Inference in Models with Distal Outcomes: A Bayesian Perspective
Latent Class Analysis, Distal Outcomes, Latent Variable Modeling, Bayesian Inference
Models with distal responses aim to evaluate the effect of categorical latent variables on an observed dependent variable that can be binary, counting or continuous. Frequentist approaches have recently been proposed to estimate latent effects on distal responses. These strategies consider simultaneous modeling of the latent class and its effect on the distal response by using Bayes rule from latent class analysis (LCA) with covariates, or by incorporating the measurement errors obtained in the LCA directly for modeling the distal response. Some of the most common procedures for classifying individuals attenuate parameter estimates. Bayesian statistical methods incorporate uncertainty in inferences by associating a priori probability distribution to the parameters, which are updated during the procedure, resulting in a posteriori distribution. In this work alternative strategies for estimating latent effects in distal responses are proposed using Bayesian inference. In addition, the proposed methodologies advance in the estimation of latent variable effects allowing the adjustment for additional observed covariates via regression models. Monte Carlo simulation studies were conducted to evaluate properties of the proposed methods in finite samples. Illustration of these methodologies is performed with analysis of the 2016 National Student Performance Examination (ENADE) data. Simulation results show that the Simultaneous Bayesian (BS) method leads to a substantial reduction of the bias in estimating the effects of the latent classes on distal responses, besides allowing the inclusion of additional covariates in the model.