Design-based inference in a mixture model for ordinal variables for a stage stratifies design

In this paper we present methods for inference on data selected by a complex sampling design for a class of statistical models for the analysis of ordinal variables. Specifically, assuming that the sampling scheme is not ignorable, we derive for the class of cub models (Combination of discrete Uniform and shifted Binomial distributions) variance estimates for a complex two stage stratified sample. Both Taylor linearization and repeated replication variance estimators are presented.We also provide design-based test diagnostics and goodness-of-fit measures. We illustrate by means of real data analysis the differences between survey-weighted and unweighted point estimates and inferences for cub model parameters