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Friday
Dec142012

A multivariate regression analysis of CRT performance & ideology, plus a preliminary diatribe against mindlessly overspecified regression models

My most recent paper, Ideology, Motivated Reasoning, and Cognitive Reflection, reports data on the relationship between ideology and the disposition to use high-level, "System 1" information processing, as opposed to intuitive, low-effort, heuristic-drive "System 2," as measured by the Cognitive Reflection Test (CRT).  

I report that there really isn't any. That's sort of surprising in light of all the attention being paid to the neo-Authoritarian Personality literature, which asserts that conservativism is characterized by closed-mindedness, aversion to complexity, and the like.

I know reviewers will want to know, "but if one controls for ..." so I've prepared a multivariate regression that includes ideology along with various other individual characteristics (gender, race, education, income, and religiosity) that have been shown to correlate with CRT scores.  Still nothing!

See for yourself by clicking on the thumbnail to the left.

But in fact, I view this analysis as pretty close to worthless -- if one is really trying to figure out if there is an association between ideology and cognitive reflection.  The idea of  "controlling for" these sorts of characteristics in order to measure the "independent" impact of "ideology" is nonsense: it treats "ideology" as some sort of disembodied "essence" inside of people, when in fact it is one facet of an integrated package of attributes that cohere with one another and are all indicators of a latent type of shared identity or style.

I've been planning for a while to go ballistic on the idea of "overspecified" regressions -- and what sort of mistake in thinking (or failing to think, really) they reflect. This isn't really the right vehicle for getting the point across, so I anticipate coming back to this topic at some point.

But as a preview, here is a short text that I prepared to go with this genuinely fantastic multivariate regression analysis of ideology & CRT.  I'm sure the note will be revised -- or dropped altogether -- before I submit the paper for publication:

Finally, a multivariate regression model that included all of these predictors was tested. That analysis can be seen as assessing the effect of ideology on CRT scores “controlling for” gender, race, education, income, and religiosity. It is doubtful, however, that such a “model” bears any meaningful relationship to reality. In the world we live in, people come in packages of demographic and political orientations, which correlate in ways suggestive of various latent forms of identity. Thus, “partialing” out the covariance of gender, race, religion, education, and income in order to estimate the “independent” effect of ideology creates a model of something (either individual characteristics disconnected from people, or people who can be randomly endowed with combinations of characteristics) not actually observed on planet earth (Berry & Feldman 1985, p. 48; Cohen, Cohen, West &  Aiken 2003, p. 419; Gelman & Hill 2006, p. 187). Absent some appropriate aggregation of all these variables into a valid latent-variable measure, a zero-order correlation furnishes a more valid estimate of the influence of subjects' political outlooks on their CRT scores than does the coefficient for that predictor in a model that treats ideology and all of these other characteristics as independent, right-hand side variables in a multivariate regression (Lieberson 1985, pp. 14-43). But for the benefit of those who prefer to regard multivariate regression as a magical black box for capturing the “causal” effect of phantom essences, as opposed to a statistical tool for measuring the relationship of valid measures of real-world phenomena, this blunderbuss analysis shows the the coefficient for Conserv_Repub remained trivially different from zero and nonsignificant (b = 0.06,  p = 0.33). When party self-identification was substituted for Conserv_Repub, that variable continued to predict an increase in CRT score as subjects’ identification with the Republican party intensified, but the effect was reduced and was only marginally significant (b = 0.10, p = 0.06).

References

Berry, W.D. & Feldman, S. Multiple regression in practice. (Sage Publications, Beverly Hills; 1985).

Cohen, J., Cohen, P., West, S.G. & Aiken, L.S. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences, Edn. 3rd. (L. Erlbaum Associates, Mahwah, N.J.; 2003).

Gelman, A. & Hill, J. Data Analysis Using Regression and Multilevel/Hierarchical Models. (Cambridge University Press, Cambridge ; New York; 2007).

Lieberson, S. Making it count : the improvement of social research and theory. (University of California Press, Berkeley; 1985).

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