Abstract
For a generalized linear model with random effects, Zeger and Karim used the Gibbs sampler to estimate the model parameters. However their methods of estimation have some drawbacks; especially in estimating the random effect components which, as stated in their paper, have 20 to 30 percent bias in the posterior mean of the random effect variances. Here we use the adaptive rejection sampling method proposed by Gilks and Wild. The adaptive rejection sampling (ARS) algorithm is an efficient and direct method to sample from complicated log-concave densities often encountered in Gibbs sampling. Good results are obtained from simulations. We applied this model to analyze data obtained from experiments on the quality of telephone connection. For diagnostic checking of our models, we used the concept of latent residuals introduced by Albert and Chib.
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