Comparison of the Unit-Lindley and Beta Mixed Model: A Bayesian Perspective

Abstract

Mixed-effects models are among the most extensively utilized methodologies for evaluating the relationship between correlated outcomes and covariates. The choice of model is contingent upon the nature of the outcome variable. In practical applications, it is frequently encountered that data are both correlated and constrained within the interval (0, 1). The beta mixed model is typically employed to analyze such bounded and correlated data scenarios. However, recent advancements in the unit Lindley (UL) mixed model have highlighted its advantages over the beta mixed model within a classical framework. This study introduces the UL mixed model and compares it to the beta mixed model utilizing a Bayesian approach. The STAN program was employed to conduct the Bayesian analysis and parameter estimation using Hamiltonian Monte Carlo (HMC) under the No-U-Turn Sampler (NUTS). The validity of both models was assessed through Monte Carlo Simulation. Furthermore, both models were applied to real data scenarios. Model comparison was performed using the Leave-One-Out Information Criterion (LOOIC) and the Watanabe-Akaike Information Criterion (WAIC). The results consistently indicated that the beta mixed model is superior to the UL mixed effect model in the Bayesian framework.