Several approaches have been proposed for latent class modeling with external variables, including one-step, two-step, and three-step estimators. However, very little is known yet about the performance of these approaches when direct effects of the external variable to the indicators of latent class membership are present. In the current article, we compare those approaches and investigate the consequences of not modeling these direct effects when present, as well as the power of residual and fit statistics to identify such effects. The results of the simulations show that not modeling direct effect can lead to severe parameter bias, especially with a weak measurement model. Both residual and fit statistics can be used to identify such effects, as long as the number and strength of these effects is low and the measurement model is sufficiently strong.
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