The General Factor of Personality: The “Big One,” a self-evaluative trait, or a methodological gnat that won’t go away?

Personality and Individual Differences 81 (2015) 13–22

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The General Factor of Personality: The ‘‘Big One,’’ a self-evaluative trait, or a methodological gnat that won’t go away? q Stacy E. Davies a,⇑, Brian S. Connelly b, Deniz S. Ones c, Adib S. Birkland d a

Korn Ferry, United States University of Toronto, Canada c University of Minnesota, United States d The Colin Powell School for Civic and Global Leadership, The City College of New York, United States b

a r t i c l e

i n f o

Article history: Received 9 May 2014 Received in revised form 21 December 2014 Accepted 5 January 2015 Available online 12 March 2015 Keywords: General Factor of Personality Meta-analysis Five factor model Method variance

a b s t r a c t Though recent research indicates that the Big Five can be subsumed under a ‘‘General Factor of Personality’’ (GFP), considerable dissention remains about whether the GFP is a substantive trait (either a ‘‘mega’’-trait or simply, positive self-evaluation), or a response artifact. To disentangle these potential explanations, we estimated GFP saturation based on scales within a single inventory (which may share response artifacts) versus between different inventories (wherein the GFP would be more substantive). Drawing on meta-analytic findings across 370 independent samples of 155,781 individuals, GFP saturation was reduced substantially when based on between inventory data (26%) compared to within inventory data (50%). These results indicate that the GFP functions as a response artifact that may be reduced by administering scales from different inventories. However, some GFP variance also appears to represent stable tendencies that span across inventories. Overall, the GFP appears to be partly a stable, self-evaluative trait and partly a set of response tendencies specific to a particular personality inventory. We discuss the implications of these results for academic and applied personality measurement. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Almost immediately after many personality researchers reached consensus that five factors tend to underlie the trait domain (Costa & McCrae, 1992; Digman, 1990; Goldberg, 1993), researchers across multiple fields began noting that the five factors are not necessarily orthogonal constructs (Digman, 1997; Ones, 1993). The noteworthy correlations among measures of the five factors has led to (often contentious) propositions that traits may exist at an even higher and more general stratosphere than that of the Big Five/five factor models. Digman (1997) noted that Emotional Stability, Agreeableness, and Conscientiousness together formed a higher-order factor named ‘‘Alpha,’’ whereas Extraversion and Openness clustered together in a higher-order factor named ‘‘Beta.’’ Alpha (later re-named ‘‘Stability;’’ DeYoung, 2006) captures basic tendencies to be properly socialized and provides an avenue for aligning the five factor model with theories ranging from Freudian impulse restraint (Freud, 1930) to Block’s ego control (Block & Block, 1980; DeYoung, 2010b). It can be q

This article is a Special issue article – ‘‘Young researcher award 2014’’.

⇑ Corresponding author.

E-mail address: [email protected] (S.E. Davies). http://dx.doi.org/10.1016/j.paid.2015.01.006 0191-8869/Ó 2015 Elsevier Ltd. All rights reserved.

interpreted as ‘‘socialization,’’ the source trait for socialized behavior. Beta (renamed as ‘‘Plasticity’’ in DeYoung, 2006) reflects core tendencies to explore one’s world and brought trait perspectives in line with theories of personal growth (Maslow, 1943; Rogers, 1961). Though the existence of Alpha and Beta as higher factors has been debated (Biesanz & West, 2004), the emergence of these meta-traits set off research trajectories into their physiological bases (DeYoung, 2010a; DeYoung, Peterson, & Higgins, 2002), behavioral outcomes (Hirsh, DeYoung, & Peterson, 2009), heritability (Jang et al., 2006), and role in integrating normal and abnormal personality (Markon, Krueger, & Watson, 2005). More recently, researchers have noted that Alpha and Beta are not orthogonal higher-order factors but are in fact correlated, potentially indicating that a General Factor of Personality (GFP) sits atop the personality hierarchy (akin to the g factor in intelligence; Figueredo, Vásquez, Brumbach, & Schneider, 2004; Musek, 2007; Rushton, Bons, & Hur, 2008). Indeed, e.g., Rushton and Irwing (2008, 2009) have documented a wide variety of personality inventories from which a GFP could be recovered. Reflecting high Emotional Stability, Extraversion, Openness, Agreeableness, and Conscientiousness, the GFP is conceptualized as a general characteristic that facilitates general survival, adaptability and success across many domains of life (Rushton & Irwing, 2008).

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Accordingly, a wealth of research has emerged in just the past 5 years depicting the GFP’s etiology and its associated outcomes (e.g., Rushton et al., 2008; Van der Linden, Te Nijenhuis, & Bakker, 2010; Van der Linden, Vreeke, & Muris, 2013; Veselka, Schermer, Petrides, & Vernon, 2009). Though there have been over 80 replications finding a GFP (in some form) in personality measures in just the 7 years since Musek (2007) influential paper, the substantive existence of the GFP remains fiercely debated. Two issues have been central to this debate. First, the substantive meaning researchers attach to the GFP has varied from that of an imperial trait sitting atop the personality hierarchy to that of a methodological artifact that, if personality research could squelch, it would be all the better for. Second, even though research often finds a GFP in personality measures, researchers have strongly debated the extent to which personality measures are actually saturated with GFP variance. The purpose of the present research is to enhance our understanding of what the GFP is and how important its role is in measuring personality. In the paragraphs that follow, we review three explanations for what the GFP is and describe research disentangling its importance. We then present our meta-analytic findings contrasting how strong the GFP is when extracted from scales within a single personality inventory versus from scales across different inventories. Moreover, we separate the influence of a GFP common across multiple inventories from within-inventory method variance (which might reflect inventory-specific response tendencies). These data are informative for debates regarding where the GFP falls in the trait-artifact continuum, and our largescale data and appropriate modeling techniques for indexing how much effect the GFP has on personality measures (Revelle & Wilt, 2013). We conclude by offering some recommendations for how personality research and measurement can be enhanced in light of findings related to the GFP. 1.1. A General Factor of Personality: what is it? Though many interpretations have been offered for the GFP, they can generally be grouped within three categories. The first of these is that the GFP represents a meaningful, substantive trait at the top of the personality hierarchy. As espoused by Rushton and colleagues (e.g., Rushton & Irwing, 2008; Rushton et al., 2008), the GFP represents possessing a broad variety of traits deemed as socially appropriate and desirable. Rushton (1985) argued that animals have evolved by generally pursuing one of two strategies for surviving natural selection: by investing substantially in a smaller number of offspring who are likely to survive (a K-strategy) or by propagating a larger number of offspring who receive relatively little parental investment (an r-strategy). Rushton et al. (2008) argued that differences in adopting K- vs. r-strategies produces high vs. low standing on the GFP, akin to social efficiency or ‘‘a suite of traits genetically organized to meet the trials of life—survival, growth, and reproduction’’ (Rushton et al., 2008, p. 1173). In support of this position, findings have shown that the GFP from employee self-reported personality is correlated with supervisor-rated job performance among employees (Van der Linden, Te Nijenhuis et al., 2010) and peer-rated Likeability and popularity among students (Van der Linden, Scholte, Cillessen, Te Nijenhuis, & Segers, 2010). An alternate perspective has been that the GFP represents a stable, self-evaluative trait akin to self-esteem (Anusic, Schimmack, Pinkus, & Lockwood, 2009). In this way, the correlations among the five factors arise not from true correlations among the latent constructs but rather from a general tendency to see oneself in a positive vs. negative light that pervades personality self-ratings. Indeed, self-esteem is strongly correlated with the GFP (Anusic et al., 2009; Erdle, Irwing, Rushton, & Park, 2010),

though researchers have disagreed as to whether this indicates that self-esteem is a biasing factor across judgments of the Big Five or whether standing on a ‘‘true’’ GFP is acting as a determinant of self-esteem (Anusic et al., 2009; Erdle, 2013; Erdle & Rushton, 2011; S ß imsßek, 2012). Interestingly Van der Linden, Te Nijenhuis et al. (2010) report that in employment settings, where one might expect to see a larger GFP due to the greater impetus to present oneself positively, the GFP saturation was similar or somewhat smaller (42%) than the other samples examined (42–62%). Finally, other researchers have argued that the GFP represents only a general response set that affects the way individuals interact with a personality inventory. For example, researchers have long documented the effects of response sets like acquiescence bias, midpoint-responding, and impression management on personality measures (Couch & Keniston, 1960; Cronbach, 1946). Such a response set could artifactually create a pattern of correlations among personality measures that do not reflect (a) correlations among actual latent traits or (b) a stable self-evaluative trait. Rather, a GFP attributable to a response set would likely represent a factor that is likely highly contextualized to the personality inventory used and the assessment setting (e.g., measures collected for research purposes vs. for personnel selection). Relatedly, Bäckström, Björklund, and Larsson (2009) found that GFP saturation was markedly reduced when personality inventories were created that minimized the effects of socially desirable responding.1 Note that these three perspectives point to markedly different directions for personality researchers to take in light of findings of the GFP, and these explanations are not mutually exclusive. To the extent that the ‘‘substantive, superordinate trait’’ perspective is correct, personality research would fruitfully begin documenting the GFP’s causes and outcomes as the field has done with the five factors. If, on the other hand, the GFP reflects primarily a self-evaluative trait, personality research would likely benefit from methods that separate Big Five trait variance from self-evaluative trait variance. Finally, if the GFP is primarily an artifact of response sets, researchers would be well served by either revising existing measures to minimize the effects of these response sets or by aggregating measures across multiple time points, contexts, or inventories. The field of personality has devoted a formidable amount of research to disentangling these three perspectives, of which two general types of designs have been particularly informative. First, researchers have used multi-rater designs for measuring personality (e.g., soliciting personality ratings from self-reports and one or more informant). For example, Anusic et al. (2009) examined whether the GFP (termed halo in their work) was correlated across raters, and Riemann and Kandler (2010) examined whether a General Factor of Personality could be extracted from multi-informant data after modeling common method effects. These multiinformant designs are powerful because they are predicated on the notion that a substantive latent GFP should manifest itself in behaviors that peers observe and base personality judgments on. Thus, multi-informant designs effectively pit ‘‘The Big One’’ explanation of the GFP against a shared method variance explanation (whether that shared method variance reflects a general self-evaluative trait or inventory-specific response styles). Individual multirater studies have shown somewhat discrepant results, with some 1 A frequent critique of the General Factor of Personality is that it may simply reflect social desirability. However, we find it particularly meaningful to disentangle socially desirable responding that emerges from having a general, positive impression of oneself that would be consistent across any measurement occasion from socially desirable responding that is dependent on the measurement context. Paulhus (1991, 2002) has made similar theoretical distinctions in separating two forms of social desirability: self-deceptive enhancement vs. impression management. Thus, a critical test of whether the GFP might represent a self-evaluative trait vs. a response set is whether researchers can methodologically reduce the effects of the GFP on self-report measures without changing the nature of the traits being measured.

S.E. Davies et al. / Personality and Individual Differences 81 (2015) 13–22

studies finding a GFP that converges across raters at the apex of personality (Rushton et al., 2009; Van der Linden et al., 2013), some finding only Alpha and Beta factors (Anusic et al., 2009; Danay & Ziegler, 2011; DeYoung, 2006), and some finding the Big Five to be relatively orthogonal (Biesanz & West, 2004). However, studies that have tended to find convergence across raters have not generally specified method factors to separate these effects from a substantive GFP (in the case of Rushton & Irwing, 2009) or modeled consensus stemming from the unique trait variance of the Big Five (as in Van der Linden et al., 2013).2 However, meta-analytic multi-informant research that has adopted such approaches has not supported the existence of a latent GFP across consensually-rated traits (Chang, Connelly, & Geeza, 2012; Gnambs, 2013). Thus, the pattern of findings suggests that the GFP is more likely localized within raters as either an evaluative trait or a response set, rather than standing as a substantive trait atop the personality hierarchy. In either case, it can still have usefulness in predicting outcomes and behaviors. Second, research has also examined whether different inventories can produce corresponding GFPs. This research is predicated on the assumption that if the GFPs produced by different inventories do not correspond to one another, the GFP is more likely to represent a response set specific to a personality inventory rather than a more general self-evaluative trait or substantive, higherorder trait. A number of studies (Loehlin, 2012; Van der Linden, Te Nijenhuis, Cremers, & Van de Ven, 2011) have shown that factor scores based on the first principal component from one inventory tend to be strongly correlated with corresponding factor scores from another inventory. However, convergence across inventories’ traits (e.g., relationships between Extraversion scales on the NEO and on the Big Five Inventory) can produce strong correlations across inventories’ GFP factor scores even when no general factor is present (Revelle & Wilt, 2013) or when all convergence is produced by the specific variance of narrow traits. Analyses that have subjected multiple inventories to joint factor analyses or that have only modeled narrow traits converging across inventories have found little support for the presence of a GFP (de Vries, 2011a; Hopwood, Wright, & Donnellan, 2011). However, such analyses require substantial sample sizes, which can be difficult to achieve when administering multiple inventories.

1.2. A General Factor of Personality: how strong is it? Apart from disentangling the meaning of the GFP, an additional issue is how pervasive its effects are on personality measures. If GFP saturation is relatively weak, disentangling its meaning (and potentially its variance associated with personality measures) 2 Much of the apparent dissension in findings and interpretations of the GFP may be tied to differing assumptions about whether the effects of the GFP should be estimated while modeling/controlling for the effects of narrower traits (e.g., the Big Five). For example, in correlating the GFP across raters, Anusic et al.’s (2009) confirmatory factor analytic model also modeled cross-rater correlations for Alpha/ Beta meta-traits and the Big Five; in contrast, Van der Linden et al. (2013) reported cross-rater correlations of GFP factor scores which do not account for lower level traits. Similar dissension has arisen in correlating the GFP with behavioral outcomes (c.f., de Vries, 2011b; Van der Linden, Scholte et al., 2010). Such modeling choices have a substantial impact in determining the magnitude of GFP correlations. If one’s goal is simply to examine the predictive power of the family of traits within a factor, omitting effects of lower-level traits is generally acceptable. On the other hand, if one’s goal is to demonstrate that the shared variance of traits within a factor represents a theoretically meaningful trait existing beyond current trait taxonomies, then demonstrating incremental prediction beyond the effects of lower level traits is necessary. This is most effectively accomplished using latent variable models that separate prediction from shared vs. specific trait variance (e.g., Chen, West, & Sousa, 2006; but for an example of a comparable regression-based approach, see Salgado, Moscoso, & Berges, 2013). We would encourage such analyses not only for the GFP but throughout the trait hierarchy.

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may not represent a prominent concern for personality researchers. However, in addition to encountering debates about whether a GFP is present across a variety of methods, researchers have also differed greatly in their findings of how strongly personality measures are saturated with the GFP (a summary table is available from authors upon request). These differences stem, in part, from discrepant analytic procedures used to calculate GFP saturation. Revelle and Wilt (2013) differentiate between three commonly used methods for depicting the strength of the general factor in GFP research. The majority of the authors reported the GFP saturation as the amount of variance accounted for by the 1st factor from an EFA (Method 1 in Revelle & Wilt, 2013). By this method, GFPs saturation ranges from 22% to 79% (mean = 41.55%, SD = 11.35). In other cases, researchers conduct a hierarchical CFA with the observed variables (often the Big Five traits) at the first level, then first order latent factors (often a and b) at the next level, and finally the latent GFP factor at the top of the hierarchy. Researchers have calculated the GFP saturation from these CFA models by multiplying the paths directly extending from the GFP factor (Method 3 in Revelle & Wilt, 2013). In the 2 first order factor case (e.g., a and b), this GFP is essentially the correlation between the first order factors. For example Rushton and Irwing (2008) show the latent factors a and b loading .67 on the GFP and report the GFP saturation as 45%. Researchers using these methods report GFP saturations that are also quite varied, ranging from 25% to 65% (mean = 45.32%, SD = 11.03). However, Revelle and Wilt note that these methods for estimating GFP saturation (variance accounted for by the first factor and the product of second-order factor loadings) are prone to mis-estimating the strength of the GFP. Specifically, in the case of variance accounted for by the first factor, these mis-estimates stem from an insensitivity to the presence of subfactors like Alpha and Beta; in the case of using second-order factor loadings, this procedure overestimates GFP saturation because its saturation is not estimated at the level of the observed Big Five measures but at that of their higher-level meta-traits. Instead, they suggest an alternate metric for indexing GFP saturation (xhierarchical, labeled as ‘‘Method 5’’ in Revelle & Wilt, 2013). Conceptually, xhierarchical focuses on the effect of the GFP on the variables themselves rather than the effect of the GFP on the first order latent factors. In CFA terms, instead of running a hierarchical model where the Big Five observed variables load on the first order latent variables of a & b, which then load on the latent GFP factor, a bifactor model is examined. The bifactor model has 3 separate latent factors (GFP, a, & b) which are orthogonal (correlations between factors are constrained to zero). Analyzing the data in this way allows us to see the direct effect of the GFP on the observed personality variables, controlling for the effects of a and b. To arrive at the GFP saturation percent, one sums the squares of the general factor loadings and divides by the sum of the total correlation matrix. Revisiting eight earlier studies, Revelle and Wilt show that using the correct xhierarchical procedure for calculating GFP saturation yields lower but more consistent estimates of GFP saturation. However, apart from the 8 datasets re-analyzed in Revelle and Wilt, the number of studies estimating GFP saturation using xhierarchical has been quite limited. 1.3. The present study Though meta-analytic research of multi-rater designs has cast doubt on the ‘‘substantive higher-order trait’’ explanation for the GFP, no large-scale or meta-analytic data has been brought to bear on multi-inventory data. Thus, it remains somewhat unclear (a) how much of the GFP reflects an inventory-specific response set and (b) how saturated personality measures are with GFP variance. The purpose of the present study is to bring meta-analytic integration to the question of the GFP’s meaning and importance.

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Specifically, we meta-analyze personality intercorrelations from a large database (370 independent samples consisting of a total of 155,781 individuals) and apply GFP saturation estimation using xhierarchical as recommended in Revelle and Wilt (2013). Using meta-analysis is particularly appropriate for both (a) integrating results across a variety of samples and instruments and (b) for capitalizing on the large sample size necessary for achieving stable CFA estimates for calculating xhierarchical. In addition, we consider a focal methodological moderator in estimating personality trait intercorrelations from scales (a) within the same personality inventory (e.g., NEO Extraversion with NEO Conscientiousness) vs. (b) between different personality inventories (e.g., NEO Extraversion with BFI Conscientiousness). The logic in separating within vs. between intercorrelations for estimating GFP saturation directly parallels that of multi-inventory research extracting a GFP (or correlating GFPs across inventories). That is, if within and between inventory analyzes produce comparable saturation from the GFP, the GFP would appear to be a relatively stable self-evaluative trait that is not affected by changes in instrumentation. However, if GFP saturation is markedly stronger within inventory than between inventories, the GFP is more likely a methodological artifact reflecting response tendencies in how individuals interact with a given personality inventory. 2. Methods Using the intercorrelations among Global Big Five traits, we examined the relationships of the lower order big five traits to both alpha/beta meta-traits and a General Factor of Personality. Specifically, we used EFAs and CFAs to estimate the general factor saturation (i.e., strength of the general factor) and used CFAs to assess the fit of models to the meta-analytic intercorrelation data. To assess a previously uninvestigated potential moderator, all of these analyses were done twice: once for correlations within inventories and once for correlations between inventories. 2.1. Meta-analytic database Compared to other meta-analyses, synthesizing intercorrelations among the five factors of personality presents a markedly different challenge. Whereas many other meta-analyses can successfully use search databases to locate relevant articles (e.g., searching for ‘‘conscientiousness AND counterproductive work behaviors’’ in PsycINFO), researchers often collect and report intercorrelations among personality scales without these intercorrelations being an explicit focus of investigation. In addition, a comprehensive search procedure would likely entail reviewing nearly a century of research on traits, not only within the main field of personality but also in domains where personality scales may be applied (e.g., clinical psychology, industrial/organizational psychology, health psychology, and political psychology). Thus, rather than striving to be exhaustive in our search, we aimed to focus on collecting sources likely to (a) use well-validated personality inventories, (b) provide in-depth scale descriptions that would facilitate accurate coding of scales, and (c) have a high probability of providing intercorrelations within and/or across inventories. We began by building our meta-analytic database by searching through a collection of over 200 psychological test manuals. Test manuals are ideal sources of data for these meta-analyses because they tend to offer more detailed information regarding the test in question than do journal articles (such as reliabilities, in-depth descriptions and definitions of the scales, and intercorrelations within and across personality inventories). Test manuals are also more likely to use normative or community samples, which may lessen the effects of range restriction or enhancement that can occur with samples of convenience. Next, we also adopted several

strategies for supplementing our collection of test manual data with published research. First, we manually searched the journals Personality and Individual Differences, the Journal of Personality and Social Psychology, and the Journal of Applied Psychology for the years 2004–2010, as these journals were particularly likely to present full correlation matrices of personality scales. Finally, we also targeted articles likely to have used faceted measures of personality (e.g., the NEO-PI-R, which splits the five factor domain into a set of narrower facets), as faceted measures likely represent broader coverage of each trait domain. Specifically, we searched in Web of Science for recognizable facet traits (e.g., ‘‘sociability’’ and ‘‘assertiveness’’ as facets of Extraversion). Within these search results, we reviewed any articles (a) that were cited over 50 times or (b) were published in Personality and Individual Differences, the Journal of Personality and Social Psychology, or the Journal of Applied Psychology. In reviewing these articles, we excluded data that was obtained by methods other than self-report (e.g., peer reports, interviews). We also excluded data from purely ipsative measures because ipsativity tends to force a pattern of negative correlations between personality scales. Since we were interested in the range of normal personality, we also excluded data from clinical inventories (e.g., MMPI, BDI, etc.) and clinical samples (e.g., psychiatric patients, prisoners, etc.). Using emerging taxonomies (Birkland, Connelly, Ones, & Davies, 2014; Connelly, Ones, Davies, & Birkland, 2013; Davies, 2012) that are a refinement of the taxonomy in Hough and Ones (2001), we coded each personality scale as representing a ‘‘Global’’ measure (broad coverage of a factor’s domain), a specific facet (a narrow trait within a single factor domain), or a compound trait (a trait spanning across multiple factor domains). Importantly, we limited our present analysis to only global measures of Emotional Stability, Extraversion, Openness (including Intellect definitions), Agreeableness, and Conscientiousness. For scales not classified in this taxonomy, scales were independently coded by the first author and the third author. Scale classifications were based on the scale descriptions, definitions, and items. Any classification disagreements between the 2 coders were discussed until consensus was reached or if consensus was not reached that measure was classified by the second author. If consensus still was not reached, the scale was excluded from further analyses. After classifying each of the measures to appropriate big five traits, this data collection effort for GFP analyses resulted in 3113 correlations across 155,781 individuals in 370 samples. Of these, 950 correlations came from manuals and 2163 came from journals. Further breaking this down, 1960 correlations came from within inventories, while 1153 correlations came from between inventories. 2.2. Meta-analytic procedures The meta-analytic procedures of Hunter and Schmidt (2004) were used to analyze the database. Hunter and Schmidt’s approach to meta-analysis is a random effects form of meta-analysis that involves statistically pooling data across studies to minimize the impact of sampling error on study findings. In addition, attenuating influences of measurement error are controlled for through corrections for attenuation. To compute unreliability corrected, true score correlations between constructs, we used the internal consistency reliability estimates in the articles to create separate reliability distributions for each of the big five traits. Mean square roots of reliabilities were .90 for Emotional Stability, .90 for Extraversion, .87 for Openness, .88 for Agreeableness, and .89 for Conscientiousness. In aggregating our meta-analytic results, some individual studies contributed multiple correlations to the database that were relevant for the same investigation. This would violate assumptions of dependency among the correlations if they were not pooled within studies before aggregating meta-analytic results across studies. For

S.E. Davies et al. / Personality and Individual Differences 81 (2015) 13–22

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Fig. 1. Confirmatory factor analytic models for separated within- and between-inventory data. Note: Unstandardized paths with the same dashed pattern were constrained to be equal.

example, in meta-analyzing the Agreeableness–Conscientiousness relationship between two different inventories, one study might report correlations between NEO-PI-R Agreeableness and HPI Prudence as well as between NEO-PI-R Conscientiousness and HPI Likability. In such cases, correlations were averaged within studies before meta-analytically averaging across studies. In other cases, single inventories can contain multiple measures of the same big five trait. For example, the 16 PF contains both the scale ‘‘apprehension’’ and the scale ‘‘tension’’ which are both classified as global Emotional Stability. Because this inventory ‘‘splits’’ the Emotional Stability domain between the two measures, correlations of each of these scales with other inventories’ big five scales would likely be underestimates of the true correlations (Nunnally, 1978). Therefore, composite correlations were computed in cases in which a single inventory contained multiple measures of the same big five construct. This composite correlation estimates the correlation for the sum of the component measures (Hunter & Schmidt, 2004). 2.3. Base confirmatory factor analysis models Following procedures in Viswesvaran and Ones (1995), we submitted each meta-analytic matrix of observed correlations to confirmatory factor analyses (CFA). Fitting latent variable models to meta-analytic intercorrelations has become common in many fields over the past 20 years and has been used to study (for example) links between job attitudes and performance (Harrison, Newman, & Roth, 2006), psychological predictors of pro-environmental behaviors (Bamberg & Möser, 2007), and the dimensionality of work commitment (Cooper-Hakim & Viswesvaran, 2005). In addition to a null model in which the big five traits were specified as orthogonal, we sequentially tested three CFA models (see Fig. 1): a general factor only model with big five traits loading only on the GFP directly, a hierarchical model with big five traits loading on their respective alpha and beta factors which then load on the GFP, and finally a bifactor model where big five traits load on the GFP and also load on their respective alpha and beta factors but those factors do not correlate with the GFP. This progression of models establishes the extent to which including the GFP and Alpha/Beta meta-traits independently capture the covariance among Big Five personality traits. To allow the models to be identified, it was necessary to constrain some parameters to be equivalent in some models. In the hierarchical model, we constrained the second order factor loadings of Alpha and Beta on the GFP to be equal (though their residual variances were freely estimated, which can produce different standardized factor loadings). In the bifactor model, we constrained Emotional Stability, Agreeableness, and Conscientiousness’s loadings on Alpha to be equal and Extraversion and Openness’s loadings on Beta to be

equal and allowed all GFP loadings to be freely estimated. We use these models to estimate the strength of GFP saturation and to compare GFP saturation across within and between inventory correlations.3 3. Results 3.1. Within inventory correlations The detailed meta-analytic within inventory intercorrelation matrix for the Global Big Five can be seen in the top portion of Table 1. The average observed, k-weighted meta-analytic intercorrelation of the Big Five was r = .20. The CFA models run were a null model where the big five were orthogonal, a model where the latent GFP factor loads directly on the Big Five (Fig. 1a), a hierarchical model with a second order latent GFP factor (Fig. 1b), and finally a bifactor model that parses out the variance in the Big Five that is due to orthogonal GFP, a and b factors (Fig. 1c). The fit statistics for each of these models can be found in Table 2. Looking at the fit statistics for TLI and RMSEA, the hierarchical model shows the best fit to the within inventory data, with strong loadings on the GFP from a and b (.82 and .61, respectively). In the bifactor model where direct paths were specified to the Big Five and both a and b’s indicators were constrained, fit worsened slightly and variance accounted for by a was completely absorbed by the GFP (perhaps because of the equality constraints on the factor loadings imposed for model identification). We used the bifactor model to estimate GFP saturation in the within-inventory data; these data produced xh = .50. 3.2. Between inventory correlations The detailed meta-analytic between inventory intercorrelation matrix for the Global Big Five can be seen in the bottom portion of Table 1. The average observed, k-weighted meta-analytic

3 An anonymous reviewer shared an independent set of analyses that compare the higher-order factor structure when estimated using confirmatory factor analysis (CFA) vs. exploratory factor analysis (EFA). CFA results produced GFP saturation of xhierarchical (xh) = .39 for within inventory matrices and xh = .25 for between inventory matrices. However, applying an EFA approach to the within inventory data reduced the GFP saturation somewhat (to xh = .30 when using maximum likelihood rotation and to xh = .34 when using principal axis rotation). Although the cross-loadings of FFM traits were consistently weak (|k|’s < .12), estimating these loadings appears to reduce GFP saturation. In the present manuscript, we retained our CFA approach to preserve parity with past research positing the GFP as a single factor atop simple-structured Alpha and Beta factors. However, the reviewer kindly agreed for these supplemental analyses to be posted in Online Supplements. We refer the interested reader to these and encourage further examination of the effects of analytic approaches on estimates of the strength of the GFP.

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Table 1 Detailed meta-analytic intercorrelations of global Big Five measures. Variables Within inventory correlations Emotional Stability with: Extraversion Openness Agreeableness Conscientiousness Extraversion with: Openness Agreeableness Conscientiousness Openness with: Agreeableness Conscientiousness Agreeableness with: Conscientiousness Between inventory correlations Emotional Stability with: Extraversion Openness Agreeableness Conscientiousness Extraversion with: Openness Agreeableness Conscientiousness Openness with: Agreeableness Conscientiousness Agreeableness with: Conscientiousness

k

N

r

SDr

SDres

q

SDq

211 154 167 166

92,111 65,095 79,610 84,256

.22 .07 .24 .27

.16 .16 .20 .17

.15 .16 .20 .17

.27 .09 .31 .33

.18 .20 .24 .21

.03 .24 .08 .02

.57 .42 .70 .68

159 158 156

71,206 75,274 74,154

.26 .16 .15

.16 .21 .16

.15 .20 .15

.33 .20 .19

.19 .26 .18

.02 .23 .11

.64 .63 .49

148 148

61,538 62,258

.15 .09

.13 .19

.12 .19

.19 .12

.16 .24

.07 .27

.45 .51

158

76,306

.32

.19

.18

.41

.23

.03

.79

89 50 48 46

18,246 11,747 11,213 11,162

.23 .06 .25 .27

.12 .14 .13 .17

.10 .12 .12 .16

.28 .08 .32 .34

.12 .15 .15 .19

.08 .17 .07 .03

.48 .33 .57 .65

61 54 71

14,638 12,502 18,405

.14 .07 .08

.14 .16 .14

.13 .15 .12

.18 .09 .09

.16 .18 .15

.08 .21 .16

.44 .39 .34

39 41

9886 11,101

.02 .00

.10 .15

.08 .14

.02 .00

.11 .17

.16 .28

.20 .28

43

12,405

.20

.15

.14

.26

.17

.02

.54

Lower CI

Upper CI

Note: k = number of independent samples; N = number of subjects; r = mean observed correlation (corrected for sampling error only); SDr = standard deviation of observed correlations; SDres = observed variability minus variability due to sampling error and unreliability in both predictor and criterion; q = true score correlation (correcting for unreliability in both measures); SDq = standard deviation of true score correlation; Lower CI = lower bound of 90% credibility interval for q; Upper CI = upper bound of 90% credibility interval for q.

Table 2 Detailed confirmatory factor analysis result: General Factor of Personality (within vs. between inventories). Model

Within-inventory Null model GFP only Hierarchical Bifactor

Model Fit df

p

data 26,544.68 3950.31 1091.74 1100.06

10 5 4 3

<.01 <.01 <.01 <.01

.00 .70 .90 .86

10 5 4 3

<.01 <.01 <.01 .08

.00 .80 .90 1.00

Between-inventory data Null Model 2981.51 GFP only 306.48 Hierarchical 120.91 Bifactor 6.76

a Loading

GFP Loading

v2

TLI

CFI

RMSEA

ES

.00 .85 .96 .96

.19 .10 .06 .07

– .48

.00 .90 .96 1.00

.15 .07 .05 .01

– .70

.48

.53

A

C

EX

– .53 ka = .82 .54

– .53

– .37 ka = .65 .15

– .39

.56

.18

OE

b Loading

ES

A

C

EX

OE

– – .38 .27 kb = .61 .33 .20

– – .48 .00

– – .54 .00

– – .56 .00

– – .65 .44

– – .40 .44

– – .30 .10 kb = .59 .44 .11

– – .70 .41

– – .37 .41

– – .39 .41

– – .77 .30

– – .18 .30

2

Notes: v = Chi square statistic; df = degrees of freedom; p = significance level of chi square statistic; TLI = Tucker Lewis index; CFI = comparative fit index; RMSEA = root mean square error of approximation; GFP, a, and b loadings reflect loadings on each factor.

intercorrelation of the Big Five was r = .14. In addition to running a null model where the Big Five were kept orthogonal, we submitted this meta-analytic observed intercorrelations matrix for between inventory correlations to the three CFA models depicted in Fig. 1. The fit statistics for each of these models can be found in the bottom portion of Table 2. Looking at the fit statistics for TLI, CFI, and RMSEA, the bifactor model shows the best fit to the between inventory data. The bifactor model fits the between factor data very well (TLI = .996 and RMSEA = .010), with the GFP being primarily defined by Extraversion and Emotional Stability. GFP saturation was markedly weaker in the between inventory data (xh = .26, though comparing xh’s across within and between inventory data is complicated by the drastic differences in loadings on a and b).

3.3. Separating the GFP from inventory method variance Within and between inventory data showed marked differences in how higher order factors were defined and in how strong the GFP saturation was. Thus, it is possible that some of the GFP factor in the within-inventory data simply reflects inventory-specific response styles akin to method variance. In addition, some of this reduction could simply be caused by imperfect construct validity of a single inventory’s Big Five measures (i.e., cross-inventory convergent validities <1.00). To generate GFP saturation estimates that correct for these influences directly, we used our within and between inventory observed correlations to compose a 10  10 Multi-Trait Multi-Method (MTMM) matrix that crossed the Big Five with two inventories. Specifically, our within-inventory correlations served

S.E. Davies et al. / Personality and Individual Differences 81 (2015) 13–22

19

Fig. 2. Confirmatory factor analytic models for multi-trait multi-inventory data. Note: Unstandardized paths with the same dashed pattern were constrained to be equal. All unstandardized paths were constrained to be equal across respective indicators of Inventory 1 and Inventory 2.

as hetero-trait mono-method correlations and our between-inventory correlations served as hetero-trait hetero-method correlations. To complete the matrix, we drew mono-trait hetero-method correlations from Pace and Brannick (2010) meta-analysis of personality convergent validities.4 We subsequently used this matrix to fit a series of CFA models (see Fig. 2) in MPlus version 6, using the harmonic mean sample size across the meta-analytic correlations of N = 21,504. Because there was no distinction between inventories, factor loadings for inventory 1 indicators were constrained to be equal to loadings for inventory 2 indicators across all models. As before, all (unstandardized) loadings on a and b were constrained to be equal within each meta-trait’s indicators. Fit statistics, factor loadings, and estimates of xh for these models appear in Table 3. First, we fit a pair of base models in which we extracted latent Big Five factors above each inventory’s indicators and (a) allowed them to correlate freely (Fig. 2a) or (b) specified correlated 4 We used estimates in tables labeled as ‘‘All tests’’ but selected estimates omitting sample size outliers. Specifically, these estimates were .51, .56, .45, .47, and .43 for Emotional Stability, Extraversion, Openness, Agreeableness, and Conscientiousness.

higher-order a/b factors. The a/b Higher-Order model fit nearly as well as the Correlated Domains model with strong second-order loadings, suggesting that a and b were effective at capturing the correlations between latent Big Five domains. Next, we examined GFP saturation with a bifactor model among the latent Big Five factors (Fig. 2c). Adding a GFP factor improved fit with moderate loadings from most of the Big Five except Extraversion (which initially produced a Heywood case because of a strong loading on the GFP). In this model, GFP saturation was xh = .44. However, adding inventory method factors (Fig. 2d) both strongly improved the fit of the model and reduced estimates of GFP saturation by almost 30% (xh = .32). Finally, we replicated the above models to estimate the effects of the GFP on the Big Five at the level of observed scales rather than at the level of latent traits (Fig. 2e and f). In these models, GFP saturation was weaker because these estimates do not correct for imperfect construct validity of the measures. However, accounting for inventory method variance reduced estimates of GFP saturation from xh = .38 to .27. Thus, a sizeable portion of what is typically estimated as the GFP appears to be response patterns localized

.37

Note: Italicized numbers reflect parameters constrained to be equal across both groups. Dashes indicate parameters not estimated. CFI = comparative fit index, TLI = Tucker-Lewis index, RMSEA = root mean square error of approximation, k’s indicate factor loadings. xh calculated based on formula 3 in Zinbarg, Yovel, Revelle, and McDonald (2006). ES = Emotional Stability, A = Agreeableness, C = Conscientiousness, EX = Extraversion, OE = Openness. a Models refit to correct Heywood case for Extraversion by constraining residual variance to be zero. b Denominator for xh was calculated from the sum of latent factor correlation matrix from the Correlated Domains model. c Denominator for xh was calculated from the sum of the input correlation matrix.

.38 .38 .27 4684.06 4689.33 202.28 GFP on observed Big Fivec Bifactor model Bifactor modela Bifactor + inventory method factors

33 34 28

.90 .90 1.00

.86 .86 .99

.08 .08 .02

.71 .71 .80

.71 .70 .65

.75 .75 .69

999 1.00 .50

.00 .09 .43

.28 .30 .46

.15 .16 .12

.15 .16 .16

.80 .75 .49

.25 .26 .14

.00

.36

.27

.28

.44 .44 .32 – – .37 – – .28 – – .27 – – .36 – – .00 .37 .39 .21 1.07 1.00 .65 .22 .24 .25 .21 .23 .18 .39 .41 .65 .00 .08 .42 .00 .07 .38 .73 .73 .67 .69 .68 .64 .66 .65 .61 .08 .08 .02 .86 .86 .99 .90 .90 1.00 4684.06 4689.33 202.28 GFP on latent Big Fiveb Bifactor model Bifactor modela Bifactor + inventory method factors

33 34 28

– – – – – – – – – – – – – – – – – – – .65 – .61 – .78 – .73 – .72 .08 .08 .85 .85 .90 .88

TLI CFI df

30 37 4513.67 5459.62 Base models Correlated domains Alpha/beta higher-order

OE EX C A kinv

ES OE EX C A

kGFP

ES OE

kb

EX C ES

A ka

v2

RMSEA Model Fit

– –

Table 3 Multi-trait multi-inventory models of GFP saturation.

– –

S.E. Davies et al. / Personality and Individual Differences 81 (2015) 13–22

xh

20

within a given personality inventory, whether the GFP is estimated in its effects on latent or observed Big Five variables.

4. Discussion While previous research has explored the GFP meta-analytically (Van der Linden, Te Nijenhuis et al., 2010), the present study served to extend the meta-analytic findings on the GFP using a wide variety of personality inventories (both explicitly Big Five measures and non) and sources (both manuals and journals) to explore the potential moderator of within vs. between inventory correlations. The results of these analyses indicate that accounting for inventory method effects reduced estimates of GFP saturation of Big Five traits by almost 30% (from xh = .44 to .32 in affecting latent Big Five traits spanning across multiple inventories or from xh = .38 to .27 when estimating the effects on single inventory scales). Thus, though most of the GFP is stable across inventories (consistent with it being either a general self-evaluative trait or possibly a superordinate trait), a large portion of the GFP also reflects an inventory-specific response set. In some ways, this is perhaps surprising given that inventory creators are generally motivated to produce factorially distinct scales, wherein they might be expected to compose and select items that would serve to reduce cross-correlations between the Big Five. However, finding such marked reductions in GFP saturation suggests that a substantial portion (but not all) of the GFP variance in self-reports perhaps reflects a particular response style in interfacing with a given inventory. It remains somewhat unclear which specific response tendencies may be diminished when using cross-inventory data. However, these findings highlight the importance of adopting a multi-inventory approach to studying higherorder personality factors. Although the GFP was substantially reduced when modeling inventory method effects, the substantive GFP remained a moderately strong factor. The variance attributable to the higher-order GFP is non-trivial, suggesting that the GFP should not be written off entirely as an artifact. Moreover, in all its forms, the GFP has a sizable impact on personality measures themselves (xh = .50 from within inventory data), suggesting that a large proportion of what we measure in the Big Five may be attributable to other effects reflected in the GFP. Marrying the findings from the present study with multi-rater findings showing the GFP to be uncorrelated across raters (Anusic et al., 2009; Chang et al., 2012; Gnambs, 2013), the GFP appears to be partially a stable, self-evaluative trait consistent across inventories and partly a set of response tendencies specific to a particular personality inventory. Self-evaluative traits have shown strong relationships with a variety of indicators of success and satisfaction (Judge & Bono, 2001), and studies have shown that indices of the GFP predict likability, popularity, and job performance (Van der Linden, Scholte et al., 2010; Van der Linden, Te Nijenhuis et al., 2010; Van der Linden et al., 2013). These findings have important implications for research linking the Big Five to these outcomes. Specifically, research should examine whether the prediction of these outcomes stems from shared variance across the Big Five (which might indicate links to self-evaluation) or from the unique variance of each Big Five trait (which would capture substantive personality relationships as typically hypothesized). Recent developments using bifactor models (e.g., Chen, Hayes, Carver, Laurenceau, & Zhang, 2012) or regressionbased transformations (e.g., Salgado et al., 2013) to separate prediction from shared versus unique variance in measures would be useful for future research. In addition, using multiple inventories and multiple informants in this research will be useful to separate substantive higher-order traits, self-evaluation, and inventoryspecific response sets.

S.E. Davies et al. / Personality and Individual Differences 81 (2015) 13–22

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