Category Archives: NEO-PI-R

A Psychometric Study of the NEO-PI-R

Galileo had the clever idea to turn a microscope into a telescope and to point it towards the night sky. His first discovery was that Jupiter had four massive moons that are now known as the Galilean moons (Space.com).

Now imagine what would have happened if Galileo had an a priori theory that Jupiter has five moons and after looking through the telescope, Galileo decided that the telescope was faulty because he could see only four moons. Surely, there must be five moons and if the telescope doesn’t show them, it is a problem of the telescope. Astronomers made progress because they created credible methods and let empirical data drive their theories. Eventually even better telescopes discovered many more, smaller moons orbiting around Jupiter. This is scientific progress.

Alas, psychologists don’t follow the footsteps of natural sciences. They mainly use the scientific method to provide evidence that confirms their theories and dismiss or hide evidence that disconfirms their theories. They also show little appreciation for methodological improvements and often use methods that are outdated. As a result, psychology has made little progress in developing theories that rest of solid empirical foundations.

An example of this ill-fated approach to science is McCrae et al.’s (1996) attempt to confirm their five factor model with structural equation modeling (SEM). When they failed to find a fitting model, they decided that SEM is not an appropriate method to study personality traits because SEM didn’t confirm their theory. One might think that other personality psychologists realized this mistake. However, other personality psychologists were also motivated to find evidence for the Big Five. Personality psychologists had just recovered from an attack by social psychologists that personality traits does not even exist, and they were all too happy to rally around the Big Five as a unifying foundation for personality research. Early warnings were ignored (Block, 1995). As a result, the Big Five have become the dominant model of personality without subjecting the theory to rigorous tests and even dismissing evidence that theoretical models do not fit the data (McCrae et al., 1996). It is time to correct this and to subject Big Five theory to a proper empirical test by means of a method that can falsify bad models.

I have demonstrated that it is possible to recover five personality factors, and two method factors, from Big Five questionnaires (Schimmack, 2019a, 2019b, 2019c). These analyses were limited by the fact that the questionnaires were designed to measure the Big Five factors. A real test of Big Five theory requires to demonstrate that the Big Five factors explain the covariations among a large set of a personality traits. This is what McCrae et al. (1996) tried and failed to do. Here I replicate their attempt to fit a structural equation model to the 30 personality traits (facets) in Costa and McCrae’s NEO-PI-R.

In a previous analysis I was able to fit an SEM model to the 30 facet-scales of the NEO-PI-R (Schimmack, 2019d). The results only partially supported the Big Five model. However, these results are inconclusive because facet-scales are only imperfect indicators of the 30 personality traits that the facets are intended to measure. A more appropriate way to test Big Five theory is to fit a hierarchical model to the data. The first level of the hierarchy uses items as indicators of 30 facet factors. The second level in the hierarchy tries to explain the correlations among the 30 facets with the Big Five. Only structural equation modeling is able to test hierarchical measurement models. Thus, the present analyses provide the first rigorous test of the five-factor model that underlies the use of the NEO-PI-R for personality assessment.

The complete results and the MPLUS syntax can be found on OSF (https://osf.io/23k8v/). The NEO-PI-R data are from Lew Goldberg’s Eugene-Springfield community sample. Theyu are publicly available at the Harvard Dataverse

Results

Items

The NEO-PI-R has 240 items. There are two reasons why I analyzed only a subset of items. First, 240 variables produce 28,680 covariances, which is too much for a latent variable model, especially with a modest sample size of 800 participants. Second, a reflective measurement model requires that all items measure the same construct. However, it is often not possible to fit a reflective measurement model to the eight items of a NEO-facet. Thus, I selected three core-items that captured the content of a facet and that were moderately positively correlated with each other after reversing reverse-scored items. Thus, the results are based on 3 * 30 = 90 items. It has to be noted that the item-selection process was data-driven and needs to be cross-validated in a different dataset. I also provide information about the psychometric properties of the excluded items in an Appendix.

The first model did not impose a structural model on the correlations among the thirty facets. In this model, all facets were allowed to correlate freely with each other. A model with only primary factor loadings had poor fit to the data. This is not surprising because it is virtually impossible to create pure items that reflect only one trait. Thus, I added secondary loadings to the model until acceptable model fit was achieved and modification indices suggested no further secondary loadings greater than .10. This model had acceptable fit, considering the use of single-items as indicators, CFI = .924, RMSEA = .025, .035. Further improvement of fit could only be achieved by adding secondary loadings below .10, which have no practical significance. Model fit of this baseline model was used to evaluate the fit of a model with the Big Five factors as second-order factors.

To build the actual model, I started with a model with five content factors and two method factors. Item loadings on the evaluative bias factor were constrained to 1. Item loadings for on the acquiescence factor were constrained to 1 or -1 depending on the scoring of the item. This model had poor fit. I then added secondary loadings. Finally, I allowed for some correlations among residual variances of facet factors. Finally, I freed some loadings on the evaluative bias factor to allow for variation in desirability across items. This way, I was able to obtain a model with acceptable model fit, CFI = .926, RMSEA = .024, SRMR = .045. This model should not be interpreted as the best or final model of personality structure. Given the exploratory nature of the model, it merely serves as a baseline model for future studies of personality structure with SEM. That being said, it is also important to take effect sizes into account. Parameters with substantial loadings are likely to replicate well, especially in replication studies with similar populations.

Item Loadings

Table 1 shows the item-loadings for the six neuroticism facets. All primary loadings exceed .4, indicating that the three indicators of a facet measure a common construct. Loadings on the evaluative bias factors were surprisingly small and smaller than in other studies (Anusic et al., 2009; Schimmack, 2009a). It is not clear whether this is a property of the items or unique to this dataset. Consistent with other studies, the influence of acquiescence bias was weak (Rorer, 1965). Secondary loadings also tended to be small and showed no consistent pattern. These results show that the model identified the intended neuroticism facet-factors.

Table 2 shows the results for the six extraversion facets. All primary factor loadings exceed .40 and most are more substantial. Loadings on the evaluative bias factor tend to be below .20 for most items. Only a few items have secondary loadings greater than .2. Overall, this shows that the six extraversion facets are clearly identified in the measurement model.

Table 3 shows the results for Openness. Primary loadings are all above .4 and the six openness factors are clearly identified.

Table 4 shows the results for the agreeableness facets. In general, the results also show that the six factors represent the agreeableness facets. The exception is the Altruism facet, where only two items show a substantial loadings. Other items also had low loadings on this factor (see Appendix). This raises some concerns about the validity of this factor. However, the high-loading items suggest that the factor represents variation in selfishness versus selflessness.

Table 5 shows the results for the conscientiousness facets. With one exception, all items have primary loadings greater than .4. The problematic item is the item “produce and common sense” (#5) of the competence facet. However, none of the remaining five items were suitable (Appendix).

In conclusion, for most of the 30 facets it was possible to build a measurement model with three indicators. To achieve fit, the model included 76 out of 2,610 (3%) secondary loadings. Many of these secondary loadings were between .1 and .2, indicating that they have no substantial influence on the correlations of factors with each other.

Facet Loadings on Big Five Factors

Table 6 shows the loadings of the 30 facets on the Big Five factors. Broadly speaking the results provide support for the Big Five factors. 24 of the 30 facets (80%) have a loading greater than .4 on the predicted Big Five factor, and 22 of the 30 facets (73%) have the highest loading on the predicted Big Five factor. Many of the secondary loadings are small (< .3). Moreover, secondary loadings are not inconsistent with Big Five theory as facet factors can be related to more than one Big Five factor. For example, assertiveness has been related to extraversion and (low) agreeableness. However, some findings are inconsistent with McCrae et al.’s (1996) Five factor model. Some facets do not have the highest loading on the intended factor. Anger-hostility is more strongly related to low agreeableness than to neuroticism (-.50 vs. .42). Assertiveness is also more strongly related to low agreeableness than to extraversion (-.50 vs. .43). Activity is nearly equally related to extraversion and low agreeableness (-.43). Fantasy is more strongly related to low conscientiousness than to openness (-.58 vs. .40). Openness to feelings is more strongly related to neuroticism (.38) and extraversion (.54) than to openness (.23). Finally, trust is more strongly related to extraversion (.34) than to agreeableness (.28). Another problem is that some of the primary loadings are weak. The biggest problem is that excitement seeking is independent of extraversion (-.01). However, even the loadings for impulsivity (.30), vulnerability (.35), openness to feelings (.23), openness to actions (.31), and trust (.28) are low and imply that most of the variance in this facet-factors is not explained by the primary Big Five factor.

The present results have important implications for theories of the Big Five, which differ in the interpretation of the Big Five factors. For example, there is some debate about the nature of extraversion. To make progress in this research area it is necessary to have a clear and replicable pattern of factor loadings. Given the present results, extraversion seems to be strongly related to experiences of positive emotions (cheerfulness), while the relationship with goal-driven or reward-driven behavior (action, assertiveness, excitement seeking) is weaker. This would suggest that extraversion is tight to individual differences in positive affect or energetic arousal (Watson et al., 1988). As factor loadings can be biased by measurement error, much more research with proper measurement models is needed to advance personality theory. The main contribution of this work is to show that it is possible to use SEM for this purpose.

The last column in Table 6 shows the amount of residual (unexplained) variance in the 30 facets. The average residual variance is 58%. This finding shows that the Big Five are an abstract level of describing personality, but many important differences between individuals are not captured by the Big Five. For example, measurement of the Big Five captures very little of the personality differences in Excitement Seeking or Impulsivity. Personality psychologists should therefore reconsider how they measure personality with few items. Rather than measuring only five dimensions with high reliability, it may be more important to cover a broad range of personality traits at the expense of reliability. This approach is especially recommended for studies with large samples where reliability is less of an issue.

Residual Facet Correlations

Traditional factor analysis can produce misleading results because the model does not allow for correlated residuals. When such residual correlations are present, they will distort the pattern of factor loadings; that is, two facets with a residual correlation will show higher factor loadings. The factor loadings in Table 6 do not have this problem because the model allowed for residual correlations. However, allowing for residual correlations can also be a problem because freeing different parameters can also affect the factor loadings. It is therefore crucial to examine the nature of residual correlations and to explore the robustness of factor loadings across different models. The present results are based on a model that appeared to be the best model in my explorations. These results should not be treated as a final answer to a difficult problem. Rather, they should encourage further exploration with the same and other datasets.

Table 7 shows the residual correlation. First appear the correlations among facets assigned to the same Big Five factor. These correlations have the strongest influence on the factor loading pattern. For example, there is a strong correlation between the warmth and gregariousness facets. Removing this correlation would increase the loadings of these two facets on the extraversion factor. In the present model, this would also produce lower fit, but in other models this might not be the case. Thus, it is unclear how central these two facets are to extraversion. The same is also true for anxiety and self-consciousness. However, here removing the residual correlation would further increase the loading of anxiety, which is already the highest loading facet. This justifies the use of anxiety as the most commonly used indicator of neuroticism.

Table 7. Residual Factor Correlations

It is also interesting to explore the substantive implications of these residual correlations. For example, warmth and gregariousness are both negatively related to self-consciousness. This suggests another factor that influences behavior in social situations (shyness/social anxiety). Thus, social anxiety would be not just high neuroticism and low extraversion, but a distinct trait that cannot be reduced to the Big Five.

Other relationships are make sense. Modesty is negatively related to competence beliefs; excitement seeking is negatively related to compliance, and positive emotions is positively related to openness to feelings (on top of the relationship between extraversion and openness to feelings).

Future research needs to replicate these relationships, but this is only possible with latent variable models. In comparison, network models rely on item levels and confound measurement error with substantial correlations, whereas exploratory factor analysis does not allow for correlated residuals (Schimmack & Grere, 2010).

Conclusion

Personality psychology has a proud tradition of psychometric research. The invention and application of exploratory factor analysis led to the discovery of the Big Five. However, since the 1990s, research on the structure of personality has been stagnating. Several attempts to use SEM (confirmatory factor analysis) in the 1990s failed and led to the impression that SEM is not a suitable method for personality psychologists. Even worse, some researchers even concluded that the Big Five do not exist and that factor analysis of personality items is fundamentally flawed (Borsboom, 2006). As a result, personality psychologists receive no systematic training in the most suitable statistical tool for the analysis of personality and for the testing of measurement models. At present, personality psychologists are like astronomers who have telescopes, but don’t point them to the stars. Imagine what discoveries can be made by those who dare to point SEM at personality data. I hope this post encourages young researchers to try. They have the advantage of unbelievable computational power, free software (lavaan), and open data. As they say, better late than never.

Appendix

Running the model with additional items is time consuming even on my powerful computer. I will add these results when they are ready.

What lurks beneath the Big Five?

Any mature science classifies the objects that it studies. Chemists classify atoms. Biologists classify organisms. It is therefore not surprising that personalty psychologists have spent a lot of their effort on classifying personality traits; that is psychological attributes that distinguish individuals from each other.

[It is more surprising that social psychologists have spent very little effort on classifying situations; a task that is now being carried out by personality psychologists (Rauthmann et al., 2014)]

After decades of analyzing correlations among self-ratings of personality items, personality psychologists came to a consensus that five broad factors can be reliably identified. Since the 1980s, the so-called Big Five have dominated theories and measurement of personality. However, most theories of personality also recognize that the Big Five are not a comprehensive description of personality. That is, unlike colors that can be produced by mixing three basic colors, specific personality traits are not just a mixture of the Big Five. Rather, the Big Five represent an abstract level in a hierarchy of personality traits. It is possible to compare the Big Five to the distinction of five classes of vertebrate animals: mammals, birds, reptiles, fish, and amphibians. Although there are important distinctions between these groups, there are also important distinctions among the animals within each class; cats are not dogs.

Although the Big Five are a major achievement in personality psychology, it also has some drawbacks. As early as 1995, personality psychologists warned that focusing on the Big Five would be a mistake because the Big Five are too broad to be good predictors of important life outcomes (Block, 1995). However, this criticism has been ignored and many researchers seem to assume that they measure personality when they administer a Big Five questionnaire. To warrant the reliance on the Big Five would require that the Big Five capture most of the meaningful variation in personality. In this blog post, I use open data to test this implicit assumption that is prevalent in contemporary personality science.

Confirmatory Factor Analysis

In 1996, McCrae et al. (1995) published an article that may have contributed to the stagnation in research on the structure of personality. In this article, the authors argued that structural equation modeling (SEM), specifically confirmatory factor analysis (CFA), is not suitable for personality researchers. However, CFA is the only method that can be used to test structural theories and to falsify structural theories that are wrong. Even worse, McCrae et al. (1995) demonstrated that a simple-structure model did not fit their data. However, rather than concluding that personality structure is not simple, they concluded that CFA is the wrong method to study personality traits. The problem with this line of reasoning is self-evident and was harshly criticized by Borsboom (2006). If we dismiss methods because they do not show a theoretically predicted pattern, we loose the ability to test theories empirically.

To understand McCrae et al.’s (1995) reaction to CFA, it is necessary to understand the development of CFA and how it was used in psychology. In theory, CFA is a very flexible method that can fit any dataset. The main empirical challenge is to find plausible models and to find data that can distinguish between competing plausible models. However, when CFA was introduced, certain restrictions were imposed on models that could be tested. The most restrictive model imposed that a measurement model should have only primary loadings and no correlated residuals. Imposing these restrictions led to the foregone conclusions that the data are inconsistent with the model. At this point, researchers were supposed to give up, create a new questionnaire with better items, retest it with CFA and find out that there were still secondary loadings that produced poor fit to the data. The idea that actual data could have a perfect structure must have been invented by an anal-retentive statistician who never analyzed real data. Thus, CFA was doomed to be useless because it could only show that data do not fit a model.

It took some time and courage to decide that the straight-jacket of simple structure has to go. Rather than giving up after a simple-structure model was rejected, the finding should encourage further exploration of the data to find models that actually fit the data. Maybe biologists initially classified whales as fish, but so what. Over time, further testing suggested that they are mammals. However, if we never get started in the first place, we will never be able to develop a structure of personality traits. So, here I present a reflective measurement model of personality traits. I don’t call it CFA, because I am not confirming anything. I also don’t call it EFA because this term is used for a different statistical technique that imposes other restrictions (e.g., no correlated residuals, local independence). We might call it exploratory modeling (EM) or because it relies on structural equation modeling, we could call it ESEM. However, ESEM is already been used for a blind computer-based version of CFA. Thus, the term EM seems appropriate.

The Big Five and the 30 Facets

Costa and McCrae developed a personality questionnaire that assesses personality at two levels. One level are the Big Five. The other level are 30 more specific personality traits.

Image result for costa mccrae facets

The 30 facets are often presented as if they are members of a domain, just like dogs, cats, pigs, horses, elephants, and tigers are mammals and have nothing to do with reptiles or bird. However, this is an oversimplification. Actual empirical data show that personality structure is more complex and that specific facets can be related to more than one Big Five factor. In fact, McCrae et al. (1996) published the correlations of the 30 facets with the Big Five factors and the table shows many, and a few substantial, secondary loadings; that is, correlations with a factor other than the main domain. For example, Impulsive is not just positively related to Neuroticism. It is also positively related to extraversion, and negatively related to conscientiousness.

Thus, McCrae et al.’s (1996) results show that Big Five data do not have a simple structure. It is therefore not clear what model a CONFIRMATORY factor analysis tries to confirm, when the CFA model imposes a simple structure. McCrae et al. (1995) agree: “If, however, small loadings are in fact meaningful, CFA with a simple structure model may not fit well” (p. 553). In other words, if an exploratory factor analysis shows a secondary loading of Anger/Hostility on Agreeableness (r = -.40), indicating that agreeable people are less likely to get angry, it makes no sense to confirm a model that sets this parameter to zero. McCrae et al. also point out that simple structure makes no theoretical sense for personality traits. “There is no theoretical reason why traits should not have meaningful loadings on three, four, or five factors:” (p. 553). The logical consequence of this insight is to fit models that allow for meaningful secondary loadings; not to dismiss modeling personality data with structural equations.

However, McCrae et al. (1996) were wrong about the correct way of modeling secondary loadings. “It is possible to make allowances for secondary loadings in CFA by fixing the loadings at a priori values other than zero” (p. 553). Of course, it is possible to fix loadings to a non-zero value, but even for primary loadings, the actual magnitude of a loading is estimated by the data. It is not clear why this approach could not be used for secondary loadings. It is only impossible to let all secondary loadings to be freely estimated, but there is no need to fix the loading of anger/hostilty on the agreeableness factor to a fixed value to model the structure of personality.

Personality psychologists in the 1990s also seemed to not fully understand how sensitive SEM is to deviations between model parameters and actual data. McCrae et al. (1996) critically discuss a model by Church and Burke (1994) because it “regarded loadings as small as ± .20 as salient secondaries” (p. 553). However, fixing a loading of .20 to a value of 0, introduces a large discrepancy that will hurt overall fit. One either has to free parameters or lower the criterion for acceptable fit. However, fixing loadings greater than .10 to zero and hoping to met standard criteria of acceptable fit is impossible. Effect sizes of r = .2 (d = .4) are not zero, and treating them as such will hurt model fit.

In short, exploratory studies of the relationship between the Big Five and facets show a complex pattern with many non-trivial (r > .1) secondary loadings. Any attempt to model these data with SEM needs to be able to account for this finding. As many of these secondary loadings are theoretically expected and replicable, allowing for these secondary loadings makes theoretical sense and cannot be dismissed as overfitting of data. Rather, imposing a simple structure that makes no theoretical sense should be considered underfiting of the data, which of course results in bad fit.

Correlated Residuals are not Correlated Errors

Another confusion in the use of structural equation modeling is the interpretation of residual variances. In the present context, residuals represent the variance in a facet scale that is not explained by the Big Five factors. Residuals are interesting for two reasons. First, they provide information about unique aspects of personality that are not explained by the Big Five. To use the analogy of animals, although cats and dogs are both animals, they also have distinct features. Residuals are analogous to these distinct features, and we would think that personality psychologists would be very interested in exploring this question. However, statistics textbooks tend to present residual variances as error variance in the context of measurement models where items are artifacts that were created to measure a specific construct. As the only purpose of the item is to measure a construct, any variance that does not reflect the intended construct is error variance. If we were only interested in measuring the Big Five, we would think about residual facet-variance as error variance. It does not matter how depressed people are. We only care about their neuroticism. However, the notion of a hierarchy implies that we do care about the valid variance in facets that is not explained by the Big Five. Thus, residual variance is not error variance.

The mistake of treating residual variance as error variance becomes especially problematic when residual variance in one facet is related to residual variance in another facet. For example, how angry people get (the residual variance in anger) could be related to how compliant people are (the residual variance in compliance). After all, anger could be elicit by a request to comply to some silly norms (e.g., no secondary loadings) that make no sense. There is no theoretical reason, why facets could only be linked by means of the Big Five. In fact, a group of researchers has attempted to explain all relations among personality facet without the Big Five because they don’t belief in broader factors (cf. Schimmack, 2019b). However, this approach has difficulties explaining the constistent primary loadings of facets on their predicted Big Five factor.

The confusion of residuals with errors accounts at least partially for McCrae et al.’s (1996) failure to fit a measurement model to the correlations among the 30 facets.

“It would be possible to specify a correlated error term between these two scales, but the interpretation of such a term is unclear. Correlated error usually refers to a nonsubstantive
source of variance. If Activity and Achievement Striving were, say, observer ratings, whereas all other variables were self-reports, it would make sense to control for this difference in method by introducing a correlated error term. But there are no obvious sources of correlated error among the NEO-PI-R facet scales in the present study” (p. 555).

The Big Five Are Independent Factors, but Evaluative Bias produces correlations among Big Five Scales

Another decision researchers have to make is whether they specify models with independent factors or whether they allow factors to be correlated. That is, are extraversion and openness independent factors or are extraversion and openness correlated. A model with correlated Big Five factors has 10 additional free parameters to fit the data. Thus, the model will is likely to fit better than a model with independent factors. However, the Big Five were discovered using a method that imposed independence (EFA and Varimax rotation). Thus, allowing for correlations among the factors seems atheoretical, unless an explanation for these correlations can be found. On this front, personality researchers have made some progress by using multi-method data (self-ratings and ratings by informants). As it turns out, correlations among the Big Five are only found in ratings by a single rater, but not in correlations across raters (e.g., self-rated Extraversion and informant-rated Agreeableness). Additional research has further validated that most of this variance reflects response styles in ratings by a single rater. These biases can be modeled with two method factors. One factor is an acquiescence factor that leads to higher or lower ratings independent of item content. The other factor is an evaluative bias (halo) factor. It represent responses to the desirability of items. I have demonstrated in several datasets that it is possible to model the Big Five as independent factors and that correlations among Big Five Scales are mostly due to the contamination of scale scores with evaluative bias. As a result, neuroticism scales tend to be negatively related to the other scales because neuroticism is undesirable and the other traits are desirable (see Schimmack, 2019a). Although the presence of evaluative biases in personality ratings has been known for decades, previous attempts at modeling Big Five data with SEM often failed to specify method factors; not surprisingly they failed to find good fit (McCrae et al., 1996. In contrast, models with method factors can have good fit (Schimmack, 2019a).

Other Problems in McCrae et al.’s Attempt

There are other problems with McCrae et al.’s (1996) conclusion that CFA cannot be used to test personality structure. First, the sample size was small for a rigorous study of personality structure with 30 observed variables (N = 229). Second, the evaluation of model fit was still evolving and some of the fit indices that they reported would be considered acceptable fit today. Most importantly, an exploratory Maximum Likelihood model produced reasonable fit, chi2/df = 1.57, RMS = .04, TLI = .92, CFI = .92. Their best fitting CFA model, however, did not fit the data. This merely shows a lack of effort and not the inability of fitting a CFA model to the 30 facets. In fact, McCrae et al. (1996) note “a long list of problems with the technique [SEM], ranging from technical difficulties in estimation
of some models to the cost in time and effort involved.” However, no science has made progress by choosing cheap and quick methods over costly and time-consuming methods simply because researchers lack the patients to learn a more complex method. I have been working on developing measurement models of personality for over a decade (Anusic et al., 2009). I am happy to demonstrate that it is possible to fit an SEM model to the Big Five data, to separate content variance from method variance, and to examine how big the Big Five factors really are.

The Data

One new development in psychology is that data are becoming more accessible and are openly shared. Low Goldberg has collected an amazing dataset of personality data with a sample from Oregon (the Eugene-Springfield community sample). The data are now publicly available at the Harvard Dataverse. With N = 857 participants the dataset is nearly four times larger than the dataset used by McCrae et al. (1996), and the ratio 857 observations and 30 variables (28:1) is considered good for structural equation modeling.

It is often advised to use different samples for exploration and then for cross-validation. However, I used the full sample for a mix of confirmation and exploration. The reason is that there is little doubt about the robustness of the data structure (the covariance/correlation matrix). The bigger issue is that a well-fitting model does not mean that it is the right model. Alternative models could also account for the same pattern of correlations. Cross-validation does not help with this bigger problem. The only way to address this is a systematic program of research that develops and tests different models. I see the present model as the beginning of such a line of research. Other researchers can use the same data to fit alternative models and they can use new data to test model assumptions. The goal is merely to boot a new era of research on the structure of personality with structural equation modeling, which could have started 20 years ago, if McCrae et al. (1996) had been more positive about the benefits of testing models and being able to falsify them (a.k.a. doing science).

Results

I started with a simple model that had five independent personality factors (the Big Five) and an evaluative bias factor. I did not include an acquiescence factor because facets are measured with scales that include reverse scored items. As a result, acquiescence bias is negligible (Schimmack, 2019a).

In the initial model facet loadings on the evaluative bias factor were fixed at 1 or -1 depending on the direction or desirability of a facet. This model had poor fit. I then modified the model by adding secondary loadings and by freeing loadings on the evaluative bias factor to allow for variation in desirability of facets. For example, although agreeableness is desirable, the loading for the modesty facet actually turned out to be negative. I finally added some correlated residuals to the model. The model was modified until it reached criteria of acceptable fit, CFI = .951, RMSEA = .044, SRMR = .034. The syntax and the complete results can be found on OSF (https://osf.io/23k8v/).

Table 3 shows the standardized loadings of the 30 facets on the Big Five and the two method factors.

There are several notable findings that challenge prevalent conceptions of personality.

The Big Five are not so big

First, the loadings of facets on the Big Five factors are notably weaker than in McCrae et al.’s Table 4 reproduced above (Table 2). There are two reasons for this discrepancy. First, often evaluative bias is shared between facets that belong to the same factor. For example, anxiety and depression have strong negative loadings on the evaluative bias factor. This shared bias will push up the correlation between the two facets and inflate factor loadings in a model without an evaluative bias factor. Another reason can be correlated residuals. If this extra shared variance is not modeled it pushes up loadings of these facets on the shared factor. The new and more accurate estimates in Table 3 suggest that the Big Five are not as big as the name implies. The loading of anxiety on neuroticism (r = .49) implies that only 25% of the variance in anxiety is captured by the neuroticism factor. Loadings greater than .71 are needed for a Big Five factor to explain more than 50% of the variance in a facet. There are only two facets where the majority of the variance in a facet is explained by a Big Five factor (order, self-discipline).

Secondary loadings can explain additional variance in some facets. For example, for anger/hostility neuroticism explains .48^2 = 23% of the variance and agreeableness explains another -.43^2 = 18% of the variance for a total of 23+18 = 41% explained variance. However, even with secondary loadings many facets have substantial residual variance. This is of course predicted by a hierarchical model of personality traits with more specific factors underneath the global Big Five traits. However, it also implies that Big Five measures fail to capture substantial personality variance. It is therefore not surprising that facet measures often predict additional variance in outcomes that it is not predicted by the Big Five (e.g., Schimmack, Oishi, Furr, & Funder, 2004). Personality researchers need to use facet level or other more specific measures of personality in addition to Big Five measures to capture all of the personality variance in outcomes.

What are the Big Five?

Factor loadings are often used to explore the constructs underlying factors. The terms neuroticism, extraversion, or openness are mere labels for the shared variance among facets with primary loadings on a factor. There has been some discussion about the Big Five factors and there meaning is still far from clear. For example, there has been a debate about the extraversion factor. Lucas, Diener, Grob, Suh, and Shao (2000) argued that extraversion is the disposition to respond strongly to rewards. Ashton, Lee, and Paunonen disagreed and argued that social attention underlies extraversion. Empirically it would be easy to answer these questions if one facet would show a very high loading on a Big Five factor. The more loadings approach one, the more a factor corresponds to a facet or is highly related to a facet. However, the loading pattern does not suggest that a single facet captures the meaning of a Big Five factor. The strongest relationship is found for self-discipline and conscientiousness. Thus, good self-regulation may be the core aspect of conscientiousness that also influences achievement striving or orderliness. However, more generally the results suggest that the nature of the Big Five factors is not obvious. It requires more work to uncover the glue that ties facets belonging to a single factor together. Theories range from linguistic structures to shared neurotransmitters.

Evaluative Bias

The results for evaluative bias are novel because previous studies failed to model evaluative bias in responses to the NEO-PI-R. It would be interesting to validate the variation in loadings on the evaluative bias factor with ratings of item- or facet-desirability. However, intuitively the variation makes sense. It is more desirable to be competent (C1, r = .66) and not depressed (N3, r = -69) than to be an excitement seeker (E5: r = .03) or compliant (A4: r = .09). The negative loading for modesty also makes sense and validates self-ratings of modesty (A5,r = -.33). Modest individuals are not supposed to exaggerate their desirable attributes and apparently they refrain from doing so also when they complete the NEO-PI-R.

Recently, McCrae (2018) acknowledged the presence of evaluative biases in NEO scores, but presented calculations that suggested the influence is relatively small. He suggested that facet-facet correlations might be inflated by .10 due to evaluative bias. However, this average is uninformative. It could imply that all facets have a loading of .33 or -.33 on the evaluative bias factor, which introduces a bias of .33*.33 = .10 or .33*-.33 = -.10 in facet-facet correlations. In fact, the average absolute loading on the evaluative bias factor is .30. However, this masks the fact that some facets have no evaluative bias and others have much more evaluative bias. For example, the measure of competence beliefs (self-effacy) C1 has a loading of .66 on the evaluative bias factor, which is higher than the loading on conscientiousness (.52). It should be noted that the NEO-PI-R is a commercial instrument and that it is in the interest of McCrae to claim that the NEO-PI-R is a valid measure for personalty assessment. In contrast, I have no commercial interest in finding more or less evaluative bias in the NEO-PI-R. This may explain the different conclusions about the practical significance of evaluative bias in NEO-PI-R scores.

In short, the present analysis suggests that the amount of evaluative bias varies across facet scales. While the influence of evaluative bias tends to be modest for many scales, scales with highly desirable traits show rather strong influence of evaluative bias. In the future it would be interesting to use multi-method data to separate evaluative bias from content variance (Anusic et al., 2009).

Measurement of the Big Five

Structural equation modeling can be used to test substantive theories with a measurement model or to develop and evaluate measurement models. Unfortunately, personality psychologists have not taken advantage of structural equation modeling to improve personality questionnaires. The present study highlights two ways in which SEM analysis of personality ratings is beneficial. First, it is possible to model evaluative bias and to search for items with low evaluative bias. Minimizing the influence of evaluative bias increases the validity of personality scales. Second, the present results can be used to create better measures of the Big Five. Many short Big Five scales focus exclusively on a single facet. As a result, these measures do not actually capture the Big Five. To measure the Big Five efficiently, a measure requires several facets with high loadings on the Big Five factor. Three facets are sufficient to create a latent variable model that separates the facet-specific residual variance from the shared variance that reflects the Big Five. Based on the present results, the following facets seem good candidates for the measurement of the Big Five.

Neuroticism: Anxiety, Anger, and Depression. The shared variance reflects a general tendency to respond with negative emotions.

Extraversion: Warmth, Gregariousness, Positive Emotions: The shared variance reflects a mix of sciability and cheerfulness.

Openness: Aesthetics, Action, Ideas. The shared variance reflects an interest in a broad range of activities that includes arts, intellectual stimulation, as well as travel.

Agreeableness: Straightforwardness, Altruism, Complicance: The shared variance represents respecting others.

Conscientiousness: Order, Self-Discipline, Dutifulness. I do not include achievement striving because it may be less consistent across the life span. The shared variance represents following a fixed set of rules.

This is of course just a suggestion. More research is needed. What is novel is the use of reflective measurement models to examine this question. McCrae et al. (1996) and some others before them tried and failed. Here I show that it is possible and useful to fit facet corelations with a structural equation model. Thus, twenty years after McCrae et al. suggested we should not use SEM/CFA, it is time to reconsider this claim and to reject it. Most personality theories are reflective models. It is time to test these models with the proper statistical method.