### Background

Bar-Anan and Vianello (2018) published a structural equation model in support of a dual-attitude model that postulates explicit and implicit attitudes towards racial groups, political parties, and the self. I used their data to argue against a dual-attitude model. Vianello and Bar-Anan (2020) wrote a commentary that challenged my conclusions. I was a reviewer of their commentary and pointed out several problems with their new model (Schimmack, 2020). They did not respond to my review and their commentary was published without changes. I wrote a reply to their commentary. In the reply, I merely pointed to my criticism of their new model. Vianello and Bar-Anan wrote a review of my reply, in which they continue to claim that my model is wrong. I invited them to discuss the differences between our models, but they declined. In this blog post, I show that Vianello and Bar-Anan lack insight into the shortcomings of their model, which is consistent with the Dunning-Kruger effect that incompetent individuals lack insight into their own incompetence. On top of this, Vianello and Bar-Anan show willful ignorance by resisting arguments that undermine their motivated belief in dual-attitude models. As I show below, Vianello and Bar-Anan’s model has several unexplained results (e.g, negative loadings on method factors), worse fit than my model, and produces false evidence of incremental predictive validity for the implicit attitude factors.

### Introduction

The skill set of psychology researchers is fairly limited. In some areas expertise is needed to create creative experimental setups. In other areas, some expertise in the use of measurement instruments (e.g., EEG) is required. However, for the most part, once data are collected, little expertise is needed. Data are analyzed with simple statistical tools like t-tests, ANOVAs, or multiple regression. These statistical methods are implemented in simple commands and no expertise is required to obtain results from statistics programs like SPSS or R.

Structural equation modeling is different because researchers have to specify a model that is fitted to the data. With complex data sets, the number of possible models that can be specified increases exponentially and it is not possible to specify all models and to simply pick the model with the best fit. Moreover, there will be many models with similar fit and it requires expertise to pick plausible models. Unfortunately, psychologists receive little formal training in structural equation modeling because graduate training relies heavily on training by supervisors rather than formal training. As most supervisors never received training in structural equation modeling, they cannot teach their graduate student how to perform these analyses. This means that expertise in structural equation modeling varies widely.

An inevitable consequence of wide variation in expertise is that individuals with low expertise have little insight into their limited abilities. This is known as the Dunning-Kruger effect that has been replicated in numerous studies. Even incentives to provide accurate performance estimates do not eliminate the overconfidence of individuals with low levels of expertise (Ehrlinger et al., 2008).

The Dunning-Kruger effect explains Vianello and Bar-Anan’s (2020) response to my article that presents another ill-fitting model that makes little theoretical sense. This overconfidence may also explain why they are unwilling to engage in a discussion of their model with me. They may not realize that my model is superior because they were unable to compare the models or to run more direct comparisons of the models. As their commentary is published in the influential journal Perspectives on Psychological Science and as many readers lack the expertise to evaluate the merits of their criticism, it is necessary to explain clearly why their criticism of my models is invalid and why their new alternative model is flawed.

### Reproducing Vianello and Bar-Anan’s Model

I learned the hard way that the best way to fit a structural equation model is to start with small models of parts of the data and then to add variables or other partial models to build a complex model. The reason is that bad fit in smaller models can be easily identified and lead to important model modifications, whereas bad fit in a complex model can have thousands of reasons that are difficult to diagnose. In this particular case, I saw new reason to even fit a complex model for attitudes to political parties, racial groups, and the self. Instead I fitted separate models for each attitude domain. Vianello and Bar-Anan (2020) take issue with this decision.

“*As for estimating method variance across attitude domains, that is the very logic behind an MTMM design (Campbell & Fiske, 1959; Widaman, 1985): Method variance is shared across measures of different traits that use the same method (e.g., among indirect measuresof automatic racial bias and political preferences). Trait variance is shared across measures of the same trait that use different methods (e.g., among direct and indirect measures of racial attitude). Separating the MTMM matrix into three separate submatrices (one for eachtrait), as Schimmack did in his article, misses a main advantage of an MTMM design.*“

This criticism is based on an outdated notion of validation by means of correlations in a multi-trait-multi-method matrix. In this MTMM tables, every trait is measured with all methods. For example, the Big Five traits are measured with students’ self-ratings, mothers’ ratings, and fathers’ ratings (5 traits x 3 methods). This is not possible for validation studies of explicit and implicit measures because it is assumed that explicit measures measure explicit constructs and implicit measures measure implicit constructs. Thus, it is not possible to fully cross traits and methods. This problem is evident in all models by Bar-Anan and Vianello and myself. Bar-Anan and Vianello make the mistake to assume that using implicit measures for several attitude domains solves this problem, but their assumption that we can use correlations between implicit measures in one domain and implicit measures in another domain to solve this problem is wrong. In fact, it makes matters worse because they fail to model method variance within a single attitude domain properly.

To show this problem, I first constructed measurement models for each attitude domain and then show that combining well-fitting models of three three domains produces a better fitting model than Vianello and Bar-Anan’s model.

### Racial Bias

In their revised model, Vianello and Bar-Anan postulate three method factors. One for explicit measures, one for IAT-related measures, and one for the Affective Missatribution Paradigm and the Evaluative Priming Task. It is not possible to estimate a separate method factor for all explicit measures, but it is possible to allow for method factors that are unique to the IAT-related measures and one that is unique to the AMP and EPT. In the first model, I fitted this model to the measures of racial bias. The model appears to have good fit, RMSEA = .013, CFI = 973. In this model, the correlation between the explicit and implicit racial bias factors is *r* = .80.

However, it would be premature to stop the analysis here because overall fit values in models with many missing values are misleading (Zhang & Savaley, 2019). Even if fit were good, it is good practice to examine the modification indices to see whether some parameters are misspecified.

Inspection of the fit indices shows one very large Modification Index of 146.04 for the residual correlation between the feeling thermometer and the preference ratings. There is a very plausible explanation for this finding. These two measures are very similar and can share method variance. For example, social desirable responding could have the same effect on both ratings. This was the reason why I included only one of the two measures in my model. An alternative is to include both ratings and allow for the correlated residual to model shared method variance.

As predicted by the MI, model fit improved, RMSEA = .006, CFI = .995. Vianello and Bar-Anan (2020) might object that this finding is post-hoc after peeking at the data, while their model is specified theoretically. However, this argument is weak. If they really theoretically predicted that feeling thermometer and direct ratings share no method variance, it is not clear what theory they have in mind. After all, shared rating biases are very common. Moreover, their model also assumes shared method variance between these factors, but it also predicts that this method variance also influences dissimilar measures like the Modern Racism Scale and even ratings of other attitude objects. In short, neither their model nor my models are based on theories, in part because psychologists have ignored to develop and validate measurement theories. Even if it were theoretically predicted that feeling-thermometer and preference ratings do not share method variance, the large MI for this parameter would indicate that this theory is wrong. Thus, the data falsify this prediction. In the modified model, the implicit-explicit correlation increases from .80 to .90, providing even less support for the dual-attitude model.

Further inspection of the MI showed no plausible further improvements of the model. One important finding in this partial model is that there is no evidence of shared method variance between the AMP and EPT, r = -.04. Thus, closer inspection of the correlations among the racial attitude domain suggests two problems for Vianello and Bar-Anan’s model. There is evidence of shared method variance between two explicit measures and there is no evidence of shared method variance between two implicit measures, namely the AMP and EPT.

Next, I built a model for the political orientation domain starting with the specification in Vianello and Bar-Anan’s model. Once more, overall fit appears to be good, RMSEA = .014, CFI = .989. In this model, the correlation between the implicit and explicit factor is r = .9. However, inspection of the MI replicates a residual correlation between feeling thermometer and preference ratings. MI = 91.91. Allowing for this shared method variance improved model fit, RMSEA = .012, CFI = .993, but had little effect on the implicit-explicit correlation, r = .91. In this model, there was some evidence of shared method variance between the AMP and EPT, r = .13.

Next, I put these two well-fitting models together, leaving each model unchanged. The only new question is how measures of racial bias should be related to measures of political orientation. It is common to allow trait factors to correlate freely. This is also what Vianello and Bar-Anan did and I followed this common practices. Thus, there is no theoretical structure imposed on the trait correlations. I did not specify any additional relations for the method factors. If such relationships exist, this should lead to low fit. Model fit seemed to be good, RMSEA = .009, CFI = .982. The biggest MI was observed for the loading of the Modern Racism Scale (MRS) on the explicit political orientation factor, MI = 197.69. This is consistent with the item content of the MRS that combines racism with conservative politics (e.g., being against affirmative action). For that reason, I included the MRS in my measurement model of political orientation (Schimmack, 2020).

Vianello and Bar-Anan (2020) criticize my use of the MRS. “*For instance, Schimmack chose to omit one of the indirect measures—the SPF—from the models, to include the Modern Racism Scale (McConahay, 1983) as an indicator of political evaluation, and to omit the thermometer scales from two of his models. We assume that Schimmack had good practical or theoretical reasons for his modelling decisions; unfortunately, however, he did not include those reasons*.” If they had inspected the MI, they would have seen that my decision to use the MRS as a different method to measure political orientation was justified by the data as well as by the item-content of the scale.

After allowing for this theoretically expected relationship, model fit improves, chi2(df = 231) = 506.93, RMSEA = .007, CFI = .990. Next I examined whether the IAT method factor for racial bias is related to the IAT method factor for political orientation. Adding this relationship did not improve fit, chi2(230) = 506.65 = RMSEA = .007, CFI = .990. More important, the correlation was not significant, *r* = -.06. This is a problem for Vianello and Bar-Anan’s model that assumes the two method factors are identical. To test this hypothesis, I fitted a model with a single IAT method factor. This model had worse fit, chi2(231) = 526.99, RMSEA = .007, CFI = .989. Thus, there is no evidence for a general IAT method factor.

I next explored the possibility of a method factor for the explicit measures. I had identified shared method variance for the feeling thermometer and preference ratings for racial bias and for political orientation. I now modeled this shared method variance with method factors and let the two method factors correlate with each other. The addition of a correlation did not improve model fit, chi2(230) = 506.93, RMSEA = .007, CFI = .990 and the correlation between the two explicit method factors was not significant, r = .00. Imposing a single method factor for both attitude domains reduced model fit, chi2(df = 229) = 568.27, RMSEA = .008, CFI = .987.

I also tried to fit a single method factor for the AMP and EPT. The model only converged by constraining two loadings. Then model fit improved slightly, chi2(df = 230) = 501.75, RMSEA = .007, CFI = .990. The problem for Vianello and Bar-Anan is that the better fit was achieved with a negative loading on the method factor. This is inconsistent with the idea that a general method factor inflates correlations across attitude domains.

In sum, there is no evidence that method factors are consistent across the two attitude domains. Therefore I retained the basic model that specified method variance within attitude domains. I then added the three criterion variables to the model. As in Vianello and Bar-Anan’s model, contact was regressed on the explicit and implicit racial bias factor and previous voting and intention to vote were regressed on the explicit and implicit political orientation factors. The residuals were allowed to correlate freely, as in Vianello and Bar-Anan’s model.

Overall model fit decreased slightly for CFI, chi2(df = 297) = 668.61, RMSEA = .007, CFI = .988. MI suggested an additional relationship between the explicit political orientation factor and racial contact. Modifying the model accordingly improved fit slightly, chi2(df = 296) = 660.59, RMSEA = .007, CFI = .988. There were no additional MI involving the two voting measures.

Results were different from Vianello and Bar-Anan’s results. They reported that the implicit factors had incremental predictive validity for all three criterion measures.

In contrast, the model I am developing here shows no incremental predictive validity for the implicit factors.

It is important to note that I create the measurement model before I examined predictive validity. After the measurement model was created, criterion variables were added and the data determined the pattern of results. It is unclear how Vianello and Bar-Anan developed a measurement model with non-existing method factors that produced the desired outcome of significant incremental validity.

To try to reproduce their full result, I also added self-esteem measures to the model. To do so, I first created a measurement model for the self-esteem measures. The basic measurement model had poor fit, chi2(df = 58) = 434.49, RMSEA = .019, CFI = .885. Once more, the MI suggested that feeling-thermometer and preference ratings shared method variance. Allowing for this residual correlation increased model fit, chi2(df = 57) = 165.77, RMSEA = .010, CFI = .967. Another MI suggested a loading of the speeded task on the implicit factor, MI = 54.59. Allowing for this loading further improved model fit, chi2(df = 56) = 110.01, RMSEA = .007, CFI = .983. The crucial correlation between the explicit and implicit factor was r = .36. The correlation in Vianello and Bar-Anan’s model was r = .30.

I then added the self-esteem model to the model with the other two attitude domains, chi2(df = 695) = 1309.59, RMSEA = .006, CFI = .982. Next I added correlations of the IAT method factor for self-esteem with the two other IAT-method factors. This improved model fit, chi2(df = 693) = 1274.59, RMSEA = .006, CFI = .983. The reason was a significant correlation between the IAT method factors for self-esteem and racial bias. I offered an explanation for this finding in my article. Most White respondents associate self with good and White with good. If some respondents are better able to control their automatic tendencies, they will show less pro-self and pro-White biases. In contrast, Vianello and Bar-Anan have no theoretical explanation for a shared method factor across attitude domains. There was no significant correlation between IAT method factors for self-esteem and political orientation. The reason is that political orientation has more balanced automatic tendencies so that method variance does not favor one direction over the other.

This model had better fit with fewer parameters than Vianello and Bar-Anan’s model, chi2(df = 679) = 1719.39, RMSEA = .008, CFI = .970. The critical results of predictive validity remained unchanged.

I also fitted Vianello and Bar-Anan’s model and added four parameters that I identified as missing from their model: (a) the loading of the MRS on the explicit political orientation factor and (b) the correlations between feeling-thermometer and preference ratings for each domain. Making these adjustments improved model fit considerably, chi2(df = 675) = 1235.59, RMSEA = .006, CFI = .984. This modest adjustment altered the pattern of results for the prediction of the three criterion variables. Unlike Vianello and Bar-Anan’s model, the implicit factors no longer predicted any of the three criterion variables.

### Conclusion

My interaction with Vianello and Bar-Anan are symptomatic of social psychologists misapplication of the scientific method. Rather than using data to test theories, data are being abused to confirm pre-existing beliefs. This confirmation bias goes against philosophies of science that have demonstrated the need to subject theories to strong tests and to allow data to falsify theories. Verificationism is so ingrained in social psychology that Vianello and Bar-Anan ended up with a model that showed significant incremental predictive validity for all three criterion measures in their model, when this model made several questionable assumptions. They may object that I am biased in the opposite direction, but I presented clear justifications for modeling decisions and my model fits better than their model. In my 2020 article, I showed that Bar-Anan also co-authored another article that exaggerated evidence of predictive validity that disappeared when I reanalyzed the data (Greenwald, Smith, Sriram, Bar-Anan, & Nosek, 2009). Ten years later, social psychologists claim that they have improved their research methods, but Vianello and Bar-Anan’s commentary in 2020 shows that social psychologists have a long way to go. If social psychologists want to (re)gain trust, they need to be willing to discard cherished theories that are not supported by data.

### References

Bar-Anan, Y., & Vianello, M. (2018). A multi-method multi-trait test of the dual-attitude perspective. *Journal of Experimental Psychology: General, 147*(8), 1264–1272. https://doi.org/10.1037/xge0000383

Ehrlinger, J., Johnson, K., Banner, M., Dunning, D., & Kruger, J. (2008). Why the unskilled are unaware: Further explorations of (absent) self-insight among the incompetent. *Organizational Behavior and Human Decision Processes, 105*(1), 98–121. https://doi.org/10.1016/j.obhdp.2007.05.002

Greenwald, A. G., Smith, C. T., Sriram, N., Bar-Anan, Y., & Nosek, B. A. (2009). Implicit race attitudes predicted vote in the 2008 U.S. Presidential election. *Analyses of Social Issues and Public Policy (ASAP), 9*(1), 241–253. https://doi.org/10.1111/j.1530-2415.2009.01195.x

Schimmack U. The Implicit Association Test: A Method in Search of a Construct. *Perspectives on Psychological Science*. October 2019. doi:10.1177/1745691619863798

Vianello M, Bar-Anan Y. Can the Implicit Association Test Measure Automatic Judgment? The Validation Continues. *Perspectives on Psychological Science*. February 2020. doi:10.1177/1745691619897960

Zhang, X. & Savalei, V. (2020) Examining the effect of missing data on RMSEA and CFI under normal theory full-information maximum likelihood, Structural Equation Modeling: A Multidisciplinary Journal, 27:2, 219-239, DOI: 10.1080/10705511.2019.1642111