A Penalized h-Likelihood Variable Selection Algorithm for Generalized Linear Regression Models with Random Effects

Reinforcement learning is one of the paradigms and methodologies of machine learning developed in the computational intelligence community. Reinforcement learning algorithms present a major challenge in complex dynamics recently. In the perspective of variable selection, we often come across situations where too many variables are included in the full model at the initial stage of modeling. Due to a high-dimensional and intractable integral of longitudinal data, likelihood inference is computationally challenging. It can be computationally difficult such as very slow convergence or even nonconvergence, for the computationally intensive methods. Recently, hierarchical likelihood (h-likelihood) plays an important role in inferences for models having unobservable or unobserved random variables. This paper focuses linear models with random effects in the mean structure and proposes a penalized h-likelihood algorithm which incorporates variable selection procedures in the setting of mean modeling via h-likelihood. The penalized h-likelihood method avoids the messy integration for the random effects and is computationally efficient. Furthermore, it demonstrates good performance in relevant-variable selection. Throughout theoretical analysis and simulations, it is confirmed that the penalized h-likelihood algorithm produces good fixed effect estimation results and can identify zero regression coefficients in modeling the mean structure.