Ignorance and Uncertainty in Incomplete Categorical Data

• Activity Number: 87
• Type: Invited
• Date/Time: Monday, August 12, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section*
• Author(s): Geert Molenberghs*+
• Affiliation(s): Center for Statistics, Belgium

Abstract

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 uncertainty arising from (unplanned) incompleteness in the data. Through the choice of an identifiable model for non-ignorable non-response, one narrows the possible data generating mechanisms to the point where inference only suffers from imprecision. Some proposals have been made for assessment of sensitivity to these modeling assumptions; many are based on fitting several plausible but competing models. For example, one could assume that the missing data are missing at random in one model, and then fit an additional model where non-random missingness is assumed. Based on data from a Slovenian plebiscite, conducted in 1991, to prepare for independence, it is shown that such an ad hoc procedure may be misleading. We propose an approach which identifies and incorporates both sources of uncertainty in inference: imprecision due to finite sampling and ignorance due to incompleteness. A simple sensitivity analysis considers a finite set of plausible models.