Identifiability and parameter redundancy in sparse contingency tables

Serveh Sharifi Far (University of St Andrews, UK)

Log-linear models are a powerful statistical tool to analyse data with categorical observations arranged in a contingency table. When sampling zeros occur in a contingency table, identifiability problems may arise which lead to parameter redundancy. Maximum likelihood estimates of some model parameters will not exist, while numerical methods in software usually report estimates for them. The main aim of this work is to develop a general methodology to identify which model parameters or linear combinations of parameters are estimable in the presence of one or more sampling zeroes in the table. The method is described for saturated log-linear models in l^m contingency tables, although the procedure is applicable to more general settings and to unsaturated models. The approach is compared with previous works, which are based on a polyhedral description and focus on estimability of cell means not natural parameters.