Log-Linear Models for Survey Data with Non-Ignorable Non-Response

SUMMARY We demonstrate the feasibility of constructing, interpreting and fitting computable log-linear models to categorical survey data with arbitrary non-nested patterns of non-ignorable non-response. Under our approach, the non-response probability for each cell of the classification defined by the categories of interest is modelled separately from the classification probability itself, and we adopt a model formulation which allows the non-response model to depend on scores, discrete covariates, continuous covariates or a mixture of types of covariate. We obtain explicit expressions for the score and information functions generated by the observed data which allow us to compute approximate standard errors and test statistics based on these functions. Through illustrative examples we quantify the fact that inferences obtained from different non-ignorable non-response models can vary considerably. This lends support to the calls in the literature for caution in using such models.