of matching person-factor scores after varimax rotation in two random subsamples for two- to seven-factor solutions for standardized items No. of factors extracted Correlations of factor scores for factor LADC a Two Three Four Five Six Seven a LADC ¼ largest absolute discriminant correlation. Person-factors 39 5 Standardization does not affect the correlations between items, so a conventional factor analysis of standardized CAQ items would yield results identical to those from the analysis of raw items reported earlier.

12 40 R. R. McCrae et al. Table 6. Correlations of factor scores from the inverse factor analyses of standardized CAQ items with factor loadings from conventional factor analyses and CAQ prototypes Person-factor Conventional factor loading for factor CAQ prototype N E O A C Resil Under Over Three person-factor solution I ** 0.43** 0.43** ** 0.44** 0.37** II ** ** 0.90** ** III * 0.77** ** ** 0.65** Five person-factor solution I ** 0.33** 0.34** ** 0.40** 0.34** II ** ** 0.83** 0.31** 0.35** III ** ** ** 0.65** IV ** 0.32** 0.34** 0.40** V ** 0.20* 0.38** 0.63** N ¼ 100 items. N ¼ Neuroticism. E ¼ Extraversion. O ¼ Openness to Experience. A ¼ Agreeableness. C ¼ Conscientiousness. *p < 0.05; **p < In a first analysis, we repeated the attempt to find replicable person-factors after varimax rotation. Table 5 reports correlations between matched factors from random halves of the sample for two- to seven-factor solutions. The results appear unequivocal: three and only three factors are clearly matched using the Everett (1983) criterion. Substantively, these can be interpreted by correlating factor scores from the three-factor solution in the full sample with the CAQ conventional factor loadings. As shown in the top panel of Table 6, Factor I 3 is strongly related to low N, Factor II 3 to A, and Factor III 3 to C and low E. Factor I 3 has some resemblance to the Resilient type of Schnabel et al. (2002), but the remaining factors do not match Over- or Undercontrolled types. Similarly, these factors do not resemble the types of the same names found by Robins et al. (1996). As in Tables 2 and 4, the three CAQ prototypes do not show one-to-one correspondences with the three personfactors, and the magnitude of the correlation between the first person-factor and Ego Resiliency is reduced when standardized CAQ items are analyzed. It is puzzling why N, E, and A should be so clearly related to replicated factors 6 when C and especially O are not. One clue comes from the fact that N, A, and E are the three largest factors in the conventional factor analysis; if C and O factors were better represented in CAQ items, they might define replicable person-factors. Guided by this hypothesis, we examined a five person-factor solution as well. The bottom panel of Table 6 shows that Factors I 5,II 5, and III 5 are essentially the same as in the three-factor analysis; Factor IV 5 is strongly related to O, and Factor V 5 is related to low C. All five trait factors appear to define person-factors in this analysis. However, Table 5 shows that the five person-factor solution was not replicable across subsamples after varimax rotation. The problem may be with this rotation; it was used in the initial analyses on the assumption that there are discrete types with dense clusters of people that would reliably guide the position of the rotated factors. But this hypothesis may be false; in fact, across existing studies in the literature and analyses in the present 6 In part, the clear replicability appears to have been a fluke. When we re-randomized the sample into two new subsamples and compared solutions across these two, the three-factor solution was again the best, but the correlations were lower, ranging from 0.81 to 0.86; the largest discriminant correlation was When we compared male and female subsamples, the two-factor solution was replicated (0.92, 0.90), but the three-factor solution was not (0.91, 0.76, 0.70; largest absolute discriminant correlation ¼ 0.60).

13 Table 7. Correlations of matching person-factor scores after targeted rotation in two random subsamples for two- to seven-factor solutions for standardized items No. of factors extracted Correlations of factor scores for factor LADC a Person-factors 41 Two Three Four Five Six Seven Factors are given in the order they emerged in the first random subsample. a LADC ¼ largest absolute discriminant correlation. study there is no consistent evidence that replicable types exist. If there are no types, then the distribution of persons in factor space will be essentially random, and varimax rotation will settle by chance on an arbitrary location. Even if the position of the axes is arbitrary, we can determine whether the same factor space is replicated across random subsamples by use of targeted rotation. Person-factors in the second subsample can be rotated to maximum congruence with corresponding personfactors in the first subsample, and correlations of their factor scores across the CAQ items can be used to evaluate factor matching. This task is simplified by the fact that rotating factors, generating factor scores, and correlating these scores with independent criteria is mathematically equivalent to rotating the correlations of the original factors with the criteria. When the criteria are interpreted in terms of convergent and discriminant validity, this is called validimax rotation (McCrae & Costa, 1989). As applied here, the factor scores from the second subsample are correlated with the factor scores from the first, and the resulting matrix is rotated toward an identity matrix to test the hypothesis that the two sets of factors can be aligned. Results are presented in Table 7. When two factors are extracted, they cannot be satisfactorily aligned, suggesting that two different factor spaces are involved and demonstrating that Procrustes rotation cannot manufacture a match that does not exist in the data. However, near-perfect matches can be found with three, four, and five factors, all of which show correlations of 0.90 or better. The sixth factor barely misses that criterion, suggesting the possibility of a sixth person-factor in the data, 7 but the seventh factor does not match. Everett s (1983) procedure specifies that we accept the solution with the largest number of replicated factors in this case, five. The fact that five person-factors are indeed replicable in the CAQ legitimizes the interpretation of the bottom panel of Table 6, in which five varimax-rotated factors are correlated with FFM factor loadings. But if there are no distinct person types, then varimax rotation is not necessarily appropriate. Because each person-factor is correlated chiefly with one FFM factor, we can use validimax rotation to find the location of axes in personfactor space that maximizes correlations with the FFM loadings. Results do not require another table: the convergent correlations are all 0.99, and the largest absolute 7 Inspection of factor scores for the CAQ items suggests that the sixth factor resembles a physical Attractiveness factor reported by Lanning (1994) as the sixth factor in expert ratings on the CAQ.

14 42 R. R. McCrae et al. discriminant correlation is The first five person-factors in the CAQ are essentially identical to the FFM. 8 The equivalence of person-factors and variable-factors is a striking result, but is probably not limited to the particular factors of the FFM. It would probably be obtained in any study in which variables had a multivariate normal distribution and a well defined factor structure. Although proponents of inverse factor analysis have generally expected to find substantively different results from those revealed by conventional factor analysis, we did not; and in retrospect it is clear why this would not be the case. Inverse factor analysis seeks people whose personalities are similar, and personality similarity must be in terms of the underlying dimensions of personality. People who are chiefly characterized by their high scores on N are most similar to other people high in N, and these people define a pole in person-factor space; the same is true for the other factors. This will necessarily be true unless there is some marked disturbance of the multivariate normal distribution that might be due to the existence of real personality types. The fact that the first five person-factors in the CAQ are completely isomorphic with item factors suggests that there are no major departures from a multivariate normal distribution in our data, and thus no types. We would encourage reanalyses of earlier data (Robins et al., 1996; York & John, 1992) using standardized CAQ items to see whether they confirm or disconfirm the isomorphism of person- and variable-factors. CONCLUSION In defending the search for personality types, John and Robins (1994) argued that no doors should be closed in the study of personality (p. 137). Certainly there is no a priori reason to rule out personality types, and there is some evidence for a replicable typology based on the FFM (Asendorpf et al., 2002), at least when self-reports are analysed (Rammstedt, Riemann, Angleitner, & Borkenau, 2004), but recent studies (Asendorpf, 2003; Pittenger, 2004; Van Leeuwen, De Fruyt, & Mervielde, 2004) have shown that continuous dimensional information is almost always superior to type classification in predicting external criteria, and the present analyses suggest that previously identified CAQ types confound individual differences with item endorsement characteristics of the instrument used. All these considerations point to the limited utility of research on types, especially using inverse factor analysis. The door to types should not be locked, but for now perhaps it should be closed. However, the door should certainly not be closed on research into the heuristics of types and traits. It is widely believed that human beings (including psychologists) find it easier to grasp and communicate discrete types than multidimensional descriptions (cf. Block & Ozer, 1982). What is not yet known is whether the ease of understanding types compensates adequately for the loss of information that occurs when individuals are described by types (Asendorpf, 2003). As Costa et al. (2002, p. S84) noted, It is an empirical question whether clinicians trained in... type constructs would be more effective at predicting client behaviour than clinicians trained in [trait] constructs. This question remains. 8 Such perfect correspondence would not be expected if one compared conventional factor loadings from one sample with inverse factor scores from another. The high correlations seen here reflect the fact that both analyses share the same measurement error as well as the same true scores.

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