How general across inventories is a general factor of personality?

Journal of Research in Personality 46 (2012) 258–263

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How general across inventories is a general factor of personality? John C. Loehlin Psychology Department, University of Texas, 1 University Station A8000, Austin, TX 78712-0187, USA

a r t i c l e

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Article history: Available online 9 February 2012 Keywords: General factor of personality (GFP) Personality inventories Big Five Eugene-Springfield Community Sample Factor analysis Human evolution

a b s t r a c t Two recent analyses addressing the generality of a general factor of personality (GFP) across different personality inventories came to markedly different conclusions. By applying the methods used by the one that found a GFP to the data used by the one that did not, it was shown that a substantial GFP could be obtained in the latter case. It was also shown that similar GFPs could be derived from sets of more broadly or more narrowly defined questionnaire scales, or from self- and others’ reports on a given inventory. Finally, it was shown that a GFP defined from eight personality inventories showed a modest degree of correlation with criterion variables such as ratings by others and act-frequency clusters. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Musek (2007) argued in favor of a ‘‘Big One,’’ a general factor of personality (GFP) analogous to the general factor g for measures of cognitive skills. Rushton and his colleagues (Rushton, Bons, & Hur, 2008) proposed that such a factor may have arisen during human evolution, contrasting individuals having personality traits conducive to effective social participation with individuals having traits handicapping social participation, such as distress, withdrawal, or disruptive behavior in social situations. Saucier describes a general factor among personality inventories as primarily evaluative, contrasting a ‘‘heterogeneous mix of desirable attributes at one pole with a mix of undesirable attributes at the other pole’’ (Saucier, 2008, p. 33). The two definitions obviously overlap, although Saucier’s does not address causes, and Rushton’s is more specifically focused on social situations. Rushton and Irwing have carried out hierarchical factor analyses of a number of personality questionnaires and inventories, a series of factor analyses culminating in a single factor at the summit, the GFP (Rushton & Irwing, 2008, 2009a, 2009b, 2009c). For the most part, these involved different samples for different inventories, so no direct comparison of the GFPs was available. A few studies have examined pairs of inventories given to the same sample, and found appreciable correlations between their GFPs: for example, GFPs from the NEO-PI and Cloninger’s Temperament and Character Inventory correlated .72 in a Japanese sample in one study (Rushton et al., 2009, Study 2), and in another, GFPs obtained from items and from scales of Eysenck’s Personality Questionnaire correlated with corresponding GFPs from Cloninger’s Tridimensional Personality Questionnaire in the range .54 to .79 in four adult Australian samples (Loehlin & Martin, 2011a). E-mail address: [email protected] 0092-6566/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jrp.2012.02.003

Recently, two multiple-inventory comparisons of GFPs have been made, one in the US by Hopwood, Wright, and Donnellan (2011) using the data from eight inventories filled out by members of the Eugene-Springfield (Oregon) Community Sample (ESCS), (Grucza & Goldberg, 2007), and one in the Netherlands involving six inventories filled out by military samples (van der Linden, te Nijenhuis, Cremers, & van de Ven, 2011). The two studies obtained their GFPs in different ways, and came to different conclusions about their generality. At the end of the abstract of their paper, Hopwood et al. state: ‘‘Overall these results fail to support a common GFP that is positioned at the top of a personality trait hierarchy’’. At the end of their abstract, van der Linden et al. say: ‘‘This evidence strengthens the view that the GFP is a substantive construct with practical relevance’’. Hopwood et al., using several exploratory and confirmatory techniques, carried out a series of hierarchical factor analyses on each inventory, culminating in a single general factor; in this they used something like the original Rushton/Irwing strategy. Van der Linden et al., on the other hand, obtained a GFP as the unrotated first principal factor of the intercorrelations of the scales for each of their inventories. The latter method was also used in the study of Rushton et al. (2009) that compared the GFPs from the NEO and the TCI. Loehlin and Martin (2011a) used the presumably closely related first principal component for their GFPs. The first purpose of the present study is to see if the difference in methods of the two studies is responsible for the difference in results, rather than (say) a difference between Oregonian civilians and Netherlands military recruits, or between the personality inventories used in the two studies. To do this, the method used by van der Linden et al. is applied to the data used by Hopwood et al., to see whether the Oregon data now yield the Netherlands result. If they do, one possible explanation is that a general factor of personality exists, but that personality is not strictly hierarchical, so

J.C. Loehlin / Journal of Research in Personality 46 (2012) 258–263

that a first factor may be a better way of assessing a GFP than a factor of factors is. In the present paper, GFPs will be obtained via the first factor method from the same data used by Hopwood et al., and compared to the GFP they obtained by the hierarchical method. The ESCS data set can also be used to address additional issues about GFPs. For example, many inventories permit scoring at more than one level—main scales and subscales, or main scales and higher-order factors. Are GFPs derived at more specific and more general levels the same? In one study using the California Psychological Inventory (CPI, Loehlin, 2011), very similar GFPs were obtained from items, scales, two levels of factors among scales, and the weights obtained in a hierarchical study by Rushton and Irwing (2009b) that used a different edition of the CPI. However, in the Australian study mentioned earlier, cross-inventory correlations were higher for GFPs derived at a lower level (items) than at a higher level (scales) (Loehlin & Martin, 2011a). Note that only a few scales (four and three, respectively) were present for the inventories in that study, whereas the CPI had eighteen scales, possibly allowing for a more satisfactory GFP estimate at the scale level for that inventory. In addition, rating by others as well as self-rating data are available for the Big Five Inventory in the ESCS data. Some investigators have found GFPs in data from self-reports but not peer reports (Biesanz & West, 2004), some in peer reports but not self-reports (Rauthmann & Kolar, 2010), and some have found similar GFPs in both self- and others’ reports (Rushton et al., 2009, Study 1). Also present for the ESCS participants were data on the frequencies with which they reported performing specific behavioral acts, such as drinking wine, writing a thank-you note, playing a piano. Thus if personality-inventory-based GFPs are found, we can ask to what extent they correlate with criterion variables such as others’ ratings and act-cluster scores. The above analyses may serve to accomplish two things. First, they may (or may not) show that the first-factor method is a more effective approach to defining a GFP than is the assumption of a strict hierarchical organization of personality. And second, the breadth of information available in the present data set permits saying considerably more about such a GFP than just that it can be calculated. An important qualification should be noted at the outset: the presence of a first factor in a matrix of correlations among personality scales does not guarantee that a meaningful GFP exists. A first factor may be extracted from any correlation matrix. It is the properties of that first factor that matter: its generality across inventories and levels of measurement, its agreement across self- and others’ ratings, its relationship to behavioral criteria. 2. Methods 2.1. Participants The participants were members of the Eugene-Springfield Community Sample (Grucza & Goldberg, 2007). This consisted of a group of approximately 1000 individuals in Oregon who agreed to participate on an ongoing basis, and who responded to a number of mailed personality inventories between the years 1993 and 2000. In 1973 the sample ranged in age from 18 to 85 years, with a mean age of 51. This was a somewhat select group: approximately 98% were white, 58% were female, and 55% had a college degree. The numbers responding to each inventory are given in Table 1—typically around 700. There were 433 individuals who had scores on all the scales of all eight inventories. 2.2. Questionnaires The eight inventories used in Hopwood et al.’s analysis are listed in Table 1. They were all standard published personality

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inventories. Further details concerning them may be found in Grucza and Goldberg (2007). 2.3. Criterion measures The others’ ratings were based on ratings by 1–3 raters who knew the individual in question well. Each informant filled out a 44-item Big Five Inventory (BFI) to describe the person being rated, responding to brief phrases like: ‘‘Is considerate and kind to almost everyone,’’ ‘‘Is outgoing, sociable,’’ and ‘‘Remains calm in tense situations.’’ The ratings were combined according to the Big Five, ipsatized within raters, and averaged over the raters of a given individual. Self-ratings by the participants were also obtained on the same BFI items. The act clusters consisted of from 6 to 14 specific acts for which the respondent indicated on a scale of how frequently he or she had done them, that ranged from (1) Never in my life, to (5) More than 15 times in the past year. ‘‘Drug use’’ included such items as ‘‘Drank beer’’ and ‘‘Smoked marijuana’’; ‘‘Erudition’’ included ‘‘Went to a public library’’ and ‘‘Read an entire book in one sitting’’; ‘‘Creativity’’ included ‘‘Wrote poetry’’ and ‘‘Acted in a play’’; ‘‘Communication’’ included ‘‘Wrote a thank-you note’’ and ‘‘Worked on a scrapbook’’; ‘‘Friendliness’’ included ‘‘Hugged someone’’ and ‘‘Started a conversation with strangers’’; and ‘‘Undependability’’ included ‘‘Broke a promise’’ and ‘‘Arrived at an event more than an hour late.’’ A complete listing of the items in the six clusters may be found in Grucza and Goldberg (2007). 2.4. Analyses As noted earlier, Hopwood et al. (2011) obtained a GFP from each of the eight inventories, using a hierarchical series of exploratory factor analyses starting with a low-order set of scales, subscales, clusters, or facets, and culminating with a single top-level factor. In the present paper, the analysis proceeded from the same initial sets of variables, but the GFP was obtained directly in each case as the first principal factor from the intercorrelations of the scales of the inventory, following the approach of van der Linden et al. (2011). Then a single GFP was obtained from the intercorrelations of the individual-inventory GFPs, as the unrotated first principal factor of those intercorrelations. This was done twice, with the intercorrelations of the Hopwood GFPs and of the present ones, and the two compared. To help in interpreting the individualinventory GFPs, the factor scores were correlated with the Big Five domain scores of the NEO. In the next step, the first-factor method was applied to a higherorder set of scales from the same inventories, for comparison with one from the lower-order scales. For seven of the eight inventories, higher-order scores were available in the ESCS data set. For the MPQ, higher-order scales were obtained as equally-weighted composites of the scales primarily loading on three higher-order factors (based on Tellegen & Waller, 2008, Table 13.3). Next, self- and others’-rating GFPs were compared, and these compared with the inventory-derived GFPs. And as a final step, overall GFP factor scores were correlated with two sets of criterion variables: the ratings by others on the Big Five dimensions, and the six behavioral act clusters. All factor analyses were carried out with SPSS 11.0.4, specifying a single unrotated principal factor, and calculating factor scores to be used in subsequent steps. First principal factors were used for the study, in conformity with van der Linden et al. (2011), although first principal components had been used for this purpose in some previous work (Loehlin, 2011; Loehlin & Martin, 2011a, 2011b). Principal factors have theoretical advantages (Loehlin, 1990), although principal components have some practical ones. As a check, the individual-inventory GFPs were done both ways, and

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Table 1 ESCS variables used for individual-inventory GFPs. Inventory

Table 3 Correlations of individual-inventory first-factor GFPs with Big Five dimensions. N of scales

Sixteen Personality Factor Questionnaire Six-Factor Personality Questionnaire California Psychological Inventory HEXACO Personality Inventory Hogan Personality Inventory Multidimensional Personality Questionnaire NEO Personality Inventory-Revised Temperament and Character InventoryRevised

GFP

Low

High

N of respondents

16 18 20 24 44 11 30 31

5 6 3 6 7 3 5 7

680 690–691 792 734 739–742 733 857 727

Notes: GFP = General Factor of Personality. ESCS = Eugene-Springfield Community Sample. Low, High = lower-, higher-order scales.

it made little difference—factor scores from the two methods correlated in the range .924 to .996 for the different inventories, with a median of .99. 3. Results and discussion 3.1. Comparison of individual-inventory GFPs For each of the eight inventories listed in Table 1, a GFP was obtained as the first principal factor of the intercorrelations among its scales, clusters, facets, or subscales, using the level from which Hopwood et al. (2011) began their hierarchical analyses—usually the lowest level available in the data set. The number of such scales for each inventory was given in Table 1. The intercorrelations among the obtained inventory GFPs are shown in Table 2. The intercorrelations of the GFPs from the different inventories are generally positive, with the exception of the MPQ and the HEXACO. In the case of the MPQ, it is obvious that the first factor has merely come out in a negative direction—reflecting all its signs aligns it with the others. The case of the HEXACO is more complicated—negative correlations with some of the other GPFs and very low positive correlations with others. We return shortly to the issue of why this inventory may be behaving differently. To provide further aid in the interpretation of the individualinventory GFPs, their correlations with the Big Five traits are shown in Table 3 (the corresponding correlations for the Hopwood GFPs are provided in parentheses for comparison). It is evident that most of the individual-inventory GFPs showed substantial negative correlations with Neuroticism, and substantial positive correlations with Extraversion, along with correlations that were typically also positive, although sometimes quite modest, with Openness, Agreeableness, and Conscientiousness. A notable exception is the Multidimensional Personality Questionnaire (MPQ), for which, as noted, the first factor appears to have come out in the negative direction: if reflected, its correlations are

N

16PF 6FPQ CPI HEX HPI MPQ NEO TCI

E .32(.45) .20(.00) .57( .52) .13( .05) .75 ( .63) .65(.22) .85( .72) .43( .50)

O .66( .18) .55( .25) .46(.57) .36(.45) .39(.52) .25(.34) .51(.67) .54(.59)

16PF 6FPQ CPI HEX MPQ HPI NEO TCI

16PF

6FPQ

CPI

HEX

MPQ

HPI

NEO

TCI

1.00

.55 1.00

.56 .61 1.00

.16 .48 .21 1.00

.40 .08 .52 .27 1.00

.50 .36 .69 .10 .69 1.00

.40 .29 .58 .06 .59 .72 1.00

.55 .43 .47 .03 .39 .60 .61 1.00

Notes: GFP = general factor of personality. See Table 1 for full inventory names. Ns = 573–741.

.35( .09) .64(.39) .44(.47) .30(.39) .17(.08) .01(.45) .14(.50) .32(.34)

C .15( .51) .09 ( .08) .04( .12) .62( .47) .28( .05) .33( .37) .34(.23) .39(.13)

.00( .16) .01( .33) .20(.17) .05(.02) .32(.38) .29( .22) .73(.58) .34(.44)

Notes: GFP = general factor of personality. N = Neuroticism, E = Extraversion, O = Openness, A = Agreeableness, C = Conscientiousness. See Table 1 for full inventory names. In parentheses: corresponding correlations from Hopwood et al. (2011, Table 3).

reasonably typical, although somewhat on the low side with respect to Extraversion and Openness. Comparing these correlations with the corresponding ones from the Hopwood et al. hierarchical analyses, it is apparent that sometimes they are fairly similar: for example, for the CPI, the HPI, the NEO, and the TCI; and sometimes fairly different, for example, for the 16PF, the FPQ, and the MPQ—and in ways that go beyond mere reversal of direction. 3.2. Overall GFPs What happens when a single general personality factor is extracted by the first-factor method from the intercorrelations of the Hopwood et al. hierarchical GPFs and from the first-factor ones of the present analysis? The results are shown in the first two columns of Table 4. The GPF based on the hierarchical analyses of Hopwood et al. has substantial loadings for only four inventories (CPI, HPI, NEO, and TCI), an intermediate loading for HEXACO, and relatively minor loadings for the other three, clearly consistent with the authors’ doubts about the presence of a GFP. However, if one obtains the GFPs from each questionnaire via its first principal factor, one finds seven of the eight inventories load substantially on a common GFP, with only HEXACO as an exception. This result is more in line with the results from van der Linden et al. (2011), and with the claims of Musek and Rushton for the existence of a general factor of personality. The HEXACO inventory is an instructive exception. Twenty of its twenty-four subscales correspond to the traditional Big Five. The other four measure a dimension labeled Honesty–Humility, with subscales Sincerity, Fairness, Greed avoidance, and Honesty. Apparently, the combination of the Agreeableness and the Table 4 First-factor GFPs from ESCS data, by two methods of obtaining initial GFPs, and from higher-order scales. Inventory

First factor Hierarchical

Table 2 Intercorrelations of individual-inventory first-factor GFPs.

A

16PF 6FPQ CPI HEX HPI MPQ NEO TCI

.24 .01 .84 .47 .75 .27 .84 .79

Lower level .67 .53 .81 .06 .87 .63 .76 .70

Higher level .47 .04 .78 .05 .85 .85 .66 .64

Notes: GFP = general factor of personality. ESCS = Eugene-Springfield Community Sample. Hierarchical: based on correlations in Hopwood et al. (2011, Table 1). Lower level: based on first principal factors from the same ESCS scales that Hopwood et al. used. Higher level: based on higher-order scales from ESCS data. In each case, the loadings are for the first principal factor from the relevant correlation matrix. Correlations more extreme than ± .5 shown in bold face. See Table 1 for full inventory names and number of subscales.

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Honesty–Humility subscales has shifted the first factor of this inventory away from that characteristic of the other seven inventories. Indeed, if one eliminates either the four Honesty–Humility subscales or the four Agreeableness subscales from the analysis, one obtains HEXACO GFPs that load .67 or .62, respectively, on the overall GFP. Thus it is clear that an inventory’s first factor can be shifted by its content. Nevertheless, seven of the eight inventories show a substantial common GFP, and the eighth joins them if one excludes one or the other of its two related sets of scales. In short, one would certainly not want to claim that every possible multidimensional personality inventory would yield the same GFP. Nevertheless, the present inventories do appear to contain a substantial common GFP when one estimates it via the first factor.

How does a GFP extracted from higher-order subscales of an inventory compare with one extracted from lower-order scales? The right-most column of Table 4 shows the result. This factor is based on the correlations of the principal factor scores from the higher-order factors from each of the eight inventories—the numbers of scales on which each was based was given in Table 1. With these smaller numbers of scales there were occasionally problems in the initial factoring—in two instances, 6FPQ and MPQ, in which extended iterations led to Heywood cases (communality estimates exceeding 1.00), iteration was terminated after three cycles. It will be seen from the Table 4 loadings that the GFP from the higher-level scales is somewhat less well defined than that from the lower-level scales, although generally resembling those from the other analyses. Individual factor scores from the lower-level and higher-level principal factors analyses were in excellent agreement, as represented by a correlation of .94 between them (based on the 433 individuals who completed all eight inventories). In a final comparison, GFPs were derived directly as first principal factors from the 194 lower-level scales and 42 higher-level scales listed in Table 1. Their factor scores proved to be correlated .95 with each other, and .96 and .88, respectively, with those derived via the inventory first factors. Their correlations with the Big Five domain scales are shown in Table 5. As might be anticipated from their high intercorrelations, the four approaches lead to GFPs all similarly oriented with respect to the Big Five: the highest correlations are positive with Extraversion and negative with Neuroticism, the correlations with Openness and Conscientiousness are positive and intermediate, and those with Agreeableness are positive and small. The two lower-level GFPs are in close agreement, the two higher-level GFPs slightly less so, with the one most different from the rest being that derived via the higher-level individual-inventory factors. It will be recalled that these last are based on fewer variables per inventory—in two cases, as few as three. 3.4. Relation of self- and others’-rating GFPs How well does a GFP based on ratings by others agree with one based on self-ratings for the same inventory? In addition to the Table 5 Correlations of principal-factor GFPs with Big Five dimensions.

All LL variables All HL variables via inventory GFPs, LL via inventory GFPs, HL

N .68 .77 .73 .55

Big Five trait

Self-rating

Others’ rating

Emotional stability Extraversion Intelligence Agreeableness Conscientiousness

.81 .20 .18 .57 .44

.94 .15 .09 .49 .33

Notes: GFP = general factor of personality, first factor among trait intercorrelations. BFI = Big Five Inventory. Others’ rating = rating of person by knowledgeable others. Ns: self-ratings 708; others’ ratings 658.

Table 7 Correlations of BFI self-ratings with NEO scales.

3.3. Lower- or higher-order scales and a GFP?

GFP

Table 6 Principal factor loadings for GFPs from BFI self-ratings and from averaged others’ ratings.

E

O

A

C

.65 .59 .66 .77

.40 .37 .46 .55

.07 .22 .11 .04

.31 .35 .33 .18

Notes: GFP = general factor of personality. N = Neuroticism, E = Extraversion, O = Openness, A = Agreeableness, C = Conscientiousness; LL = lower-level, HL = higherlevel. Ns = 433–439.

N Emotional stability Extraversion Intelligence Agreeableness Conscientiousness

E .37 .11 .05 .09 .10

O .06 .48 .11 .05 .01

A .07 .06 .42 .10 .13

C .08 .01 .04 .30 .07

.15 .10 .04 .01 .31

Notes: N = 637.

eight standard personality inventories that were used by Hopwood et al. (2011), the Big Five Inventory (BFI), which consists of brief descriptive phrases, was filled out by the ESCS participant and by one or more individuals recruited by the participant that knew him or her well. Table 6 shows first principal factors for both. It is evident that the patterns of factor loadings for the self- and others’ ratings correspond quite well. Factor scores for the two correlated .79, based on an N of 658 for whom both were available. Thus GFPs for self- and others’ ratings on the same inventory agreed. However, these GFPs were somewhat different from the consensus GFPs obtained for the eight standard inventories, and, indeed, from those obtained with a different Big Five measure, the NEO, which was part of that consensus. A direct comparison of the NEO and the self-rated BFI, shown in Table 7, suggests that they are far from identical in how they define and measure the Big Five dimensions: the correlations of corresponding scales are in the range .30 to .48 (after reflecting NEO Neuroticism so it is aligned with BFI Emotional Stability). A comparison of Table 6 with Tables 3 and 5 suggests that the BFI GPFs agree with the others in emphasizing Emotional Stability/Neuroticism, but load Agreeableness and Conscientiousness relatively more than Extraversion. The correlations of the GFP self- and others’-rating factor scores from the BFI with the GFP from the lowerlevel inventory scales were .29 and .34 respectively (Ns of 408 and 388), and with the GFP from the NEO were .29 and .33 (Ns of 637 and 599). These correlations are all highly statistically significant, but are notably smaller than those between the self- and otherbased GFPs from the same instrument, or those between GFPs based on higher- and lower-level scales of the eight inventories. 3.5. Relation of GFPs to others’ ratings and to behavioral acts Table 8 shows the relationship of a GFP, as obtained from the first factor among lower-level inventory first factors, to two kinds of criterion data: ratings by others and behavioral act clusters. As Table 8 indicates, a GFP derived from the eight inventories correlates significantly with most of the averaged others’ ratings and most of the behavioral act clusters. The correlations are not high— they are typically in the .10 to .30 range—but they are evidence that the GFP is not wholly artifactual. Most are comparable to the .23 and .28 obtained in the Netherlands between first-factor-based GFPs

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Table 8 Correlations of principal-factor GFP with two kinds of criterion data. Averaged others’ rating

r

Act cluster

Extraversion Agreeableness Conscientiousness Emotional stability Intelligence

.30 .11 .06 .29 .20

Drug use Erudition Creativity Communication Friendliness Undependability

Table 9 Hypothetical numerical example illustrating differences in methods of obtaining a general factor.

r .03 .17 .29 .20 .24 .10

Notes: GFP = general factor of personality, from first factor among lower-level inventory first factors. Ns: others’ ratings 388; act clusters 421. All rs significant at <.05 except those with Conscientiousness and Drug use.

and job performance ratings (van der Linden, te Nijenhuis, & Bakker, 2010). 4. General discussion The present study has provided evidence that GFPs obtained as unrotated first factors have considerable (although not complete) generality across personality inventories and levels of measurement. In contrast to somewhat conflicting previous results in the literature, GFPs derived in this way from self-reports and from others’ reports were substantially correlated. Finally, these GFPs showed modest correlations with behavioral act clusters. Thus the present study suggests that measuring the GFP as a first factor among the traits measured by personality inventories leads to more broadly generalizable results than assuming that a strict hierarchical relationship holds among personality traits. A strict hierarchy is a rather odd way to look at personality, in any case. For cognitive traits, it is plausible to think of some overall general property of the nervous system (perhaps speed, connectivity, size of working memory) that enhances performance for a variety of cognitive tasks, and accounts for the fact that people with larger vocabularies tend also to do better on spatial puzzles. It seems less intuitive that social efficacy, in a Rushtonian interpretation, would in itself be a cause of more agreeable people being more conscientious, and so forth—although the presence of a GFP suggests that they are. How general should a GFP be expected to be? Obviously, a failure of some particular scale of some particular inventory to load on an overall GFP should be of no great concern. The inventories used in this study were derived in different ways for different purposes, and trait areas well represented in some may be skimpily covered or absent in others. Even inventories nominally measuring the same traits may not agree very closely on a scale-by-scale basis (cf. the NEO and BFI, see Table 7). Must a GFP be equally related to all personality traits? It would seem essential for something claiming to be a GFP that it be related to a fairly broad range of personality traits, but that it be related to every one of them to the same degree would not seem to be a sensible requirement. Theorists in the cognitive domain seem quite willing to say that some cognitive tasks are more heavily loaded with g than others are—that, for example, the Block Design subtest of the Wechsler Adult Intelligence Scale is a better measure of g than is Forward Digit Span. On the whole, the GFPs in the present study are appreciably correlated with all of the Big Five traits, although more highly with some (e.g., Extraversion and Neuroticism) than with others. How important is a GFP in accounting for trait relationships? It very much depends on how it is assessed. An artificial numerical example illustrates this (see Table 9). Suppose we have six traits in two clusters, and observe correlations of .8 among traits within clusters and .3 of traits between clusters, as shown in the correlation matrix at the left of the figure. Fitting a simple hierarchical model yields equal loadings of .61 at

Correlations

1.0 .8 1.0 .8 .8 1.0 .3 .3 .3 1.0 .3 .3 .3 .8 1.0 .3 .3 .3 .8 .8 1.0

First factor

Two factors

GF

Schmid–Leiman C1

C2

GF

GF

.55 .55 .55 .55 .55 .55

.71 .71 .71 .00 .00 .00

.00 .00 .00 .71 .71 .71

.71 .71 .71 .71 .71 .71

.74 .74 .74 .74 .74 .74

BF .50 .50 .50 .50 .50 .50

Notes: GF = general factor; C1 and C2 = clusters; BF = bipolar factor.

the upper level and .89 at the lower level, which (taken to enough decimal places) will reproduce the original correlations exactly. Applying a Schmid–Leiman transformation (Schmid & Leiman, 1957) suggests that the single upper-level factor, considered as a general factor, has loadings of .55 on each of the observed variables, with factors specifying two orthogonal clusters accounting for the rest. However, if one obtains an unrotated first factor from the correlation matrix, as indicated in the column headed ‘‘First factor,’’ the loadings on this factor are .71. This does as well as one can in reproducing the correlations with a single factor, although it does not reproduce them as well as the preceding method. However, if one extracts two unrotated factors, as shown in the ‘‘Two factor’’ columns, the first will be a general factor with loadings of .74 on all six variables, and the second a bipolar factor with positive loadings of .50 on one cluster and negative loadings of .50 on the other. And these two factors reproduce the original correlation matrix as well as the hierarchical model does. The point of this example is not to demonstrate that one or the other of the approaches is correct—it is a hypothetical example, and either can explain the data. A Rushtonian might interpret the latter case as a general factor of social efficacy plus a second factor distinguishing modes of achieving it, say via agency or communion, to use Bakan’s (1966) terms. The first factor method, the one used in the present paper, produces general-factor loadings intermediate to those of the other two. In terms of the Schmid–Leiman solution, it provides an overestimate of the GFP. In terms of the two-factor solution, it provides an underestimate. One might argue for it as a good general-purpose compromise. The primary finding of the present study is in a sense methodological: a substantial and quite general GFP emerged when unrotated first factors were used, but did not with hierarchical factor analyses. Seven of the eight inventories loaded substantially on the overall GFP; the eighth, HEXACO, failed to do so because of a greater number of scales in the area of honesty, humility, and agreeableness—if this emphasis was diminished, HEXACO joined the rest. Yet the methodological result is of broader interest. The ability to assess a general factor of personality in a simple and straightforward way should facilitate further explorations with it: for example, its ability to predict a wider range of criteria, or a study of its nature and origins. Nothing in the preceding discussion should be taken as suggesting that in the real world we should extract a GFP and then stop. There are specific factors of personality to deal with in addition to a GFP. If one shows that the GFP may be responsible for more variance than had previously been thought, this does not imply that it accounts for all of it. The present study adds to the evidence that a GFP is a fairly generalizable and quite readily measurable phenomenon. What can be said of its nature and origins? We cannot readily go back to prehistory to see if a GFP emerged, as Rushton and his colleagues speculate, via selection for effective social participation among early humans. Indirect evidence of this comes from twin studies that

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find the GFP to be substantially heritable, with the bulk of its genetic variance non-additive, a possible result of genetic selection for a trait. Results on the latter point, however, have been mixed: Rushton et al. (2008, 2009) found marked non-additivity in several twin studies; Loehlin and Martin (2011a) found a modest amount of non-additivity for adult twins, but two studies of adolescent twins (Loehlin, 2011; Loehlin & Martin, 2011a) found little evidence of non-additivity. There are some difficulties in the evolutionary hypothesis itself: simultaneous selection for two desirable traits will change the population mean on both traits, but will not, of itself, create a within-population correlation between them—indeed, a simple simulation suggests that it will diminish any existing correlation of this kind, due to the restriction of range on both variables (Loehlin, 2011). However, there is evidence from a study of female Australian twins that stable extraverts and neurotic introverts tended to have relatively more offspring than the opposite combinations (Eaves, Martin, Heath, Hewitt, & Neale, 1990). Such a reproductive pattern could lead to an individual-differences dimension contrasting Extraversion and Neuroticism, although it would not lead to a pattern of increasing social efficiency for humans as a whole, as proposed by Rushton et al. (2008). Of course, one cannot rule out the possibility of one evolutionary pattern shifting to another over time, but clearly, this would complicate the picture. One alternative view of a GFP is that it is real, but reflects the implicit personality theories of its raters—whether rating themselves or others (McCrae, Jang, Livesley, Riemann, & Angleitner, 2001). Consistent with this view is the fact that a GFP derived solely from nonshared environmental covariance (via correlations of differences between members of monozygotic twin pairs) was virtually identical with a GFP derived in the ordinary way from covariance reflecting both genetic and environmental factors (Loehlin & Martin, 2011b). Nevertheless, it remains possible that both views are correct, if it is assumed that implicit personality theories are veridical—that their associations among traits mirror, at least broadly, biologically-based associations among these traits. Two ways of addressing this issue suggest themselves. One is to study trait associations at a biological level, and see if something corresponding to a general factor exists that is aligned with rater-based GFPs. The second is to proceed developmentally. In the study mentioned earlier (Loehlin & Martin, 2011b), the GFP of adolescents appeared to be somewhat different in character from that of adults but the use of a different form of the test for the adolescents rendered this result somewhat ambiguous. A longitudinal study—perhaps one starting at younger ages—would seem desirable. A third view does not dispute the existence of a general factor, but holds that it is primarily evaluative in character, rather than a personality trait as such (e.g., Pettersson, Turkheimer, Horn, & Menatti, 2011). It is not entirely clear whether such a general factor would appear in ratings by others as well as by the self—under some interpretations it might be expected to appear in both, with the two being uncorrelated across persons. In the present study, of course, the two were substantially correlated. In summary, although the idea of a GFP of some sort appears to be tenable, it is clear that a good deal remains to be learned about its nature and origins. Acknowledgments I am grateful to Lew Goldberg for permitting me to use the ESCS data, to Chris Hopwood and Maureen Barckley for helping make it

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