Bayesian Nonlinear Latent variable Models with Mixed Non-normal Variables and Covariates for Multi-sample Psychological Data

Thanoon Y Thanoon,Robiah Adnan,Athar Talal Hamed

doi:10.18187/pjsor.v15i3.2689

Abstract

The purpose of this paper is to develop a latent variable model with nonlinear covariates and latent variables. Mixed ordered categorical and dichotomous variables and covariates with two different types of thresholds (with equal and unequal spaces) are used in Bayesian multi-sample nonlinear latent variable models and the Gibbs sampling method is applied for estimation and model comparison. Hidden continuous normal distribution (censored normal distribution) and (truncated normal distribution with known parameters) are used to handle the problem of mixed ordered categorical and dichotomous data. Hidden continuous normal distribution (truncated normal distribution with known parameters) is used to handle the problem of mixed ordered categorical and dichotomous data in covariates. Statistical analysis, which involves the estimation of parameters, standard deviations and their highest posterior density, are discussed. The proposed procedure is illustrated using psychological data with the results obtained from the OpenBUGS program.

Highlights

Latent variable models (LVMs) (Lee, 2007) are a statistical technique for modelling a sequence of correlated data to estimate the interrelationships among manifest and latent variables
The main objective of this paper is to propose a Bayesian approach for analysing multisample nonlinear LVMs with mixed variables and covariates
The objective of this section is to present results of a simulation study to reveal the empirical performance of the Bayesian estimates and the Deviance Information Criterion (DIC) for model comparison

Summary

Introduction

Latent variable models (LVMs) (Lee, 2007) are a statistical technique for modelling a sequence of correlated data to estimate the interrelationships among manifest and latent variables. Many researchers have proposed models that contain nonlinear terms among the manifest and latent variables. Lee and Song (2002) offer a specific method for applying the Bayesian approach in factor analysis They created an analysis model that implements joint Bayesian estimates for the factor scores and structural parameters as they are related to the determined constraints allowing multiple findings to be determined simultaneously.

Objectives

Results

Conclusion