Variable selection for the multivariate correlated response vector generalized linear model based on MCMC methods

The Multivariate Correlated Response Vector Generalized Linear Model is an important yet structurally complex class of generalized linear models. Commonly used variable selection methods, such as LASSO (Least Absolute Shrinkage and Selection Operator), are ineffective in efficiently identifying the crucial variables for this type of model. In this paper, we propose a novel variable selection method based on Markov chain Monte Carlo (MCMC) methods, specifically the Random Search method, to address this issue. This approach proves to be an effective variable selection method, as demonstrated by simulation analyses indicating its superior efficiency compared to LASSO and exhaustive subset search methods.