Workplace panel survey data analysis using Bayesian cumulative probit linear mixed model

Longitudinal data are measured repeatedly over time from the same subject.Therefore, the repeated outcomes have correlations, and it is necessary to estimate the covariate effect on the response variable while explaining the correlations.In longitudinal ordinal data analysis, the covariate effect is estimated using generalized linear mixed models using a logit link function or a probit link function.In this paper, we review the generalized linear mixed models and marginalized models with the two types of link functions for longitudinal ordinal data analysis.Specifically, a Bayesian cumulative probit linear mixed model with the probit link function is used to analyze Korean workplace panel survey (WPS) data, which is longitudinal ordinal data.In the model, the correlation matrix is high-dimensional and positive definite, and it is estimated using the hypersphere decomposition.In the WPS data, corporate training participation rate is considered as a response variable.Assuming different correlation structures, several models are compared.For the most suitable model, some explanatory variables, the annual effect, profit sharing schemes status, average annual training hours per person, and labor union status, have effects on corporate training participation rate.