Review on the boundary solutions in the analysis of an incomplete contingency table

Abstract: In the analysis of an incomplete contingency table, nonresponse models incorporating the missing mechanism are used to estimate nonresponses. There are three missing mechanisms, missing at random (MAR), not missing at random (NMAR) and missing completely at random (MCAR). The estimation results differ depending on the embedded missing mechanism in the nonresponse model. When the NMAR mechanism is assumed, it has been known that the nonresponse model has boundary solution problems. Boundary solutions are defined as the cell probabilities of certain columns are estimated to be zero, leading to distort estimation results. In this paper, boundary solution problems are reviewed with the reason, the identification of occurrence, and the method to overcome. The introduction of the analysis of an incomplete contingency table is also provided with the real data analysis.

Keywords: incomplete contingency table, boundary solutions, ML estimation, Bayesian method, NMAR model.