Wald Test of Mean Equality for Potential Latent Class Predictors in Mixture Modeling

For mixture models, frequently there can be many potential class pre-dictors. In this note we describe a procedure that can be used to select the most important of these variables. Including a large number of class pre-dictors in the model during the estimation could potentially lead to very slow computation as well as unclear results due to collinearity in the predic-tors. We can instead estimate the mixture model without the covariates as a first step. Consequently for each potential class predictor variable X we can evaluate the conditional class specific means for that variable E(X|C) using the estimated model with a categorical latent class variable C. Typically, the stronger the predictor X, the bigger the differences between these con-ditional means across the different classes. We can evaluate the statistical significance of the class specific mean differences by conducting a Wald test for the following hypothesis: E(X|C = 1) = E(X|C = 2) =... = E(X|C = k), where k is the number of classes in the estimated model. Mplus will comput