Longitudinal ordinal responses are commonly analyzed in biomedical studies and are often fitted by the generalized estimating equations (GEE) approach. The assessment of model fit is an important issue for model inference. The purpose of this article is to develop goodness-of-fit tests for GEE models with longitudinal ordinal data based on residual analysis using the global odds ratio as a measure of association. Our method can be regarded as an alternative approach of Lin's tests (Computational Statistics and Data Analysis 2010; 54:1872-1880) by considering a variety of working correlation structures. Two tests related to Pearson chi-squared and unweighted sum of residual square are proposed and two propositions of the approximate expectation and variance of the proposed test statistics are derived.
