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. This paper introduces 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.
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