Tag Archives: Personality Structure

A Psychometric Study of the NEO-PI-R

Big Five, CFA, confirmatory factor analysis, MPLUS, NEO-PI-R, Personality, Personality Measurement, Personality Structure, SEM, Structural Equation Modeling

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 They also show little appreciation for methodological improvements and often use methods that are outdated.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.

When Personality Psychologists are High

Personality, Personality Measurement,

Correction (8/31/2019): In an earlier version, I misspelled Colin DeYoung’s name. I wrote DeYoung with a small d. I thank Colin DeYoung for pointing out this mistake.

Introduction

One area of personality psychology aims to classify personality traits. I compare this activity to research in biology where organisms are classified into a large taxonomy.

In a hiearchical taxnomy, the higher levels are more abstract, less descriptive, but also comprise a larger group of items. For example, there are more mammals (class) than dogs (species).

in the 1980s, personality psychologists agreed on the Big Five. The Big Five represent a rather abstract level of description that combines many distinct traits into traits that are predominantly related to one of the Big Five dimensions. For example, talkative falls into the extraversion group.

To illustrate the level of abstraction, we can compare the Big Five to the levels in biology. After distinguishing vertebrate and invertebrate animals, there are five classes of vertebrate animals: mammals, fish, reptiles, birds, and amphibians). This suggests that the Big Five are a fairly high level of abstraction that cover a broad range of distinct traits within each dimension.

The Big Five were found using factor or pincipal component analysis (PCA). PCA is a methematical method that reduces the covariances among personality ratings to a smaller number of factors. The goal of PCA is to capture as much of the variance as possible with the smallest number of components. Evidently there is a trade-off. However, often the first components account for most of the variance while additional components add very little additional information. Using various criteria, five components seemed to account for most of the variance in personality ratings and the first five components could be identified in different datasets. So, the Big Five were born.

One important feature of PCA is that the components are independent (orthogonal). This is helpful to maximize the information that is captured with five dimensions. If the five dimensions would correlated, they would present overlapping variances and this redundancy would reduce the amount of explained variance. Thus, the Big Five are conceptually independent because they were discovered with a method that enforced independence.

Scale Scores are not Factors

While principal component analysis is useful to classify personality traits, it is not useful to do basic research on the causes and consequences of personality. For this purpose, personality psychologists create scales. Scales are usually created by summing items that belong to a common factor. For example, responses to the items “talkative,” “sociable,” and “reserved” are added up to create an extraversion score. Ratings of the item “reserved” are reversed so that higher scores reflect extraversion. Importantly, sum scores are only proxies of the components or factors that were identified in a factor analysis or a PCA. Thus, we need to distinguish between extraversion-factors and extraversion-scales. They are not the same thing. Unfortunately, personality psychologists often treat scales as if they were identical with factors.

Big Five Scales are not Independent

Now something strange happened when personalty psychologists examined the correlations among Big Five SCALES. Unlike the factors that were independent by design, Big Five Scales were not independent. Moreover, the correlations among Big Five scales were not random. Digman (1997) was the first to examine these correlations. The article has garnered over 800 citations.

Digman examined these correlations conducted another principal component analysis of the correlations. He found two factors. One factor for extraversion and openesss and the other factor for agreeableness and conscientiousness (and maybe low neuroticism). He proposed that these two factors represent an even higher level in a hierarchy of personality traits. Maybe like moving from the level of classess (mammals, fish, reptiles) to the level Phylum; a level that is so abstract that few people who are not biologists are familiar with.

Digman’s article stimulated further research on higher-order factors of personality, where higher means even higher than the Big Five, which are already at a fairly high level of abstraction. Nobody stopped to wonder how there could be higher-order factors if the Big Five are actually independent factors, and why Big Five scales show systematic correlations that were not present in factor analyses.

Instead personality psychologists speculated about the biological underpinning of the higher order factors. For example, Jordan B. Peterson (yes, them) and colleagues proposed that serotonin is related to higher stability (high agreeableness, high conscientiousness, and low neuroticism) (DeYoung, Peterson, and Higgins, 2002).

Rather than interpreting this finding as evidence that response tendencies contribute to correlations among Big Five scales, they interpreted this finding as a substantive finding about personality, society in the context of psychodynamic theories.

Only a few years later, separated from the influence of his advisor, DeYoung (2006) published a more reasonable article that used a multi-method approach to separate personality variance from method variance. This article provided strong evidence that a general evaluative bias (social desirable responding) contributes to correlations among Big Five Scales, which was formalized in Anusic et al.’s (200) model with an explicit evaluative bias (halo) factor.

However, the idea of higher-order factors was sustained by finding cross-method correlations that were consistent with the higher-order model.

After battling Colin as a reviewer, when we submitted a manuscript on halo bias in personality ratings, we finally were able to publish a compromise model that also included the higher order factors (stability/alpha; plasticity/beta), although we had problems identifying the alpha factor in some datasets.

The Big Mistake

Meanwhile, another article built on the 2002 model that did not control for rating biases and proposed that the correlation between the two higher-order factors implies that there is an even higher level in the hierarchy. The Big Trait of Personality makes people actually have more desirable personalities; They are less neurotic, more sociable, open, agreeable, and conscientious. Who wouldn’t want one of them as a spouse or friend? However, the 2006 article by DeYoung showed that the Big One only exists in the imagination of individuals and is not shared with perceptions by others. This finding was replicated in several datasets by Anusic et al. (2009).

Although claims about the Big One were already invalidated when the article was published, it appealed to some personality psychologists. In particular, white supremacist Phillip Rushton found the idea of a generally good personality very attractive and spend the rest of his life promoting it (Rushton & Irving, 2011; Rushton Bons, & Hur, 2008). He never realized the distinction between a personality factor, which is a latent construct, and a personality scale, which is the manifest sum-score of some personality items, and ignored DeYoung’s (2006) and other (Anusic et al., 2009) evidence that the evaluative portion in personality ratings is a rating bias and not substantive covariance among the Big Five traits.

Peterson and Rushton are examples of pseudo-science that mixes some empirical findings with grand ideas about human nature that are only loosely related. Fortunately, interest in the general factor of personality seems to be decreasing.

Higher Order Factors or Secondary Loadings?

Ashton, Lee, Goldberg, and deVries (2009) put some cold water on the idea of higher-order factors. They pointed out that correlations between Big Five Scales may result from secondary loadings of items on Big Five Factors. For example, the item adventurous may load on extraversion and openness. If the item is used to create an extraversion scale, the openness and extraversion scale will be positively correlated.

As it turns out, it is always possible to model the Big Five as independent factors with secondary loadings to avoid correlations among factors. After all, this is how exploratory factor analysis or PCA are able to account for correlations among personality items with independent factors or components. In an EFA, all items have secondary loadings on all factors, although some of these correlations may be small.

There are only two ways to distinguish empirically between a higher-order model and a secondary-loading model. One solution is to obtain measures of the actual causes of personality (e.g., genetic markers, shared environment factors, etc.) If there are higher order factors, some of the causes should influence more than one Big Five dimension. The problem is that it has been difficult to identify causes of personality traits.

The second approach is to examine the number of secondary loadings. If all openness items load on extraversion in the same direction (e.g., adventurous, interest in arts, interest in complex issues), it suggests that there is a real common cause. However, if secondary loadings are unique to one item (adventurous), it suggests that the general factors are independent. This is by no means a definitive test of the structure of personality, but it is instructive to examine how many items from one trait have secondary loadings on another trait. Even more informative would be the use of facet-scales rather than individual items.

I have examined this question in two datasets. One dataset is an online sample with items from the IPIP-100 (Johnson). The other dataset is an online sample with the BFI (Gosling and colleagues). The factor loading matrices have been published in separate blog posts and the syntax and complete results have been posted on OSF (Schimmack, 2019b; 2019c).

IPIP-100

Neuroticism items show 8 out of 16 secondary loadings on agreeableness, and 4 out of 16 secondary loadings on conscientiousnes.

Item#NEOACEVBACQ
Neuroticism
easily disturbed30.44-0.25
not easily bothered10-0.58-0.12-0.110.25
relaxed most of the time17-0.610.19-0.170.27
change my mood a lot250.55-0.15-0.24
feel easily threatened370.50-0.25
get angry easily410.50-0.13
get caught up in my problems420.560.13
get irritated easily440.53-0.13
get overwhelmed by emotions450.620.30
stress out easily460.690.11
frequent mood swings560.59-0.10
often feel blue770.54-0.27-0.12
panic easily800.560.14
rarely get irritated82-0.52
seldom feel blue83-0.410.12
take offense easily910.53
worry about things1000.570.210.09
SUM0.83-0.050.000.07-0.02-0.380.12

Agreeableness items show only one secondary loading on conscientiousness and one on neuroticism.

Agreeableness
indifferent to feelings of others8-0.58-0.270.16
not interested in others’ problems12-0.58-0.260.15
feel little concern for others35-0.58-0.270.18
feel others’ emotions360.600.220.17
have a good word for everybody490.590.100.17
have a soft heart510.420.290.17
inquire about others’ well-being580.620.320.19
insult people590.190.12-0.32-0.18-0.250.15
know how to comforte others620.260.480.280.17
love to help others690.140.640.330.19
sympathize with others’ feelings890.740.300.18
take time out for others920.530.320.19
think of others first940.610.290.17
SUM-0.030.070.020.840.030.410.09

Finally, conscientiousness items show only one secondary loading on agreeableness.

Conscientiousness
always prepared20.620.280.17
exacting in my work4-0.090.380.290.17
continue until everything is perfect260.140.490.130.16
do things according to a plan280.65-0.450.17
do things in a half-way manner29-0.49-0.400.16
find it difficult to get down to work390.09-0.48-0.400.14
follow a schedule400.650.070.14
get chores done right away430.540.240.14
leave a mess in my room63-0.49-0.210.12
leave my belongings around64-0.50-0.080.13
like order650.64-0.070.16
like to tidy up660.190.520.120.14
love order and regularity680.150.68-0.190.15
make a mess of things720.21-0.50-0.260.15
make plans and stick to them750.520.280.17
neglect my duties76-0.55-0.450.16
forget to put things back 79-0.52-0.220.13
shirk my duties85-0.45-0.400.16
waste my time98-0.49-0.460.14
SUM-0.03-0.010.010.030.840.360.00

Of course, there could be additional relationships that are masked by fixing most secondary loadings to zero. However, it also matters how strong the secondary loadings are. Weak secondary loadings will produce weak correlations among Big Five scales. Even the secondary loadings in the model are weak. Thus, there is little evidence that neuroticism, agreeableness, and conscientiousness items are all systematically related as predicted by a higher-order model. At best, the data suggest that neuroticism has a negative influence on agreeable behaviors. That is, people differ in their altruism, but agreeable neurotic people are less agreeable when they are in a bad mood.

Results for extraversion and openness are similar. Only one extraversion item loads on openness.

Extraversion
hard to get to know7-0.45-0.230.13
quiet around strangers16-0.65-0.240.14
skilled handling social situations180.650.130.390.15
am life of the party190.640.160.14
don’t like drawing attention to self30-0.540.13-0.140.15
don’t mind being center of attention310.560.230.13
don’t talk a lot32-0.680.230.13
feel at ease with people 33-0.200.640.160.350.16
feel comfortable around others34-0.230.650.150.270.16
find it difficult to approach others38-0.60-0.400.16
have little to say57-0.14-0.52-0.250.14
keep in the background60-0.69-0.250.15
know how to captivate people610.490.290.280.16
make friends easily73-0.100.660.140.250.15
feel uncomfortable around others780.22-0.64-0.240.14
start conversations880.700.120.270.16
talk to different people at parties930.720.220.13
SUM-0.040.880.020.06-0.020.370.01

And only one extraversion item loads on openness and this loading is in the opposite direction from the prediction by the higher-order model. While open people tend to like reading challenging materials, extraverts do not.

Openness
full of ideas50.650.320.19
not interested in abstract ideas11-0.46-0.270.16
do not have good imagination27-0.45-0.190.16
have rich vocabulary500.520.110.18
have a vivid imagination520.41-0.110.280.16
have difficulty imagining things53-0.48-0.310.18
difficulty understanding abstract ideas540.11-0.48-0.280.16
have excellent ideas550.53-0.090.370.22
love to read challenging materials70-0.180.400.230.14
love to think up new ways710.510.300.18
SUM-0.02-0.040.75-0.01-0.020.400.09

The next table shows the correlations among the Big Five SCALES.

Scale CorrelationsNEOAC
Neuroticism (N)–
Extraversion (E)-0.21–
Openness (O)-0.160.13–
Agreeableness (A)-0.130.270.17–
Conscientiousness (C)-0.170.110.140.20–

The pattern mostly reflects the influence of the evaluative bias factor that produces negative correlations of neuroticism with the other scales and positive correlations among the other scales. There is no evidence that extraversion and openness are more strongly correlated in the IPIP-100. Overall, these results are rather disappointing for higher-order theorists.

The next table shows the correlations among the Big Five Scales.

Scale CorrelationsNEOAC
Neuroticism (N)–
Extraversion (E)-0.21–
Openness (O)-0.160.13–
Agreeableness (A)-0.130.270.17–
Conscientiousness (C)-0.170.110.140.20–

The pattern of correlations reflects mostly the influence of the evaluative bias factor. As a result, the neuorticism scale is negatively correlated with the other scales and the other scales are positively correlated with each other. There is no evidence for a stronger correlation between extraversion and openness because there are no notable secondary loadings. There is also no evidence that agreeableness and conscientiousness are more strongly related to neuroticism. Thus, these results show that DeYoung’s (2006) higher-order model is not consistent across different Big Five questionnaires.

Big Five Inventory

DeYoung found the higher-order factors with the Big Five Inventory. Thus, it is particularly interesting to examine the secondary loadings in a measurement model with independent Big Five factors (Schimmack, 2019b).

Neuroticism items have only one secondary loading on agreeableness and one on conscientiousness and the magnitude of these loadings is small.

Item#NEOACEVBACQ
Neuroticism
depressed/blue40.33-0.150.20-0.480.06
relaxed9-0.720.230.18
tense140.51-0.250.20
worry190.60-0.080.07-0.210.17
emotionally stable24-0.610.270.18
moody290.43-0.330.18
calm34-0.58-0.04-0.14-0.120.250.20
nervous390.52-0.250.17
SUM0.79-0.08-0.01-0.05-0.02-0.420.05

Four out of nine agreeableness items have secondary loadings on neuroticism, but the magnitude of these loadings is small. Four items also have loadings on conscientiousness, but one item (forgiving) has a loading opposite to the one predicted by the hgher-order model.

Agreeableness
find faults w. others20.15-0.42-0.240.19
helpful / unselfish70.440.100.290.23
start quarrels 120.130.20-0.50-0.09-0.240.19
forgiving170.47-0.140.240.19
trusting 220.150.330.260.20
cold and aloof27-0.190.14-0.46-0.350.17
considerate and kind320.040.620.290.23
rude370.090.12-0.63-0.13-0.230.18
like to cooperate420.15-0.100.440.280.22
SUM-0.070.00-0.070.780.030.440.04

For conscientiousness, only two items have a secondary loading on neuroticism and two items have a secondary loading on agreeableness.

Conscientiousness
thorough job30.590.280.22
careless 8-0.17-0.51-0.230.18
reliable worker13-0.090.090.550.300.24
disorganized180.15-0.59-0.200.16
lazy23-0.52-0.450.17
persevere until finished280.560.260.20
efficient33-0.090.560.300.23
follow plans380.10-0.060.460.260.20
easily distracted430.190.09-0.52-0.220.17
SUM-0.050.00-0.050.040.820.420.03

Overall, these results provide no support for the higher-order model that predicts correlations among all neuroticism, agreeableness, and conscientiousness items. These results are also consistent with Anusic et al.’s (2009) difficulty of identifying the alpha/stability factor in a study with the BFI-S, a shorter version of the BFI.

However, Anusic et al. (2009) did find a beta-factor with BFI-S scales. The present analysis of the BFI do not replicate this finding. Only two extraversion items have small loadings on the openness factor.

Extraversion
talkative10.130.70-0.070.230.18
reserved6-0.580.09-0.210.18
full of energy110.34-0.110.580.20
generate enthusiasm160.070.440.110.500.20
quiet21-0.810.04-0.210.17
assertive26-0.090.400.14-0.240.180.240.19
shy and inhibited310.180.64-0.220.17
outgoing360.720.090.350.18

And only one openness item has a small loading that is opposite to the predicted direction. Extraverts are less likely to like reflecting.

Openness 
original50.53-0.110.380.21
curious100.41-0.070.310.24
ingenious 150.570.090.21
active imagination200.130.53-0.170.270.21
inventive25-0.090.54-0.100.340.20
value art300.120.460.090.160.18
like routine work35-0.280.100.13-0.210.17
like reflecting40-0.080.580.270.21
few artistic interests41-0.26-0.090.15
sophisticated in art440.070.44-0.060.100.16
SUM0.04-0.030.76-0.04-0.050.360.19

In short, there is no support for the presence of a higher-order factor that produces overlap between extraversion and openness.

The pattern of correlations among the BFI scales, however, might suggest that there is an alpha factor because neuroticism, agreeableness and conscientiousness tend to be more strongly correlated with each other than with other dimensions. This shows the problem of using scales to study higher-order factors. However, there is no evidence for a higher-order factor that combines extraversion and openness as the correlation between these traits is an unremarkable r = .18.

Scale CorrelationsNEOAC
Neuroticism (N)–
Extraversion (E)-0.26–
Openness (O)-0.110.18–
Agreeableness (A)-0.280.160.08–
Conscientiousness (C)-0.230.180.070.25–

So, why did DeYoung (2006) find evidence for higher-order factors? One possible explanation is that BFI scale correlations are not consistent across different samples. The next table shows the self-report correlations from DeYoung (2006) below the diagonal and discrepancies above the diagonal. Three of the four theoretically important correlations tend to be stronger in DeYoung’s (2006) data. It is therefore possible that the secondary loading pattern differs across the two datasets. It would be interesting to fit an item-level model to DeYoung’s data to explore this issue further.

Scale CorrelationsNEOAC
Neuroticism (N)–0.100.03-0.06-0.08
Extraversion (E)-0.16–0.070.010.03
Openness (O)-0.080.25–-0.020.02
Agreeableness (A)-0.360.150.06–-0.01
Conscientiousness (C)-0.310.210.090.24–

In conclusion, an analysis of the BFI also does not support the higher-order model. However, results seem to be inconsistent across different samples. While this suggests that more research is needed, it is clear that this research needs to model personality at the level of items and not with scale scores that are contaminated by evaluative bias and secondary loadings.

Conclusion

Hindsight is 20/20 and after 20 years of research on higher-order factors a lot of this research looks silly. How could there be higher order factors for the Big Five factors if the Big Five are independent factors (or components) by default. The search for higher-order factors with Big Five scales can be attributed to methodological limitations, although higher-order models with structural equation modeling have been around since the 1980. It is rather obvious that scale scores are impure measures and that correlations among scales are influenced by secondary loadings. However, even when this fact was pointed out by Ashton et al. (2009), it was ignored. The problem is mainly due to the lack of proper training in methods. Here the problem is the use of scales as indicators of factors, when scales introduce measurement error and higher-order factors are method artifacts.

The fact that it is possible to recover independent Big Five factors from questionnaires that were designed to measure five independent dimensions says nothing about the validity of the Big Five model. To examine the validity of the Big Five as a valid model of the highest level in a taxonomy of personality trait it is important to examine the relationship of the Big Five with the diverse population of personality traits. This is an important area of research that could also benefit from proper measurement models. This post merely focused on the search for higher order factors for the Big Five and showed that searching for higher-order factors of independent factors is a futile endeavor that only leads to wild speculations that are not based on empirical evidence (Peterson, Rushton).

Even DeYoung and Peterson seems to have realized that it is more important to examine the structure of personality below rather than above the Big Five (DeYoung, Quility, & Peterson, 2007) . Whether 10 aspects, 16 factors (Cattell) or 30 facets (Costa & McCrae) represent another meaningful level in a hierarchical model of personality traits remains to be examined. Removing method variance and taking secondary loadings into account will be important to separate valid variance from noise. Also, factor analysis is superior to principle component analysis unless the goal is simply to describe personality with atheoretical components that capture as much variance as possible.

Correct me if you can

This blog post is essentially a scientific article without peer-review. I prefer this mode of communication over submitting manuscript to traditional journals where a few reviewers have the power to prevent research from being published. This happened with a manuscript that Ivana Anusic and I submitted and that was killed by Colin DeYoung as a reviewer. I prefer open reviews and I invite Colin to write an open review of this “article.” I am happy to be corrected and any constructive comments would be a welcome contribution to advancing personality science. Simply squashing critical work so that nobody gets to see it is not advancing science. The new way of conducting open science with open submissions, open reviews is the way to go. Of course, others are also invited to engage in the debate. So, let’s start a debate with the thesis “Higher-order factors of the Big Five do not exist.”