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 perform a comparative study of the different approaches to compute Bayes factors by applying them to two different data sets. The computations involved with finding Bayes factors pose many challenges-especially for large problems and we discuss how one can overcome them. A number of approaches are reviewed for approximating the Bayes factor comparing the models with and without the random effects in question. 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.

Then we talk briefly about the frequestist and Bayesian approaches to inference for these models.

We start with a description of generalized linear models with random effects. 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.

Bayes test models