Abstract

This study investigated estimation bias arising from the omission of direct effects between external variables and indicators in latent class analysis (LCA) and latent profile analysis (LPA). Two studies were conducted, each addressing a different type of external variable and mixture model. Specifically, Study 1 examined situations in which covariates directly affected indicators in LCA, whereas Study 2 examined situations in which indicators directly affected an outcome variable in LPA. In both studies, parameters were estimated using two-step and three-step approaches, and the results were compared across models with and without direct effects. In Study 1, the two-step approach yielded lower overall bias when covariate direct effects were included in the model than when they were omitted. Bias increased with the magnitude of the covariate direct effects and the number of omitted direct effects. Similarly, in Study 2, models that included direct effects of indicators on the outcome variable exhibited substantially lower mean relative bias and Type I error rates than models that omitted these effects. These findings suggest that explicitly modeling direct effects between external variables and indicators can improve the accuracy of parameter estimation.