Fitting a multilevel linear model to a sample of contingency tables using generalized least squares

In this work we propose a new approach for estimating multilevel models in contingency tables. This approach is based mainly on the use of the linear model as fundamental base to elaborate inference methods and the application of algorithms of iterative generalized least squares for the estimation of the fixed and random parameters. As illustration it is considered a logistic regression model in two levels and the proposed procedure is applied to a real problem from the literature. Finally, we carried out a brief simulation study to examine the behaviour of the estimates.