Simultaneous Fixed and Random Effects Selection in Order-restricted Mixed Effects Models

When dealing with longitudinal data, if we directly select a specific model for modeling without any prior information about the existence of significant random effects before utilizing the mixed model, it may result in the misuse of the model, thereby affecting the final estimation results. This paper investigates a variable selection method that can jointly select both fixed and random effects in Bayesian mixed model under order constraints. This method can effectively prevent model misuse. A computationally feasible Gibbs algorithm is proposed for posterior inference. The performance of our proposal is evaluated by simulated data and two real applications related to Blood lead levels and Ramus bone heights. Results show that the proposed approaches perform very well in various situations.