This blog post reports the results of an analysis that predicts variation in scores on the Satisfaction with Life Scale (Diener et al., 1985) from variation in satisfaction with life domains. A bottom-up model predicts that evaluations of important life domains account for a substantial amount of the variance in global life-satisfaction judgments (Andrews & Withey, 1976). However, empirical tests of this prediction fail to show this (Andrews & Withey, 1976).
Here I used the data from the Panel Study of Income Dynamics (PSID) well-being supplement in 2016. The analysis is based on 8,339 respondents. The sample is the largest national representative sample with the SWLS, although only respondents 30 or order are included in the survey.
The survey also included Cantril’s ladder, which was included in the model, to identify method variance that is unique to the SWLS and not shared with other global well-being measures. Andrews & Withey found that about 10% of the variance is unique to a specific well-being scale.
The PSID-WB module included 10 questions about specific life domains: house, city, job, finances, hobby, romantic, family, friends, health, and faith. Out of these 10 domains, faith was not included because it is not clear how atheists answer a question about faith.
The problem with multiple regression is that shared variance among predictor variables contributes to the explained variance in the criterion variable, but the regression weights do not show this influence and the nature of the shared variance remains unclear. A solution to this problem is to model the shared variance among predictor variables with structural equation modeling. I call this method Variance Decomposition Analysis (VDA).
Model 1 used a general satisfaction (GS) factor to model most of the shared variance among the nine domain satisfaction judgments. However, a single factor model did not fit the data, indicating that the structure is more complex. There are several ways to modify the model to achieve acceptable fit. Model 1 is just one of several plausible models. The fit of model 1 was acceptable, CFI = .994, RMSEA = .030.
Model 1 used two types of relationships among domains. For some domain relationships, the model assumes a causal influence of one domain on another domain. For other relationship, it is assumed that judgments about the two domains rely on overlapping information. Rather than simply allowing for correlated residuals, this overlapping variance was modelled as unique factors with constrained loadings for model identification purposes.
Financial satisfaction (D4) was assumed to have positive effects on housing (D1) and job (D3). The rational is that income can buy a better house and pay satisfaction is a component of job satisfaction. Financial satisfaction was also assumed to have negative effects on satisfaction with family (D7) and friends (D8). The reason is that higher income often comes at a cost of less time for family and friends (work-life balance/trade-off).
Health (D9) was assumed to have positive effects on hobbies (D5), family (D7), and friends (D8). The rational was that good health is important to enjoy life.
Romantic (D6) was assumed to have a causal influence on friends (D8) because a romantic partner can fulfill many of the needs that a friend can fulfill, but not vice versa.
Finally, the model includes a path from job (D3) to city (D2) because dissatisfaction with a job may be attributed to few opportunities to change jobs.
Housing (D1) and city (D2) were assumed to have overlapping domain content. For example, high house prices can lead to less desirable housing and lower the attractiveness of a city.
Romantic (D6) was assumed to share content with family (D7) for respondents who are in romantic relationships.
Friendship (D8) and family (D7) were also assumed to have overlapping content because couples tend to socialize together.
Finally, hobby (D5) and friendship (D8) were assumed to share content because some hobbies are social activities.
Figure 2 shows the same figure with parameter estimates.
The most important finding is that the loadings on the general satisfaction (GS) factor are all substantial (> .5), indicating that most of the shared variance stems from variance that is shared across all domain satisfaction judgments.
Most of the causal effects in the model are weak, indicating that they make a negligible contribution to the shared variance among domain satisfaction judgments. The strongest shared variances are observed for romantic (D6) and family (D7) (.60 x .47 = .28) and housing (D1) and city (D2) (.44 x .43 = .19).
Model 1 separates the variances of the nine domains into 9 unique variances (the empty circles next to each square) and five variances that represent shared variances among the domains (GS, D12, D67, D78, D58). This makes it possible to examine how much the unique variances and the shared variances contribute to variance in SWLS scores. To examine this question, I created a global well-being measurement model with a single latent factor (LS) and the SWLS items and the Ladder measures as indicators. The LS factor was regressed on the nine domains. The model also included a method factor for the five SWLS items (swlsmeth). The model may look a bit confusing, but the top part is equivalent to the model already discussed. The new part is that all nine domains have a causal error pointing at the LS factor. The unusual part is that all residual variances are named, and that the model includes a latent variable SWLS, which represents the sum score of the five SWLS items. This makes it possible to use the model indirect function to estimate the path from each residual variance to the SWLS sum score. As all of the residual variance are independent, squaring the total path coefficients yields the amount of variance that is explained by a residual and the variances add up to 1.
GS has many paths leading to SWLS. Squaring the standardized total path coefficient (b = .67) yields 45% of explained variance. The four shared variances between pairs of domains (d12, d67, d78, d58) yield another 2% of explained variance for a total of 47% explained variance from variance that is shared among domains. The residual variances of the nine domains add up to 9% of explained variance. The residual variance in LS that is not explained by the nine domains accounts for 23% of the total variance in SWLS scores. The SWLS method factor contributes 11% of variance. And the residuals of the 5 SWLS items that represent random measurement error add up to 11% of variance.
These results show that only a small portion of the variance in SWLS scores can be attributed to evaluations of specific life domains. Most of the variance stems from the shared variance among domains and the unexplained variance. Thus, a crucial question is the nature of these variance sources. There are two options. First, unexplained variance could be due to evaluations of specific domains and shared variance among domains may still reflect evaluations of domains. In this case, SWLS scores would have high validity as a global measure of subjective evaluations of domains. The other possibility is that shared variance among domains and unexplained variance reflects systematic measurement error. In this case, SWLS scores would have only 6% valid variance if they are supposed to reflect global evaluations of life domains. The problem is that decades of subjective well-being research have failed to provide an empirical answer to this question.
Model 2: A bottom-up model of shared variance among domains
Model 1 assumed that shared variance among domains is mostly produced by a general factor. However, a general factor alone was not able to explain the pattern of correlations and additional relationships were added to the model Model 2 assume that shared variance among domains is exclusively due to causal relationships among domains. Model fit was good, CFI = .994, RMSEA = .043.
Although the causal network is not completely arbitrary, it is possible to find alternative models. More important, the data do not distinguish between Model 1 and Model 2. Thus, the choice of a causal network or a general factor is arbitrary. The implication is that it is not clear whether 47% of the variance in SWLS scores reflect evaluations of domains or some alternative, top-down, influence.
This does not mean that it is impossible to examine this question. To test these models against each other, it would be necessary to include objective predictors of domain (e.g., income, objective health, frequency of sex, etc.) in the model. The models make different predictions about the relationship of these objective indicators to the various domain satisfactions. In addition, it is possible to include measures of systematic method variance (e.g., halo bias) or predictors of top-down effects (e.g., neuroticism) in the model. Thus, the contribution of domain-specific evaluations to SWLS scores is an empirical question.
It is widely assumed that the SWLS is a valid measure of subjective well-being and that SWLS scores reflect a summary of evaluations of specific life domains. However, regression analyses show that only a small portion of the variance in global well-being judgments is explained by unique variance in domain satisfaction judgments (Andrews & Withey, 1976). In fact, most of the variance stems from the shared variance among domain satisfaction judgments (Model 1). Here I show that it is not clear what this shared variance represents. It could be mostly due to a general factor that reflects internal dispositions (e.g., neuroticism) or method variance (halo bias), but it could also result from relationships among domains in a complex network of interdependence. At present it is unclear how much top-down and bottom-up processes contribute to shared variance among domains. I believe that this is an important research question because it is essential for the validity of global life-satisfaction measures like the SWLS. If respondents are not reflecting about important life domains when they rate their overall well-being, these items are not measuring what they are supposed to measure; that is, they lack construct validity.
Naive and more sophisticated conceptions of science assume that empirical data are used to test theories and that theories are abandoned when data do not support them. Psychological journals give the impression that psychologists are doing exactly that. Journals are filled with statistical hypothesis tests. However, hypothesis tests are not theory tests because only results that confirm a theoretical prediction (by falsifying the null-hypothesis) get published; p < .05 (Sterling, 1959). As a result, psychology journals are filled with theories that have never been properly tested. Chances are that some of these theories are false.
To move psychology towards being a science, it is time to subject theories to empirical tests and to replace theories that do not fit the data with theories that do. I have argued elsewhere already that higher-order models of personality are a bad idea with little empirical support (Schimmack, 2019a). Colin DeYoung responded to this criticism of his work (DeYoung, 2019). In this blog post, I present a new approach to the testing of structural theories of personality with confirmatory factor analysis (CFA). The advantage of CFA is that it is a flexible statistical method that can formalize a variety of competing theories. Another advantage of CFA is that it is possible to capture and remove measurement error. Finally, CFA provides fit indices that make it possible to compare models and to select models that fit the data better. Although CFA celebrates its 50th birthday this year, psychologists still have to appreciate its potential for testing personality theories (Joreskog, 1969).
What are Higher-Order Factors?
The notion of a factor has a clear meaning in psychology. A factor is a common cause that explains, at least in a statistical sense, why several variables are correlated with each other. That is, a factor represents the shared variance among several variables that is assumed to be caused by a common cause rather than by direct causation among the variables.
In traditional factor analysis, factors explain correlations among observed variables such as personality ratings. The notion of higher-order factors implies that first-order factors that explain correlations among items are correlated (i.e., not independent) and that these correlations among factors are explained by another set of factors, which are called higher-order factors.
In empirical tests of higher-order factors it has been overlooked that the Big Five factors are already higher-order factors in a hierarchy of personality traits that explain correlations among more specific personality traits like sociability, curiosity, anxiety, or impulsiveness. Instead ALL tests of higher-order models have relied on items or scales that measure the Big Five. This makes it very difficult to study the higher-order structure of personality because results will vary depending on the selection of items that are used to create Big Five scales.
A much better way to test higher-order models is to fit a hierarchical CFA model to data that represent multiple basic personality traits. A straightforward prediction of a higher-order model is that all or at least most facets that belong to a common higher order factor should be correlated with each other.
For example, Digman (1997) and DeYoung (2006) suggested that extraversion and openness are positively correlated because they are influenced by a common factor, called beta or plasticity. As extraversion is conceived as a common cause of sociability, assertiveness, and cheerfulness and openness is conceived as a common cause of being imaginative, artistic, and reflective, the model makes the straightforward prediction that sociability, assertiveness, and cheerfulness are positively correlated with being imaginative, artistic, and reflective.
One problem in testing structural models of personality is that personality ratings are imperfect indicators of personality. Some of the measurement error in personality ratings is random, but other sources of variance are systematic. Two sources have been reliably identified, namely acquiescence and evaluative bias (Anusic et al., 2009; Biderman et al., 2019). DeYoung (2006) also found evidence for evaluative bias in a multi-rater study. Thus, there is agreement between DeYoung and me that some of the correlations among personality ratings do not reflect the structure of personality, but rather systematic measurement error. It is necessary to control for these method factors when studying the structure of personality traits and to examine the correlation among Big Five traits because method factors distort these correlations in mono-method studies. In two previous posts, I found no evidence of higher-order factors when I fitted hierarchical models to the 30 facets of the NEO-PI-R and another instrument with 24 facets (Schimmack, 2019b, 2019c). Here I take another look at this question by examining more closely the pattern of correlations among personality facets before and after controlling for method variance.
From 2010 to 2012 I posted a personality questionnaire with 303 items on the web. Visitors were provided with feedback about their personality on the Big Five dimensions and specific personality facets. Earlier I presented a hierarchical model of these data with three items per facet (Schimmack, 2019). Subsequently, I examined the loadings of the remaining items on these facets. Here I presents results for 179 items with notable loadings on one of the facets (Item.Loadings.303.xlsx; when you open file in excel, selected items are highlighted in green). The use of more items per facets makes the measurement model of facets more stable and ensures more stable facet correlations that are more likely to replicate across studies with different item sets. The covariance matrix for all 303 items is posted on OSF (web303.N808.cov.dat) so that these results presented below can be reproduced.
I first constructed a measurement model. The aim was not to test a structural model, but to find a measurement model that can be used to test structural models of personality. Using CFA for exploration seems to contradict its purpose, but reading the original article by Joreskog shows that this approach is entirely consistent with the way he envisoned CFA to be used. It is unclear to me who invented the idea that CFA should follow an EFA analysis. This makes little sense because EFA may not fit some data if there are hierarchical relationships or correlated residuals. So, CFA modelling has to start with a simple theoretical model that then may need to be modified to fit some data, which leads to a new model to be tested with new data.
To develop a measurement model with reasonable fit to the data, I started with a simple model where items had fixed primary loadings and no secondary loadings, while all factors were allowed to be correlated with each other. This is a simple structure model. It is well known that this model does not fit real data. I then modified the model based on modification indices that suggested (a) secondary loadings, (b) relaxed the constraint of a primary loading, or (c) suggested correlated item residuals. This way a model with reasonable fit to the data was obtained, CFI = .775, RMSEA = .040, SRMR = .042 (M0.Measurement.Model.inp on OSF). Although CFI was below the standard criterion of .95, model fit was considered acceptable because the only source of misfit to the model would be additional small secondary loadings (< .2) or correlated residuals that have little influence on the magnitude of the facet correlations.
Below I present the correlations among the facets. The full correlation matrix is broken down into sections that are theoretically meaningful. The first five tables show the correlations among facets that share the same Big Five factor.
There are three main neuroticism facets: anxiety, anger/hostility, and depression. A fourth facet was originally intended to be an openness to emotions facet, but it correlated more highly with neuroticism (Schimmack, 2009c). All four facets show positive correlations with each other and most of these correlations are substantial, except the strong emotions and depression facets.
Results for extraversion show that all five facets are positively correlated with each other. All correlations are greater than .3, but none of the correlations are so high as to suggest that they are not distinct facets.
Openness facets are also positively correlated, but some correlations are below .2, and one correlation is only .16, namely the correlation between openness to activities and art.
The correlations among agreeableness facets are more variable and the correlation between modesty and trust is slightly negative, r = -.05. The core facet appears to be caring which shows high correlations with morality and forgiveness.
All correlations among conscientiousness facets are above .2. Self-discipline shows high correlations with competence beliefs and achievement striving.
Overall, these results are consistent with the Big Five model.
The next tables examine correlations among sets of facets belonging to two different Big Five traits. According to Digman and DeYoung’s alpha-beta model, extraversion and openness should be correlated. Consistent with this prediction, the average correlation is r = .16. For ease of interpretation all correlations above .10 are highlighted in grey, showing that most correlations are consistent with predictions. However, the value facet of openness shows lower correlations with extraversion facets. Also, the excitement seeking facet of extraversion is more strongly related to openness facets than other facets.
The alpha-beta model also predicts negative correlations among neuroticism and agreeableness facets. Once more, the average correlation is consistent with this prediction, r = -.15. However, there is also variation in correlations. In particular, the anger facet is more strongly negatively correlated with agreeableness facets than other neuroticism facets.
As predicted by the alpha-beta model, neuroticism facets are negatively correlated with conscientiousness facets, average r = -.21. However, there is variation in these correlations. Anxiety is less strongly negatively correlated with conscientiousness facets than other neuroticism facets. Maybe, anxiety sometimes has similar effects as conscientiousness by motivating people to inhibit approach motivated, impulsive behaviors. In this context, it is noteworthy that I found no strong loading of impulsivity on neuroticism (Schimmack, 2019c).
The last pair are agreeableness and conscientiousness facets, which are predicted to be positively correlated. The average correlation is consistent with this prediction, r = .15.
However, there is notable variation in these correlations. A2-Morality is more strongly positively correlated with agreeableness than other agreeableness facets, in particular trust and modesty which show weak correlations with conscientiousness.
The alpha-beta model also makes predictions about other pairs of Big Five facets. As alpha and beta are conceptualized as independent factors, these correlations should be weaker than those in the previous tables and close to zero. However, this is not the case.
First, the average correlation between neuroticism and extraversion is negative and nearly as strong as the correlation between neuroticism and agreeableness, r = -.14. In particular, depression is strongly negatively related to extraversion facets.
The average correlation between extraversion and agreeableness facets is only r = .07. However, there is notable variability. Caring is more strongly related to extraversion than other agreeableness facets, especially with warmth and cheerfulness. Cheerfulness also tends to be more strongly correlated with agreeableness facets than other extraversion facets.
Extraversion and conscientiousness facets are also positively correlated, r = .15. Variation is caused by stronger correlations for the competence and self-discipline facets of conscientiousness and the activity facet of extraversion.
Openness facets are also positively correlated with agreeableness facets, r = .10. There is a trend for the O1-Imagination facet of openness to be more consistently correlated with agreeableness facets than other openness facets.
Finally, openness facets are also positively correlated with conscientiousness facets, r = .09. Most of this average correlation can be attributed to stronger positive correlations of the O4-Ideas facet with conscientiousness facets.
In sum, the Big Five facets from different Big Five factors are not independent. Not surprisingly, a model with five independent Big Five factors reduced model fit from CFI = .775, RMSEA = .040 to CFI = .729, RMSEA = .043. I then fitted a model that allowed for the Big Five factors to be correlated without imposing any structure on these correlations. This model improved fit over the model with independent dimensions, CFI = .734, RMSEA = .043.
The pattern of correlations is consistent with a general evaluative factor rather than a model with independent alpha and beta factors.
Not surprisingly, fitting the alpha-beta model to the data reduced model fit, CFI = .730, RMSEA = .043. In comparison, a mode with a single evaluative bias factor had better fit, CFI = .732, RMSEA = .043.
In conclusion, the results confirm previous studies that a general evaluative dimension produces correlations among the Big Five factors. DeYoung’s (2006) multi-method study and several other multi-method studies demonstrated that this dimension is mostly rater bias because it shows no convergent validity across raters.
Facet Correlations with Method Factors
To remove the evaluative bias from correlations among facets, it is necessary to model evaluative bias at the item level. That is, all items load on an evaluative bias factor. This way the shared variance among indicators of a facet reflects only facet variance and no evaluative variance. I also included an acquiescence factor, although acquiescence has a negligible influence on facet correlations.
It is not possible to let all facets to be correlated freely when method factors are included in a model because this model is not identified. To allow for a maximum of theoretically important facet correlations, I freed parameters for facets that belong to the same Big Five factor, facets that are predicted to be correlated by the alpha-beta model, and additional correlations that were suggested by modification indices. Loadings on the evaluative bias factor were constraint to 1 unless modification indices suggested that items had stronger or weaker loadings on the evaluative bias factor. This model fitted the data as well as the original measurement model, CFI = .778 vs. 775, RMSEA = .040 vs. .040. Moreover, modification indices did not suggest any further correlations that could e freed to improve model fit.
The main effect of controlling for evaluative bias is that all facet correlations were reduced. However, it is particularly noteworthy to examine the correlations that are predicted by the alpha-beta model.
The average correlation for extraversion and openness facets is r = .07. This average is partially driven by stronger correlations of the excitement seeking facet with openness facets than other excitement facets. There are only four other correlations above .10, and 9 of the 25 correlations are negative. Thus, there is little support for a notable general factor that produces positive correlations between extraversion and openness facets.
The average correlation for neuroticism and agreeableness is r = -.06. However, the pattern shows mostly strong negative correlations for the anger facet of neuroticism with agreeableness facets. In addition, there is a strong positive correlation between anxiety and morality, r = .20. This finding suggests that anxiety may also serve the function to inhibit immoral behavior.
The average correlation for neuroticism and conscientiousness is r = -.07. While there are strong negative correlations, r = -.30 for anger and deliberation, there is also a strong positive correlation, r = .22 for self-discipline and anxiety. Thus, the relationship between neuroticism and conscientiousness facets is complex.
The average correlation for agreeableness and conscientiousness facets is r = .01. Moreover, none of the correlations exceeded r = .10. This finding suggests that agreeableness and conscientiousness are independent Big Five factors, which contradicts the prediction by the alpha-beta model.
The finding also raises questions about the small but negative correlations of neuroticism with agreeableness (r = -.06) and conscientiousness (r = -.07). If these correlations were reflecting the influence of a common factor alpha that influences all three traits, one would expect a positive relationship between agreeableness and conscientiousness. Thus, these relationships may have another origin, or there is some additional negative relationship between agreeableness and conscientiousness that cancels out a potential influence of alpha.
Removing method variance also did not eliminate relationships between facets that are not predicted to be correlated by the alpha-beta model. The average correlation between neuroticism and extraversion facets is r = -.05, which is small, but not notably smaller than the predicted correlations (r = .01 to .07).
Moreover, some of these correlations are substantial. For example, excitement seeking is negatively related to anxiety (r = -.24) and warmth is negatively related to depression (r = -.22). Any structural model of personality structure needs to take these findings into account.
A Closer Examination of Extraversion and Openness
There are many ways to model the correlations among extraversion and openness facets. Here I demonstrate that the correlation between extraversion and openness depends on the modelling of secondary loadings and correlated residuals. The first model allowed for extraversion and openness to be correlated. It also allowed for all openness facets to load on extraversion and for all extraversion facets to load on openness. Residual correlations were fixed to zero. This model is essentially an EFA model.
Model fit was as good as for the baseline model, CFI = .779 vs. 778, RMSEA = .039 vs. .040. The pattern of secondary loadings showed two notable positive loadings. Excitement seeking loaded on openness and open to activities loaded on E. In this model the correlation between extraversion and neuroticism was .08, SE = .17. Thus, the positive correlation in the model without secondary loadings was caused by not modelling the pattern of secondary loadings.
However, it is also possible to fit a model that produces a strong correlation between E and O. To do so, the loadings excitement seeking and openness to actions can be set to zero. This pushes other secondary loadings to be negative, which is compensated by a positive correlation between extraversion and openness. This model has the same overall fit as the previous model, both CFI = .779, both RMSEA = .039, but the correlation between extraversion and openness jumps to r = .70. The free secondary loadings are all negative.
The main point of this analysis is to show the importance of facet correlations for structural theories of personality traits. In all previous studies, including my own, the higher-order structure was examined using Big Five scales. However, the correlation between an Extraversion Scale and an Openness Scale provides insufficient information about the relationship between the Extraversion Factor and the Openness Factor because scales always confound information about secondary loadings, residual correlations, and factor correlations.
The goal for future research is to find ways to test competing structural models. For example, the second model suggests that any interventions that increase extraversion would decrease openness to ideas, while the first model does not make this prediction.
Personality psychologists have developed and tested structural models of personality traits for nearly a century. In the 1980s, the Big Five factors were identified. The Big Five have been relatively robust in future replication attempts and emerged also in this investigation. However, there has been little progress in developing and testing hierarchical models of personality that explain what the Big Five are and how they are related to more specific personality traits called facets. There have also been attempts to find even broader personality dimensions. An influential article by Digman (1997) proposed that a factor called alpha produces correlations among neuroticism, agreeableness, and conscientiousness, while a beta factor links extraversion and openness. As demonstrated before, Digman’s results could not be reproduced and ignored evaluative bias in personality ratings (Anusic et al., 2009). Here, I show that empirical tests of higher-order models need to use a hierarchical CFA model because secondary loadings create spurious correlations among Big Five scales that distort the pattern of correlations among the Big Five factors. Based on the present results, there is no evidence for Digman’s alpha and beta factors.
Psychological science has a replication crisis. Many textbook findings, especially in social psychology, failed to replicate over the past years. The reason for these surprising replication failures is that psychologists have used questionable research practices to produce results that confirm theories rather than using statistical methods to test theories and to let theories fail if the evidence does not support them. However, falsification of theories is a sign of scientific progress and it is time to subject psychological theories to real tests.
In personality psychology, the biggest theory is Big Five theory. In short, Big Five theory postulates that variation in personality across individuals can be described with five broad personality dimensions: neuroticism, extraversion, openness, agreeableness, and conscientiousness. Textbooks also claim that the Big Five are fairly universal and can be demonstrated in different countries and with different languages.
One limitation of these studies is that they often use vague criteria to claim that the Big Five have been found or that personality traits are universal. Psychometricians have developed rigorous statistical methods to test these claims, but these methods are rarely used by personality psychologists to test Big Five theory. Some personality psychologists even claimed that these methods should not be used to test Big Five theory because they fail to support the Big Five (McCrae et al., 1996). I have argued that it is time to test Big Five theory with rigorous methods and to let the data decide whether the Big Five exist or not. Other personality psychologists have also started to subject Big Five theory to more rigorous tests (Soto & John, 2017).
Big Five Theory
Big Five theory does not postulate that there are only five dimensions of personality. Rather, it starts with the observation that many important personality traits have been identified and labeled in everyday life. There are hundreds of words that describe individual differences such as helpful, organized, friendly, anxious, curious, or thoughtful. Big Five theory postulates that these personality traits are systematically related to each other. That is, organized individuals are also more likely to be thoughtful and anxious individuals are also more likely to be irritable and sad. Big Five theory explains these correlations among personality traits with five independent factors; that is some broad personality trait that causes covariations among more specific traits that are often called facets. For example, a general disposition to experience more intense unpleasant feelings may produce correlations among the disposition to experience more anxiety, anger, and sadness.
The main prediction of Big Five theory is that the pattern of correlations among personality traits should be similar across different samples and measurement instruments, and that factor analysis produces the same pattern of correlations.
Testing Big Five Theory
A proper psychometric test of Big Five theory requires a measurement model of the facets. If facets are not measured properly, it is impossible to examine the pattern of correlations among the facets. Thus, a proper test of Big Five theory requires fitting a hierarchical model to personality ratings. The first level of the hierarchy specifies a fairly large number of facets that are supposed to be related to one or more Big Five dimensions. The second level of the hierarchy specifies the Big Five factors so that it is possible to examine the relationships (factor loadings) of the facets on the Big Five factors. At present, very few studies have tried to test Big Five theory with hierarchical models. Soto and John (2017) tested Big Five theory with three facets for each Big Five domain and found reasonably good fit for their hierarchical models (see Figure for their model).
Although Soto and Johns’s (2017) article is a step in the right direction, it does not provide a thorough test of Big Five theory for several reasons. First, the model allows facets to correlate freely rather than testing the prediction that these correlations are produced by a Big Five factor. Second, models with only three indicators have zero degrees of freedom and produce perfect fit to the data. Thus, more than three facets are needed to test the prediction that Big Five factors account for the pattern of correlations among facets. Third, the model was fitted separately for each Big Five domain. Thus, there is no information about the relationship of facets to other Big Five factors. For example, the anger facet of neuroticism tends to show negative loadings on agreeableness. Whether such relationships are consistent across datasets is also important to examine.
In a recent blog post, I presented I tried to fit a Big Five model to the 30 facets of the NEO-PI-R (Schimmack, 2019a). Table 1 shows the factor loadings of the 30 facets on the Big Five factors.
The results were broadly consistent with the theoretical Big Five structure. However, some facets did not show the predicted pattern. For example, excitement seeking did not load on extraversion. Other facets had rather weak loadings. For example, the loading of Impulsivity on neuroticism implies that less than 10% of the variance in impulsivity is explained by neuroticism. These results do not falsify Big Five theory by any means. However, they provide the basis for further theory development and refinement of personality theory. However, before any revisions of Big Five theory are made, it is important to examine the replicability of the factor structure in hierarchical measurement models.
From 2010 to 2012 I posted a personality questionnaire with 303 items on the web. Visitors were provided with feedback about their personality on the Big Five dimensions and the 30 facets. In addition to the items that were used to provide feedback, the questionnaire contained several additional items that might help to improve measurement of facets. Furthermore, the questionnaire included some items about life-satisfaction because I have an interest in the relationship between personality traits and life-satisfaction. The questionnaire also included four questions about desirable attributes, namely attractiveness, intelligence, fitness, and broad knowledge. These questions have been used before to demonstrate evaluative biases in personality ratings (Anusic et al., 2009).
Simple correlations and factor analysis were used to identify three indicators of the 30 NEO-facets. Good indicators should show moderate and similar correlations to each other. During this stage it became apparent that the item-set failed to capture the self-consciousness facet of neuroticism and the dutifulness facet of conscientiousness. Thus, these two facets could not be included in the model.
I first fitted a model that allowed the 28 facets to be correlated freely. This model evaluates the measurement of the 28 facets and provides information about the pattern of correlations among facets that Big Five theory aims to explain. This model showed very high correlations between the neuoroticism-facet anger and the agreeableness-facet compliance (r = .8), the warmth and gregariousness facets of extraversion (r = 1) , and the anxiety and vulnerability facets of neuroticism (r = .8). These correlations raise concerns about the discriminant validity of these facets and create problems in fitting a hierarchical model to the data. Thus, I dropped the vulnerability, gregariousness, and compliance items and facets from the model. Thus, the final model had 83 items, 26 facets, and factors for life-satisfaction and for desirable attributes.
The model fit for the model with correlated factors was accepted considering the RMSEA fit index, but below standard criteria for the CFI. However, examination of the modification indices showed that only freeing weak secondary loadings would further improve model fit. Thus, the model was considered adequate and model fit of this model served as a comparison standard for the hierarchical model, CFI = .867, RMSEA = .037.
The hierarchical model specified the Big Five as independent factors. In addition, it included an acquiescence factor and an evaluative bias factor. The evaluative bias factor was allowed to correlate with the desirable attribute factor (cf. Anusic et al., 2009). Life-satisfaction was regressed on the facets, but only significant facets were retained in the final model. Model fit of this model was comparable to model fit of the baseline model, CFI = .861, RMSEA = .040.
The first set of tables shows the item loadings on the primary factor, the evaluative bias factor, the acquiescence factor, and secondary loadings. Facet names are based on the NEO-PI-R.
Primary loadings of neuroticism items on their facets are generally high and secondary loadings are small (Table 1). Thus, the four neuroticism facets were clearly identified.
The measurement model for the extraversion facets also showed high primary loadings (Table 2).
For openness, one item of the values facet had a low loading, but the other two items clearly identified the facet (Table 3).
All primary loadings for the four agreeableness facets were above .4 and the facets were clearly identified (Table 4).
Finally, the conscientiousness facets were also clearly identified (Table 5).
In conclusion, the measurement model for the 24 facets showed that all facets were measured well and that the item content matches the facet labels. Thus, the basic requirement for examining the structural relationships among facets have been met.
The most important result are the loadings of the 24 facets on the Big Five factors. These results are shown in Table 6. To ease interpretation, primary loadings greater than .4 and secondary loadings greater than .2 are printed in bold. Results that are consistent with the previous study of the NEO-PI-R are highlighted with a gray background.
15 of the 24 primary loadings are above .4 and replicate results with the NEO-PI-R. This finding provides support for the Big Five model.
There are also four consistent loadings below .4, namely for the impulsivity facet of neuroticism, the openness facets feelings and actions, and the agreeableness facet of trust. This finding suggests that the model needs to be revised. Either there are measurement problems or openness is not related to emotions and actions. Problems with agreeableness have led to the creation of an alternative model with six factors (Ashton & Lee) that distinguishes two aspects of agreeableness.
There are eight facets with inconsistent loading patterns. Activity loaded with .34 on extraversion. More problematic was the high secondary loading on conscientiousness, suggesting that activity level is not clearly related to a single Big Five trait. The results for excitement seeking were particularly different. Excitement seeking did not load at all on extraversion in the NEO-PI-R model, but the loading in this sample was high.
The loading for values on openness was .45 for the NEO-PI-R and .29 in this sample. Thus, the results are more consistent than the use of the arbitrary .4 value suggests. Values are related to openness, but the relationship is weak and openness explains no more than 20% of the variance in holding liberal versus conservative values.
For agreeableness, compliance was represented by the anger facet of neuroticism, which did not load above .4 on agreeableness although the loading came close (-.32). Thus, the results do not require a revision of the model based on the present data. The biggest problem was that the modesty facet did not load highly on the agreeableness facet (.21). More research is needed to examine the relationship between modesty and agreeableness.
Results for conscientiousness were fairly consistent with theory and the loading of the deliberation facet on conscientiousness was just shy of the arbitrary .4 criterion (.37). Thus, no revision to the model is needed at this point.
The consistent results provide some robust markers of the Big Five, that is facets with high primary and low secondary loadings. Neuroticism is most clearly related to high anxiety and high vulnerability (sensitivity to stress), which could not be distinguished in the present dataset. However, other negative emotions like anger and depression are also consistently related to neuroticism. This suggests that neuroticism is a general disposition to experience more unpleasant emotions. Based on structural models of affective experiences, this dimension is related to Negative Activation and tense arousal.
Extraversion is consistently related to warmth and gregariousness, which could not be separated in the present dataset as well as assertiveness and positive emotions. One interpretation of this finding is that extraversion reflects positive activation or energetic arousal, which is a distinct affective system that has been linked to approach motivation. Structural analyses of affect also show that tense arousal and energetic arousal are two separate dimensions. The inconsistent results for action may reflect the fact that activity levels can also be influenced by more effortful forms of engagement that are related to conscientiousness. Extraverted activity might be more intrinsically motivated by positive emotions, whereas conscientious activity is more driven by extrinsic motivation.
The core facets of openness are fantasy/imagination, artistic interests, and intellectual engagement. The common feature of these facets is that attention is directed. The mind is traveling rather than being focused on the immediate situation. A better way to capture openness to feelings might be to distinguish feelings that arise from actual events versus emotions that are elicited by imagined events or art.
The core features of agreeableness are straighforwardness, altruism, and tender-mindedness, which could not be separated from altruism in this dataset. The common feature is a concern about the well-being of others versus a focus on the self. Trust may not load highly on agreeableness because the focus of trust is individuals own well-being. Trusting others may be beneficial for the self if others are trustworthy or harmful if they are not. However, it is not necessary to trust somebody in need to help them unless helping is risky.
The core feature of conscientiousness is self-discipline. Order and achievement striving (which is not the best label for this facet) also imply that conscientious people can stay focused on things that need to be done and are not easily distracted. Conscientious people are more likely to follow a set of rules.
There are only a few consistent secondary loadings. This suggest that many secondary loadings may be artifacts of item-selection or participant selection. The few consistent secondary loadings make theoretical sense. Anger loads negatively on agreeableness and this facet is probably best considered a blend of high neuroticism and low agreeableness.
Assertiveness shows a positive loading on conscientiousness. The reason is that conscientious people may have a strong motivation to follow their internal norms (a moral compass) and that they are wiling to assert these norms if necessary.
The openness to feelings facet has a strong “secondary” loading on neuroticism, suggesting that this facet does not measure what it was intended to measure. It just seems to be another measure of strong feelings without specifying the valence.
Finally, deliberation is negatively related to extraversion. This finding is consistent with the speculation that extraversion is related to approach motivation. Extraverts are more likely to give in to temptations, whereas conscientious individuals are more likely to resist temptations. In this context, the results for impulsivity are also noteworthy. At least in this dataset, implusive behaviors that were mostly related to eating were more strongly related to extraversion than to neuroticism. If neuroticism is strongly related to anxiety and avoidance behavior, it is not clear why neurotic individuals would be more impulsive. However, if extraversion reflects approach motivation, it makes more sense that extraverts are more likely to indulge.
Of course, these interpretations of the results are mere speculations. In fact, it is not even clear that the Big Five account for the correlations among facets. Some researchers have proposed that facets may directly influence each other. While this is possible, such models will have to explain the consistent pattern of correlations among facets. The present results are at least consistent with the idea that five broader dispositions explain some of these correlations.
Neuroticism is a broad disposition to experience a range of unpleasant emotions, not just anxiety.
Extraversion is a broad disposition to be actively and positively engaged.
Openness is a broad disposition to focus on internal processes (thoughts and feelings) rather than on external events and doing things.
Agreeableness is a broad disposition to be concerned with the well-being of others as opposed to being only concerned with oneself.
Conscientiousness is a broad disposition to be guided by norms and rules as opposed to being guided by momentary events or impulses.
While these broad dispositions account for some of the variance in specific personality traits, facets, facets add additional information that is not captured by the Big Five. The last column in Table 1 shows the residual (i.e., unexplained) variances in the facets. While the amount of unepxlained variance varies considerable across facets, the average is high (57%) and this estimate is consistent with the estimate in the NEO-PI-R (58%). Thus, the Big Five provide only a very broad and unclear impression of individuals’ personality.
Residual Correlations among Facets
Traditional factor analysis does not allow for correlations among the residual variances of indicators. CFA models that do not include these correlations have poor fit. I was only able to produce reasonable fit to the NEO-PI-R data by including correlated residuals in the model. This was also the case for this dataset. Table 7 shows the residual correlations. For the ease of interpretation, residual correlations that were consistent across models are highlighted in green.
As can be seen, most of the residual correlations were inconsistent across datasets. This shows that the structure of facet correlations is not stable across these two datasets. This complicates the search for a structural model of personality because it will be necessary to uncover moderators of these inconsistencies.
While dozens of articles have correlated Big Five measures with life-satisfaction scales, few studies have examined how facets are related to life-satisfaction (Schimmack, Oishi, Furr & Funder, 2004). The most consistent finding has been that the depression facet explains unique variance above and beyond neuroticism. This was also the case in this dataset. Depression was by far the strongest predictor of life-satisfaction (-.56). The only additional significant predictor that was added to the model was the competence facet (.22). Contrary to previous studies, the cheerfulness facet did not predict unique variance in life-satisfaction judgments. More research at the facet level and with other specific personality traits below the Big Five is needed. However, the present results confirm that facets contain unique information that contributes to the prediction of outcome variables. This is not surprising given the large amount of unexplained variance in facets.
Table 8 shows the loadings of the four desirable attributes on the DA factor. Loadings are similar to those in Anusic et al. (2009). As objective correlations among these characteristics are close to zero, the shared variance can be interpreted as an evaluative bias. Items did not load on the evaluative bias factor to examine the relationship with the evaluative bias factor at the factor level.
Unexpectedly, the DA factor correlated only modestly with the evaluative bias factor for the facet-items, r = .38. This correlation is notably weaker than the correlation reported by Anusic et al. (2009), r = .76. This raises some questions about the nature of the evaluative bias variance. It is unfortunate that we do not know more about this persistent variance in personality ratings, one-hundred years after Thorndike (1920) first reported it.
In an attempt to replicate a hierarchical model of personality, I was only partially successful to cross-validate the original model. On the positive side, 15 out of 24 distinct facets had loadings on the predicted Big Five factor. This supports the Big Five as a broad model of personality. However, I also replicated some results that question the relationship between some facets and Big Five factors. For example, impulsiveness does not seem to be a facet of neuroticism and openness to actions may not be a facet of openness. Moreover, there were many inconsistent results that suggest the structure of personality is not as robust as one might expect. More research is needed to identify moderators of facet correlations. For example, in student samples anxiety may be a positive predictor of achievement striving, whereas it may be unrelated or negatively related to achievement striving in middle or old age.
Past research with exploratory methods has also ignored that the Big Five do not explain all of the correlations among facets. However, these correlations also seem to vary across samples.
All of these results do not make for neat and sexy JPSP article that proposes a simple model of personality structure, but the present results do suggest that one should not trust such simple models because personality structure is much more complex and unstable than these models suggest.
I can only repeat that personality research will only make progress by using proper methods that can actually test and falsify structural models. Falsification of simple and false models is the impetus for theory development. Thus, for the sake of progress, I declare that the Big Five model that has been underpinning personality research for 40 needs to be revised. Most importantly, progress can only be made if personality measures do not already assume that the Big Five are valid. Measures like the BFI-2 (Soto & John) or the NEO-PI-R have the advantage that they capture a wide range of personality differences at the facet level. Surely there are more than 15, 24, or 30 facets. So more research about personality at the facet level is required. Personality research might also benefit from a systematic model that integrates the diverse range of personality measures that have been developed for specific research questions from attachment styles to machiavellianism. All of this research would benefit from the use of structural equation modeling because SEM can fit a diverse range of models and provides information of model fit.
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.
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.
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).
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.
Running the model with additional items is time consuming even on my powerful computer. I will add these results when they are ready.
Most published psychological measures are unvalid. (subtitle) *unvalid = the validity of the measure is un-known.
This blog post served as a first draft for a manuscript that is currently under review at Meta-Psychology. You can find the latest version here (pdf).
8 years ago, psychologists started to realize that they have a replication crisis. Many published results do not replicate in honest replication attempts that allow the data to decide whether a hypothesis is true or false.
The replication crisis is sometimes attributed to the lack of replication studies before 2011. However, this is not the case. Most published results were replicated successfully. However, these successes were entirely predictable from the fact that only successful replications would be published (Sterling, 1959). These sham replication studies provided illusory evidence for theories that have been discredited over the past eight years by credible replication studies.
New initiatives that are called open science are likely to improve the replicability of psychological science in the future, although progress towards this goal is painfully slow.
This blog post addresses another problem in psychological science. I call it the validation crisis. Replicability is only one necessary feature of a healthy science. Another necessary feature of a healthy science is the use of valid measures. This feature of a healthy science is as obvious as the need for replicability. To test theories that relate theoretical constructs to each other (e.g., construct A influences construct B for individuals drawn from population P under conditions C), it is necessary to have valid measures of constructs. However, it is unclear which criteria a measure has to fulfill to have construct validity. Thus, even successful and replicable tests of a theory may be false because the measures that were used lacked construct validity.
The classic article on “Construct Validity” was written by two giants in psychology; Cronbach and Meehl (1955). Every graduate student of psychology and surely every psychologists who published a psychological measure should be familiar with this article.
The article was the result of an APA task force that tried to establish criteria, now called psychometric properties, for tests to be published. The result of this project was the creation of the construct “Construct validity”
The chief innovation in the Committee’s report was the term construct validity. (p. 281).
Cronbach and Meehl provide their own definition of this construct.
Construct validation is involved whenever a test is to be interpreted as a measure of some attribute or quality which is not “operationally defined” (p. 282).
In modern language, construct validity is the relationship between variation in observed test scores and a latent variable that reflects corresponding variation in a theoretical construct (Schimmack, 2010).
Thinking about construct validity in this way makes it immediately obvious why it is much easier to demonstrate predictive validity, which is the relationship between observed tests scores and observed criterion scores than to establish construct validity, which is the relationship between observed test scores and a latent, unobserved variable. To demonstrate predictive validity, one can simply obtain scores on a measure and a criterion and compute the correlation between the two variables. The correlation coefficient shows the amount of predictive validity of the measure. However, because constructs are not observable, it is impossible to use simple correlations to examine construct validity.
The problem of construct validation can be illustrated with the development of IQ scores. IQ scores can have predictive validity (e.g., performance in graduate school) without making any claims about the construct that is being measured (IQ tests measure whatever they measure and what they measure predicts important outcomes). However, IQ tests are often treated as measures of intelligence. For IQ tests to be valid measures of intelligence, it is necessary to define the construct of intelligence and to demonstrate that observed IQ scores are related to unobserved variation in intelligence. Thus, construct validation requires clear definitions of constructs that are independent of the measure that is being validated. Without clear definition of constructs, the meaning of a measure reverts essentially to “whatever the measure is measuring,” as in the old saying “Intelligence is whatever IQ tests are measuring. This saying shows the problem of research with measures that have no clear construct and no construct validity.
In conclusion, the challenge in construct validation research is to relate a specific measure to a well-defined construct and to establish that variation in test scores are related to variation in the construct.
What are Constructs
Construct validation starts with an assumption. Individuals are assumed to have an attribute, today we may say personality trait. Personality traits are typically not directly observable (e.g., kindness rather than height), but systematic observation suggests that the attribute exists (some people are kinder than others across time and situations). The first step is to develop a measure of this attribute (e.g., a self-report measure “How kind are you?”). If the test is valid, variation in the observed scores on the measure should be related to the personality trait.
A construct is some postulated attribute of people, assumed to be reflected in test performance (p. 283).
The term “reflected” is consistent with a latent variable model, where unobserved traits are reflected in observable indicators. In fact, Cronbach and Meehl argue that factor analysis (not principle component analysis!) provides very important information for construct validity.
We depart from Anastasi at two points. She writes, “The validity of a psychological test should not be confused with an analysis of the factors which determine the behavior under consideration.” We, however, regard such analysis as a most important type of validation. (p. 286).
Factor analysis is useful because factors are unobserved variables and factor loadings show how strongly an observed measure is related to variation in a an unobserved variable; the factor. If multiple measures of a construct are available, they should be positively correlated with each other and factor analysis will extract a common factor. For example, if multiple independent raters agree in their ratings of individuals’ kindness, the common factor in these ratings may correspond to the personality trait kindness, and the factor loadings provide evidence about the degree of construct validity of each measure (Schimmack, 2010).
In conclusion, factor analysis provides useful information about construct validity of measures because factors represent the construct and factor loadings show how strongly an observed measure is related to the construct.
It is clear that factors here function as constructs (p. 287).
The term convergent validity was introduced a few years later in another seminal article on validation research by Campbell and Fiske (1959). However, the basic idea of convergent validity was specified by Cronbach and Meehl (1955) in the section “Correlation matrices and factor analysis”
If two tests are presumed to measure the same construct, a correlation between them is predicted (p. 287).
If a trait such as dominance is hypothesized, and the items inquire about behaviors subsumed under this label, then the hypothesis appears to require that these items be generally intercorrelated (p. 288)
Cronbach and Meehl realize the problem of using just two observed measures to examine convergent validity. For example, self-informant correlations are often used in personality psychology to demonstrate validity of self-ratings. However, a correlation of r = .4 between self-ratings and informant ratings is open to very different interpretations. The correlation could reflect very high validity of self-ratings and modest validity of informant ratings or the opposite could be true.
If the obtained correlation departs from the expectation, however, there is no way to know whether the fault lies in test A, test B, or the formulation of the construct. A matrix of intercorrelations often points out profitable ways of dividing the construct into more meaningful parts, factor analysis being a useful computational method in such studies. (p. 300)
A multi-method approach avoids this problem and factor loadings on a common factor can be interpreted as validity coefficients. More valid measures should have higher loadings than less valid measures. Factor analysis requires a minimum of three observed variables, but more is better. Thus, construct validation requires a multi-method assessment.
The term discriminant validity was also introduced later by Campbell and Fiske (1959). However, Cronbach and Meehl already point out that high or low correlations can support construct validity. Crucial for construct validity is that the correlations are consistent with theoretical expectations.
For example, low correlations between intelligence and happiness do not undermine the validity of an intelligence measure because there is no theoretical expectation that intelligence is related to happiness. In contrast, low correlations between intelligence and job performance would be a problem if the jobs require problem solving skills and intelligence is an ability to solve problems faster or better.
Only if the underlying theory of the trait being measured calls for high item intercorrelations do the correlations support construct validity (p. 288).
Quantifying Construct Validity
It is rare to see quantitative claims about construct validity. Most articles that claim construct validity of a measure simply state that the measure has demonstrated construct validity as if a test is either valid or invalid. However, the previous discussion already made it clear that construct validity is a quantitative construct because construct validity is the relation between variation in a measure and variation in the construct and this relation can vary . If we use standardized coefficients like factor loadings to assess the construct validity of a measure, construct validity can range from -1 to 1.
Contrary to the current practices, Cronbach and Meehl assumed that most users of measures would be interested in a “construct validity coefficient.”
There is an understandable tendency to seek a “construct validity coefficient. A numerical statement of the degree of construct validity would be a statement of the proportion of the test score variance that is attributable to the construct variable. This numerical estimate can sometimes be arrived at by a factor analysis” (p. 289).
Cronbach and Meehl are well-aware that it is difficult to quantify validity precisely, even if multiple measures of a construct are available because the factor may not be perfectly corresponding with the construct.
Rarely will it be possible to estimate definite “construct saturations,” because no factor corresponding closely to the construct will be available (p. 289).
And nobody today seems to remember Cronbach and Meehl’s (1955) warning that rejection of the null-hypothesis, the test has zero validity, is not the end goal of validation research.
It should be particularly noted that rejecting the null hypothesis does not finish the job of construct validation (p. 290)
The problem is not to conclude that the test “is valid” for measuring- the construct variable. The task is to state as definitely as possible the degree of validity the test is presumed to have (p. 290).
One reason why psychologists may not follow this sensible advice is that estimates of construct validity for many tests are likely to be low (Schimmack, 2010).
The Nomological Net – A Structural Equation Model
Some readers may be familiar with the term “nomological net” that was popularized by Cronbach and Meehl. In modern language a nomological net is essentially a structural equation model.
The laws in a nomological network may relate (a) observable properties or quantities to each other; or (b) theoretical constructs to observables; or (c) different theoretical constructs to one another. These “laws” may be statistical or deterministic.
It is probably no accident that at the same time as Cronbach and Mehl started to think about constructs as separate from observed measures, structural equation model was developed as a combination of factor analysis that made it possible to relate observed variables to variation in unobserved constructs and path analysis that made it possible to relate variation in constructs to each other. Although laws in a nomological network can take on more complex forms than linear relationships, a structural equation model is a nomological network (but a nomological network is not necessarily a structural equation model).
As proper construct validation requires a multi-method approach and demonstration of convergent and discriminant validity, SEM is ideally suited to examine whether the observed correlations among measures in a mulit-trait-multi-method matrix are consistent with theoretical expectations. In this regard, SEM is superior to factor analysis. For example, it is possible to model shared method variance, which is impossible with factor analysis.
Cronbach and Meehl also realize that constructs can change as more information becomes available. It may also occur that the data fail to provide evidence for a construct. In this sense, construct validiation is an ongoing process of improved understanding of unobserved constructs and how they are related to observable measures.
Ideally this iterative process would start with a simple structural equation model that is fitted to some data. If the model does not fit, the model can be modified and tested with new data. Over time, the model would become more complex and more stable because core measures of constructs would establish the construct validity, while peripheral relationships may be modified if new data suggest that theoretical assumptions need to be changed.
When observations will not fit into the network as it stands, the scientist has a certain freedom in selecting where to modify the network (p. 290).
Too often psychologists use SEM only to confirm an assumed nomological network and it is often considered inappropriate to change a nomological network to fit observed data. However, SEM is as much testing of an existing construct as exploration of a new construct.
The example from the natural sciences was the initial definition of gold as having a golden color. However, later it was discovered that the pure metal gold is actually silver or white and that the typical yellow color comes from copper impurities. In the same way, scientific constructs of intelligence can change depending on the data that are observed. For example, the original theory may assume that intelligence is a unidimensional construct (g), but empirical data could show that intelligence is multi-faceted with specific intelligences for specific domains.
However, given the lack of construct validation research in psychology, psychology has seen little progress in the understanding of such basic constructs such as extraversion, self-esteem, or wellbeing. Often these constructs are still assessed with measures that were originally proposed as measures of these constructs, as if divine intervention led to the creation of the best measure of these constructs and future research only confirmed their superiority.
Instead many claims about construct validity are based on conjectures than empirical support by means of nomological networks. This was true in 1955. Unfortunately, it is still true over 50 years later.
For most tests intended to measure constructs, adequate criteria do not exist. This being the case, many such tests have been left unvalidated, or a finespun network of rationalizations has been offered as if it were validation. Rationalization is not construct validation. One who claims that his test reflects a construct cannot maintain his claim in the face of recurrent negative results because these results show that his construct is too loosely defined to yield verifiable inferences (p. 291).
Given the difficulty of defining constructs and finding measures for it, even measures that show promise in the beginning might fail to demonstrate construct validity later and new measures should show higher construct validity than the early measures. However, psychology shows no development in measures of the same construct. The most widely used measure of self-esteem is still Rosenberg’s scale from 1965 and the most widely used measure of wellbieng is still Diener et al.’s scale from 1984. It is not clear how psychology can make progress, if it doesn’t make progress in the development of nomological networks that provide information about constructs and about the construct validity of measures.
Cronbach and Meehl are clear that nomological networks are needed to claim construct validity.
To validate a claim that a test measures a construct, a nomological net surrounding the concept must exist (p. 291).
However, there are few attempts to examine construct validity with structural equation models (Connelly & Ones, 2010; Zou, Schimmack, & Gere, 2013). [please share more if you know some]
One possible reason is that construct validation research may reveal that authors initial constructs need to be modified or their measures have modest validity. For example, McCrae, Zonderman, Costa, Bond, and Paunonen (1996) dismissed structural equation modeling as a useful method to examine the construct validity of Big Five measures because it failed to support their conception of the Big Five as orthogonal dimensions with simple structure.
Recommendations for Users of Psychological Measures
The consumer can accept a test as a measure of a construct only when there is a strong positive fit between predictions and subsequent data. When the evidence from a proper investigation of a published test is essentially negative, it should be reported as a stop sign to discourage use of the test pending a reconciliation of test and construct, or final abandonment of the test (p. 296).
It is very unlikely that all hunches by psychologists lead to the discovery of useful constructs and development of valid tests of these constructs. Given the lack of knowledge about the mind, it is rather more likely that many constructs turn out to be non-existent and that measures have low construct validity.
However, the history of psychological measurement has only seen development of more and more constructs and more and more measures to measure this increasing universe of constructs. Since the 1990s, constructs have doubled because every construct has been split into an explicit and an implicit version of the construct. Presumably, there is even implicit political orientation or gender identity.
The proliferation of constructs and measures is not a sign of a healthy science. Rather it shows the inability of empirical studies to demonstrate that a measure is not valid or that a construct may not exist. This is mostly due to self-serving biases and motivated reasoning of test developers. The gains from a measure that is widely used are immense. Thus, weak evidence is used to claim that a measure is valid and consumers are complicit because they can use these measures to make new discoveries. Even when evidence shows that a measure may not work as intended (e.g., Bosson et al., 2000), it is often ignored (Greenwald & Farnham, 2001).
Just like psychologist have started to appreciate replication failures in the past years, they need to embrace validation failures. Some of the measures that are currently used in psychology are likely to have insufficient construct validity. If this was the decade of replication, the 2020s may become the decade of validation, and maybe the 2030s may produce the first replicable studies with valid measures. Maybe this is overly optimistic, given the lack of improvement in validation research since Cronbach and Meehl (1955) outlined a program of construct validation research. Ample citations show that they were successful in introducing the term, but they failed in establishing rigorous criteria of construct validity. The time to change this is now.