Bayesian Computation via the Gibbs Sampler for Mixture Models with Gaussian Distal Outcomes

ABSTRACT

Models with distal outcomes have been commonly used to evaluate the effect of categorical latent variables on an observed dependent variable, which can be binary, counting, or continuous. Several approaches have been recently proposed for modeling continuous distal outcomes. Some recent strategies consider simultaneous modeling of the latent class and its effect on the distal response through the use of the Bayes theorem applied to latent class analysis (LCA) with covariates or through the incorporation of the measurement errors from LCA directly in the estimation procedure for the parameters of the structural submodel. Classify-analyze approaches have also been used for this purpose for several years, but simulation studies had shown the attenuation of their estimates. More recently, Bayesian LCA and other Bayesian approaches for latent variable modeling were proposed and made available in statistical software. We propose four alternative strategies using Bayesian estimation for the structural parameters in the mixture models with distal outcomes. We also consider extensions to allow control for observed covariates in the structural submodel for the distal outcome. Monte Carlo simulation studies were conducted to evaluate the properties of the proposed methods in finite samples. Illustration of these methodologies is carried out with the analysis of the data from the 2006 ENADE (National Student Performance Exam) in Brazil. The simulation results show that the Bayesian Simultaneous method leads to a substantial bias reduction when estimating the effects of the latent variable on the distal outcome.

KEYWORDS:

• Latent class analysis
• distal outcomes
• latent variable modeling
• Bayesian inference

Additional information

Funding

G.S.B was partially supported by a FAPESB (Fundação de Amparo a Pesquisa do Estado da Bahia)/Brazil scholarship (BOL0495/2018). L.D.A was partially supported by a FAPESB grant (RED005/2014) and by a FIOTEC grant (IGM-009-FEX-17).