Latent profile analysis with covariates using the three-step method: The impact of nonnormal indicators and direct effects

Latent profile analysis (LPA) is a popular statistical modeling technique designed to identify latent subgroups in the population based on a set of continuous indicator variables. It is closely related to latent class analysis (LCA), which is the name given to a mixture model using categorical indicators. In some cases, researchers using LPA may wish to include a covariate predicting latent subgroup membership. Naively including the covariate in the LCA model (known as the 1-step approach) is problematic because the presence of the covariate is likely to alter the makeup of the latent classes. In other words, class membership is then conditioned not only on the indicators but also the covariate itself. The optimal approach for including such covariates for LCA models is the 3-step estimator, which accounts for the random error associated with the latent class model based on the indicators. This model preserves the latent class structure associated only with the indicators while simultaneously including the covariate in the model. The goal of the current study is to extend this earlier work on LCA by examining the performance of the 3-step estimator with LPA. In addition, the study also investigated the impact of the indicator variables’ distribution on the performance of the 3-step estimator. Results show that for normally distributed indicators with equal latent subgroup variances, the 3-step estimator performs well at estimating the covariate relationship for as few as 6 indicators and 200 individuals. However, when the indicators were skewed and/or the subgroup variances differed, 12 indicators and samples in excess of 500 were necessary for the 3-step estimator to yield accurate covariate coefficient estimates.