MIMIC DIF Testing When the Latent Variable Variance Differs Between Groups

Multiple indicators multiple causes (MIMIC) models (Joreskog & Golberger 1975) can be employed in a psychometric context to test for differential item functioning (DIF) between groups on the measurement of a latent variable (Muthén 1989). MIMIC DIF models can be attributed some favorable properties when compared to alternative DIF testing methods (i.e., Item Response Theory-Likelihood Ratio DIF) such as having generally small sample size requirements while simultaneously maintaining reliably low Type 1 error rates and sufficient DIF detection power (Woods 2009). The mechanism by which MIMIC models test for DIF is to regress a latent variable and its non-anchor indicators onto an exogenous (grouping) variable. This allows the model to account for differences in the mean of the latent variable across groups, while also testing for uniform DIF in individual items. However, the model does not allow heterogeneity in the covariance structure of the latent variables themselves—it is assumed to be equal across groups. A simulation study was conducted to examine the consequences of violating this assumption for the MIMIC DIF model. In this simulation, the following characteristics were varied: sample size, DIF effect magnitude, heterogeneity in latent variance between groups, magnitude of the group mean difference on the latent variable, and the ratio of focal group size to reference group size. Results suggest that violating the model's equality of latent covariance structure assumption leads to systematically biased parameter estimates on factor loadings and estimates of the latent group mean difference, inflated Type 1 error in DIF detection, and several other undesirable statistical side-effects.