Modeling Measurement Error When Using Cognitive Test Scores in Social Science Research

In many areas of social science, researchers want to use latent measures of ability as independent variables. Often cognitive test scores are used to measure this latent trait. Many social scientists do not model the measurement error inherent in the test score. I introduce the Mixed Effects Structural Equations (MESE) model to model the measurement error when a cognitive test score is used as a measure of ability as an independent variable. Unlike the typical linear regression model, which ignores the error and produces biased regression coefficients, the MESE model assumes measurement error. . Unlike the typical errors-in-variables (EIV; Anderson, 1984) model which uses classic test theory (CTT) to model homoskadastic measurement error by ability, the MESE model uses item response theory to model heteroskadastic measurement error by ability. The IRT model handles the well-known identifiability issues of the EIV model. While the Plausible Value Methodology which is a marginal estimation procedure (Mislevy, 1991) produces consistent regression coefficients, a primary analyst is required to produce a set of “plausible values” for use by the secondary analyst. Inconsistent estimates can occur using plausible values if data used in the regression equation is collected after the plausible values are produced. The MESE model can be used with any test or assessment and any data set. A number of simulation studies explore the sensitivity of the MESE model assumptions, noting in particular that the prior on ability must be conditioned on the covariates in the regression equation in order to avoid bias in the estimate of the regression coefficients. The MESE model is also used to examine the issue of black-white wage gaps. I show that estimates using the MESE model differ markedly from estimates when an elementary linear regression is used. I find that most, though not all, of the black-white wage gap is plausibly attributed to the black-white skills gap. I also explore the hypothesis that education and ability must be included in the model and find some evidence to support this claim. I find no evidence to support the hypothesis that the return to skills is unequal across race.