In the 1980s, personality psychologists celebrated the emergence of a five-factor model as a unifying framework for personality traits. Since then, the so-called Big-5 have dominated thinking and measurement of personality.

Two decades later, Ashton and Lee proposed an alternative model with six factors. This model has come to be known as the HEXACO model.

A recent special issue in the European Journal of Personality discussed the pros and cons of these two models. The special issue did not produce a satisfactory resolution between proponents of the two models.

In theory, it should be possible to resolve this dispute with empirical data, especially given the similarities between the two models. Five of the factors are more or less similar between the two models. One factor is Neuroticism with anxiety/worry as a key marker of this higher-order trait. A second factor is Extraversion with sociability and positive energy as markers. A third factor is Openness with artistic interests as a common marker. A forth factor is conscientiousness with orderliness and planful actions as markers. The key differences between the two models is concerned with pro-social and anti-social traits. In the Big Five model, a single higher-order trait of agreeableness is assumed to produce shared variance among all of these traits (e.g., morality, kindness, modesty). The HEXACO model assumes that there are two higher-order traits. One is also called agreeableness and the other one is called honesty and humility.

As Ashton and Lee (2005) noted, the critical empirical question is how the Big Five model accounts for the traits related to the honesty-humility factor in the HEXACO model. Although the question is straightforward, empirical tests of it are not. The problem is that personality researchers often rely on observed correlations between scales and that correlations among scales depend on the item-content of scales. For example, Ashton and Lee (2005) reported that the Big-Five Mini-Marker scale of Agreeableness correlated only *r* = .26 with their Honesty-Humility scale. This finding is not particularly informative because correlations between scales are not equivalent to correlations between the factors that the scales are supposed to reflect. It is also not clear whether a correlation of *r* = .26 should be interpreted as evidence that Honesty-Humility is a separate higher-order factor at the same level as the other Big Five traits. To answer this question, it would be necessary to provide a clear definition of a higher-order factor. For example, higher-order factors should account for shared variance among several primary factors that have only low secondary loadings on other factors.

Confirmatory factor analysis (CFA) addresses some of the problems of correlational studies with scale scores. One main advantage of CFA is that models do not depend on the item selection. It is therefore possible to fit a theoretical structure to questionnaires that were developed for a different model. I therefore used CFA to see whether it is possible to fit the Big Five model to the HEXACO-100 questionnaire that was explicitly designed to measure 4 primary factors (facets) for each of the six HEXACO higher-order traits. Each primary factor was represented by four items. This leads to 4 x 4 x 6 = 96 items. After consultation with Michael Ashton, I did not include the additional four altruism items.

### Measurement Model

The Big-Five or HEXACO models are higher-order models that are supposed to explain the pattern of correlations among the primary factors. In order to test these models, it is necessary to first establish a measurement model for the primary factors. Starting point for the measurement model was a model with a simple structure where each item only has a primary loading on its designated factor. For example, the anxiety item “I sometimes can’t help worrying about little things” loaded only on the anxiety factor. All 24 primary factors were allowed to correlate freely with each other.

It is well-known that few data fit a simple structure for two reasons. First, the direction of items can influence responses. This can be modeled with an acquiescence factor that codes whether an item is a direct or a reverse coded items. Second, it is difficult to write items that reflect only variation in the intended primary trait. Thus, many items are likely to have small, but statistically significant, secondary loadings on other factors. These secondary loadings need to be modeled to achieve acceptable model fit, even if they have little practical significance. Another problem is that two items of the same factor may share additional variance because they share similar wordings or item content. For example, the two items “I clean my office or home quite frequently” and the reverse coded item “People often joke with me about the messiness of my room or desk” share specific content. This shared variance between items needs to be modeled with correlated residuals to achieve acceptable model fit.

Researchers can use Modification Indices to identify secondary loadings and correlated residuals that have a strong influence on model fit. Freeing the identified parameters improves model fit and can produce a measurement model with acceptable model fit. Moreover, MI can also provide information that there are no more fixed parameters that have a strong negative effect on model fit.

After modifying the simple-structure model accordingly, I established a measurement model that had acceptable fit, RMSEA = .021, CFI = .936. Although the CFI did not reach the threshold of .950, the MI did not show any further improvements that could be made. Freeing further secondary loadings resulted in secondary loadings less than .1. Thus, I stopped at this point.

16 primary factors had primary factor loadings of .4 or higher for all items. The remaining 8 primary factors had 3 primary factor loadings of .4 or higher. Only 4 items had secondary loadings greater than .3. Thus, the measurement model confirmed the intended structure of the questionnaire.

Importantly, the measurement model was created without imposing any structure on the correlations among higher-order factors. Thus, the freeing of secondary loadings and correlated residuals did not bias the results in favor of the Big Five or HEXACO model. Rather, the fit of the measurement model can be used to evaluate the fit of theoretical models about the structure of personality.

A simplistic model that is often presented in textbooks would imply that only traits related to the same higher-order factor are correlated with each other and that all other correlations are close to zero. Table 1 shows the correlations for the HEXACO-Agreeableness (A-Gent = gentle, A-Forg = forgiving, A-Pati = patient, & A-Flex = flexible) and the HEXACO-honesty-humility (H-Gree = greed-avoidance, H-Fair = fairness, H-Mode = modest, & H-Sinc = sincere) factors.

In support of the Big Five model, all correlations are positive. This suggests that all primary factors are related to a single higher-order factor. In support of the HEXACO model, correlations among A-factors and correlations among H-factors tend to be higher than correlations of A-factors with H-factors. Three notable exceptions are highlighted in red and all of them involve modesty. Modesty is more strongly related to A-Gent and A-Flex than to H-Mode.

Table 2 shows the correlations of the A and H factors with the four neuroticism factors (N-Fear = fear, N-Anxi = anxiety, N-Depe = dependence, N-Sent = sentimental). Notable correlations greater than .2 are highlighted. For the most part, the results show that neuroticism and pro-social traits are unrelated. However, there are some specific relations among factors. Notably, all four HEXACO-A factors are negatively related to anxiety. This shows some dissociation between A and H factors. In addition, fear is positively related to fairness and negatively related to sincerity. Sentimentality is positively related to fairness and modesty. Neither the Big Five model nor the HEXACO model has explanations for these relationships.

Table 3 shows the correlation with the Extraversion factors (E-soci = Sociable, E-socb = bold, E-live = lively, E-Sses = self-esteem). There are few notable relationships between A and H factors on the one hand and E factors on the other hand. This supports the assumption of both models that pro-social traits are unrelated to extraversion traits, including being sociable.

Table 4 shows the results for the Openness factors. Once more there are few notable relationships. This is consistent with the idea that pro-social traits are fairly independent of Openness.

Table 5 shows the results for conscientiousness factors (C-Orga = organized, C-Dili = diligent, C-Perf = Perfectionistic, & C-Prud = prudent). Most of the correlations are again small, indicating that pro-sociality is independent of conscientiousness. The most notable exceptions are positive correlations of the conscientiousness factors with fairness. This suggests that fairness is related to conscientiousness.

Table 6 shows the remaining correlations among the N, E, O, and C factors.

The green triangles show correlations among the primary factors belonging to the same higher-order factor. The strong correlations confirm the selection of primary factors to be included in the HEXACO-100. Most of the remaining correlations are below .2. The grey fields show correlations greater than .2. The most notable correlations are for diligence (C-Dili), which is correlated with all E-factors. This suggests a notable secondary loading of diligence on the higher-order factor E. Another noteworthy finding is a strong correlation between self-esteem (E-Sses) and anxiety (N-anx). This is to be expected because self-esteem is known to have strong relationships with neuroticism. It is surprising, however, that self-esteem is not related to the other primary factors of neuroticism. One problem in interpreting these results is that the other neuroticism facets are unique to the HEXACO-100.

In conclusion, inspection of the correlations among the 24 primary factors shows clear evidence for 5 mostly independent factors that correspond to the Big Five factors. In addition, the correlations among the pro-social factors show a distinction between the four HEXACO-A factors and the four HEXACO-H factors. Thus, it is possible to represent the structure with 6 factors that correspond to the HEXACO model, but the higher-order A and H factors would not be independent.

**A Big Five Model of the HEXACO-100**

I fitted a model with five higher-order factors to examine the ability of the Big Five model to explain the structure of the HEXACO-100. Importantly, I did not alter the measurement model of the primary factors. It is clear from the previous results that a simple-structure would not fit the data. I therefore allowed for secondary loadings of primary factors on the higher-order factors. In addition, I allowed for residual correlations among primary factors. Furthermore, when several primary factors showed consistent correlated residuals, I modeled them as factors. In this way, the HEXACO-A and HEXACO-H factors could be modeled as factors that account for correlated residuals among pro-social factors. Finally, I added a halo factor to the model. The halo factor has been identified in many Big Five questionnaires and reflects the influence of item-desirability on responses.

Model fit was slightly less than model fit for the measurement model, RMSEA = .021 vs. .021, CFI = .927 vs. .936. However, inspection of MI did not suggest additional plausible ways to improve the model. Figure 1 shows the primary loadings on the Big Five factors and the two HEXACO factors, HEXACO-Agreeableness (HA) and HEXACO-Honesty-Humility.

The first notable observation is that primary factors have loadings above .5 for four of the Big Five factors. For the Agreeableness factor, all loadings were statistically significant and above .2, but four loadings were below .5. This shows that agreeableness explains less variance in some primary factors than the other Big Five factors. Thus, one question is whether the magnitude of loadings on the Big Five factors should be a criterion for model selection.

The second noteworthy observation is that the model clearly identified HEXACO-A and HEXACO-H as distinct factors. That is, the residuals of the corresponding primary factors were all positively correlated. All loadings were above .2, but several of the loadings were also below .5. Moreover, for the HEXACO-A factors the loadings on the Big5-A factor were stronger than the loadings on the HEXACO-A factor. Modesty (H-Mode) also loaded more highly on Big5-A than HH. The results for HEXACO-A are not particularly troubling because the HEXACO model does not consider this factor to be particularly different from Big5-A. Thus, the main question is whether the additional shared variance among HEXACO-H factors warrants the creation of a model with six factors. That is, does Honesty-Humility have the same status as the Big Five factors?

**Alternative Model 1**

The HEXACO model postulates six factors. Comparisons of the Big Five and HEXACO model tend to imply that the HEXACO factors are just as independent as the Big Five factors. However, the data show that HEXACO-A factors and HEXACO-H factors are not as independent of each other as other factors. To fit a six-factor model to the data, it would be possible to allow for a correlation between HEXACO-A and HEXACO-H. To make this model fit as well as the Big-Five model, an additional secondary loading of modesty (H-Mode) on HEXACO-A was needed, RMSEA = .22, CFI = .926. This secondary loading was low, r = .25, and is not displayed in Figure 2.

The most notable finding is a substantial correlation between Hexaco-A and Hexaco-H of r = .49. Although there are no clear criteria for practical independence, this correlation is strong and suggests that there is an important common factor that produces a positive correlation between these two factors. This makes this model rather unappealing. The main advantage of the Big Five model would be that it captures the highest level of independent factors in a hierarchy of personality traits.

### Alternative Model 2

An alternative solution to represent the correlations among HEXACO-A and HEXACO-H factors is to treat HEXACO-A and HEXACO-H as independent factors and to allow for secondary loadings of HEXACO-H factors on HEXACO-A or vice versa. Based on the claim that the H-factor adds something new to the structure, I modelled secondary loadings of the primary H-factors on HEXACO-A. Fit was the same as for the first alternative model, RMSEA = .22, CFI = .927. Figure 3 shows substantial secondary loadings for three of the four H-factors, and for modesty the loading on the HEXACO-A factor is even stronger than the loading on the HEXACO-H factor.

The following table shows the loading pattern along with all secondary loadings greater than .1. Notable secondary loadings greater than .3 are highlighted in pink. Aside from the loading of some H-factors on A, there are some notable loadings of two C-factors on E. This finding is consistent with other results that high achievement motivation is related to E and C.

The last column provides information about correlated residuals (CR) in the last column. Primary factors with the same letter have a correlated residual. For example, there is a strong negative relationship between anxiety (N-anxiety) and self-esteem (E-Sses) that was apparent in the correlations among the primary factors in Table 6. This relationship could not be modeled as a negative secondary loading on neuroticism because the other neuroticism factors showed much weaker relationships with self-esteem.

### Discussion

In sum, the choice between the Big5 model and the HEXACO model is a relatively minor stylistic choice. The Big Five model is a broad model that predicts variance in a wide variety of primary personality factors that are often called facets. There is no evidence that the Big Five model fails to capture variation in the primary factors that are used to measure the Honesty-Humility factor of the HEXACO model. All four H-factors are related to a general agreeableness factor. Thus, it is reasonable to maintain the Big Five model as a model of the highest level in a hierarchy of personality traits and to consider the H-factor a factor that explains additional relationships among pro-social traits. However, an alternative model with Honesty-Humility as a sixth factor is also consistent with the data. This model only appears different from the Big Five model if secondary loadings are ignored. However, all H-factors had secondary loadings on agreeableness. Thus, agreeableness remains a broader trait that links all pro-social traits, while Honesty-Humility explains additional relationships among a subset of this factors. If Honesty-Humility is indeed a distinct global factor it should be possible to find primary factors that are uniquely related to this factor without notable secondary loadings on Agreeableness. If such traits exists, they would strengthen the support for the HEXACO model. On the other hand, if all traits that are related to Honesty-Humility also load on Agreeableness, it seems more appropriate to treat Honesty-Humility as a lower-level factor in the hierarchy of traits. In conclusion, these structural models did not settle the issue, but they clarify the issue. Agreeableness factors and Honesty-Humilty factors form distinct, but related clusters of primary traits. This empirical finding can be represented with a Five-Factor model with Honest-Humility as shared variance among some pro-social traits or it can be represented with six factors and secondary loadings.

### Prediction

A major source of confusion in research on the structure of personality is the failure to distinguish between factors and scales. Many proponents of the HEXACO model point out that the HEXACO scales, especially the Honesty-Humilty scale, explain variance in criterion variables that is not explained by Big-Five scales. It has also been observed that the advantage of the HEXACO scales depends on the Big-Five scales that are used. The reason for these findings is that scales are imperfect measures of their intended factors. They also contain information about the primary factors that were used to measure the higher-order factors. The advantage of the HEXACO-100 is that it measures 24 primary factors. There is nothing special about the Honesty-Humility factor. As Figure 1 shows, the honesty-humilty factor explains only a portion of the variance in its designated primary factors, namely .67^2 = 45% of the variance in greed-avoidance, .55^2 = 30% of the variance in fairness, .32^2 = 10% of the variance in modesty, and .41^2 = 17% of the variance in sincerity. Averaging these scales to form a Honesty-Humilty scale destroys some of this variance and inevitably lowers the ability to predict some criterion variable that is strongly related to one of these primary factors. There is also no reason why Big Five questionnaires should not include some primary factors of Honesty-Humility and the NEO-PI-3 does include modesty and fairness.

Personality psychologists need to distinguish more clearly between factors and scales. The correlation of the NEO-PI-3 agreeableness scale will be different from those with the HEXACO-A scale or the BFI2-agreeableness scale. Scale correlations are biased by the choice of items, unless items are carefully selected to maximize correlation with the latent factor. For research purposes, researchers should use latent variable models that can decompose an observed correlation into the influence of the higher-order factor and the influence of specific factors.

Personality researchers should also carefully think about the primary factors they may want to include in their studies. For example, even researchers who favor a HEXACO model may include additional measures of anger and depression to explore the contribution of affective dispositions to outcome measures. Similarly, Big Five researchers may want to supplement their Big Five questionnaires with measures of primary traits related to honesty and morality if the Big-Five measure does not capture them. A focus on the highe-order factors is only justified in studies that require short measures with a few items.

### Conclusion

My main contribution to the search for a structural model of personality is to examine this question with a statistical tool that makes it possible to test structural models of factors. The advantage of this method is that it is possible to separate structural models of factors from the items that are used to measure factors. While scales of the same factor can differ sometimes dramatically, structural models of factors are independent of the specific items that are used to measure a factor as long as some items reflect variance in the factor. Using this approach, I showed that the Big Five and HEXACO model only differ in the way they represent covariation among some primary factors. It is incorrect to claim that Big Five models fail to represent variation in honesty or humility. It is also incorrect to assume that all pro-social traits are independent after their shared variance in agreeableness is removed. Future research needs to examine more carefully the structural relationships among primary traits that are not explained by higher-order factors. This research question has been neglected because exploratory factor analysis is unable to examine this question. I therefore urge personality researchers to adopt confirmatory factor analysis to advance research on personality structure.