Sensitivity analysis for incomplete contingency tables: the Slovenian plebiscite case

Classical inferential procedures induce conclusions from a set of data to a population of interest, accounting for the imprecision resulting from the stochastic component of the model. Less attention is devoted to the uncerta inty arising from (unplanned) incompleteness in the data. Through the choic e of an identifiable model for non-ignorable non-response, one narrows the possible data-generating mechanisms to the point where inference only suffe rs from imprecision. Some proposals have been made for assessing the sensit ivity to these modelling assumptions; many are based on fitting several pla usible but competing models. For example, we could assume that the missing data are missing at random in one model, and then fit an additional model w here non-random missingness is assumed. On the basis of data from a Sloveni an plebiscite, conducted in 1991, to prepare for independence, it is shown that such an ad hoc procedure may be misleading. We propose an approach whi ch identifies and incorporates both sources of uncertainty in inference: im precision due to finite sampling and ignorance due to incompleteness. A sim ple sensitivity analysis considers a finite set of plausible models. We tak e this idea one step further by considering more degrees of freedom than th e data support. This produces sets of estimates (regions of ignorance) and sets of confidence regions (combined into regions of uncertainty).