A multifaceted sensitivity analysis of the Slovenian public opinion survey data

Abstract

Many models to analyse incomplete data have been developed that allow the missing data to be missing not at random. Awareness has grown that such models are based on unverifiable assumptions, in the sense that they rest on the (incomplete) data only in part, but that inferences nevertheless depend on what the model predicts about the unobserved data, given the observed data. This explains why, nowadays, considerable work is being devoted to assess how sensitive models for incomplete data are to the particular model chosen, a family of models chosen and the effect of (a group of) influential subjects. For each of these categories, several proposals have been formulated, studied theoretically and/or by simulations, and applied to sets of data. It is, however, uncommon to explore various sensitivity analysis avenues simultaneously. We apply a collection of such tools, some after extension, to incomplete counts arising from cross-classified binary data from the so-called Slovenian public opinion survey. Thus for the first time bringing together a variety of sensitivity analysis tools on the same set of data, we can sketch a comprehensive sensitivity analysis picture. We show that missingness at random estimates of the proportion voting in favour of independence are insensitive to the precise choice of missingness at random model and close to the actual plebiscite results, whereas the missingness not at random models that are furthest from the plebiscite results are vulnerable to the influence of outlying cases. Our approach helps to illustrate the value of comprehensive sensitivity analysis. Ideas are formulated on the methodology's use beyond the data analysis that we consider.