Fitting log-linear models with ignorable and non-ignorable missing data

We describe Stata macros that implement the composite link approach to missing data in log-linear models first described by David Rindskopf (Psychometrika, 1992, V57, 29-42). When a missing value occurs among the variables that form a contingency table, the resulting observation contributes to the frequencies of a table of lower dimension than the full table being collapsed along the dimension of the missing variable. Our primary interest lies in constructing a model for the full dimensional table. The composite link approach maps the observed cells of this collapsed table to the corresponding unobserved cells of the full dimensional table. This mapping allows expected cells frequencies for observed cells to be obtained from the expected cell frequencies for the unobserved cells, the latter being derived from a near standard log-linear model. A preliminary macro reorganizes the data from a file of individual records with possibly missing variable values to a file where each record represents either an observed cell frequency or an unobserved cell that contributes to an observed cell. The records also contain the necessary design variables and interaction terms to allow the second macro, an adaptation of Stata's original glm procedure, to fit log-linear models that assume the missing values are MCAR, MAR or conform to some non-ignorable model. We illustrate the use of the macros. The primary contributors to this work were Colin Taylor and Alan Taylor (Institute of Psychiatry, London) and Daphne Kounali (now MRC Environmental Epidemiology).