The Empirical Cressie-Read Test Statistics for Longitudinal Generalized Linear Models

For the marginal longitudinal generalized linear models (GLMs), we develop the empirical Cressie-Read (ECR) test statistic approach which has been proposed for the independent identically distributed (i.i.d.) case. The ECR test statistic includes empirical likelihood as a special case. By adopting this ECR test statistic approach and taking into account the within-subject correlation, the efficiency theory results of estimation and testing based on ECR are established under some regularity conditions. Although a working correlation matrix is assumed, there is no need to estimate the nuisance parameters in the working correlation matrix based on the quadratic inference function (QIF). Therefore, the proposed ECR test statistic is asymptotically a standard limit under the null hypothesis. It is shown that the proposed method is more efficient even when the working correlation matrix is misspecified. We also evaluate the finite sample performance of the proposed methods via simulation studies and a real data analysis.