Pairwise residuals and diagnostic tests for misspecified dependence structures in models for binary longitudinal data

Maximum likelihood estimation of models for binary longitudinal data is typically inconsistent if the dependence structure is misspecified. Unfortunately, diagnostics specifically designed for detecting such misspecifications are scant. We develop residuals and diagnostic tests based on comparing observed and expected frequencies of response patterns over time in the presence of arbitrary time-varying and time-invariant covariates. To overcome the sparseness problem, we use lower-order marginal tables, such as two-way tables for pairs of time-points, aggregated over covariate patterns. Our proposed pairwise concordance residuals are valuable for exploratory diagnostics and for constructing both generic tests for misspecified dependence structure as well as targeted adjacent pair concordance tests for excess serial dependence. The proposed methods are straightforward to implement and work well for general situations, regardless of the number of time-points and the number and types of covariates.