Generalized linear models with random effects are becoming increasingly popular in situations where one needs to relate a non-normal response variable to a set of predictors and the responses are correlated. We start with a description of generalized linear models with random effects. Then we talk briefly about the frequestist and Bayesian approaches to inference for these models. In many applications, the magnitude of the variance components corresponding to one or more of the random effects are of interest, especially the point null hypothesis that one or more of the variance components is zero. A number of approaches are reviewed for approximating the Bayes factor comparing the models with and without the random effects in question. The computations involved with finding Bayes factors pose many challenges---especially for large problems and we discuss how one can overcome them.;We perform a comparative study of the different approaches to compute Bayes factors by applying them to two different data sets.;A common criticism of Bayes factors is that they are sensitive to the prior distributions used for the parameters of the models being compared. We develop an approach to study the sensitivity of the Bayes factor (comparing the models with and without the random effects in question) to the prior distributions used for the variance components and apply that to the two data sets to find out that the Bayes factor in question is indeed sensitive to the prior distributions used for the variance components.
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