Correlated binary responses are very common in longitudinal and repeated measures studies. Random effects models are often used to analyze such data and the h-likelihood estimating procedure provides an inferential tool. The objective of this study is to introduce goodness-of-fit score statistics for the fixed part of these models. The proposed statistics are based on processes that partition the observations into mutually exclusive groups. Weighted versions of these statistics are also introduced and are based on the correlation between an appropriately adjusted candidate covariate for entrance into the model and the model residuals. A simulation study indicates that the weighted statistics perform better than their unweighted counterparts, whereas the statistics that are based on the partitioning of the covariate space seem to perform slightly better compared with those based on other grouping procedures. The use of the proposed statistics is illustrated using a real data example.