Goodness of fit tests for random effect models with binary responses estimated viah-likelihood

Abstract

The objective of this study is to introduce goodness of fit statistics for thesystematic part of random effect models. These statistics are formed as scoretests and are based on partitioning the observations into mutually exclusivegroups. Weighted versions of these statistics are also introduced which arebased on the correlation between an appropriately adjusted candidate covariatefor entrance into the model and the model residuals. In addition tothis, weighted cumulative and moving sum processes are also provided witha goal to detect, in a more effecient way, various departures from the nullmodel, as compared to the usual cumulative and moving sums. The estimatingprocedure that is used throughout this study is the h-likelihood, sothe quantities needed for the above mentioned statistics are derived basedon this estimating approach. The simulations were designed so as to examinethe performance of the tests under different factors, such as sample size,magnitude of random effects’ variance, type of the model misspecification,etc. The results indicate the superior performance of the weighted tests ofany type (either those based on partitioning or those based on cumulativesums), there are cases, however, were some unweighted tests displayed a similarpower as their weighted analogous. The proposed tests are illustratedwith the use of two real datasets.