Variable selection remains a difficult problem, especially for generalized linear mixed models (GLMMs). While some frequentist approaches to simultaneously select joint fixed and random effects exist, primarily through the use of penalization, existing approaches for Bayesian GLMMs exist only for special cases, like that of logistic regression. In this work, we apply the Stochastic Search Variable Selection (SSVS) approach for the joint selection of fixed and random effects proposed in Yang et al. (2020) for linear mixed models to Bayesian GLMMs. We show that while computational issues remain, SSVS serves as a feasible and effective approach to jointly select fixed and random effects. We demonstrate the effectiveness of the proposed methodology to both simulated and real data. Furthermore, we study the role hyperparameters play in the model selection.

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