Estimating Nonhierarchical and Nested Log-Linear Models

Abstract

The recent literature on-log-linear models incorrectly implies that the Iterative Proportional Fitting (IPF) algorithm and associated computer programs such as ECTA can only be used to estimate hierarchical (not nonhierarchical) log-linear models. While ECTA and similar programs are designed for the estimation of hierarchical models, it is shown here that the IPF algorithm (and existing computer programs such as ECTA) can be used to estimate any nonhierarchical model and also many nested log-linear models. The former result follows directly from the symmetry between qualitative/categorical indicator variables and appropriately defined “interaction variables.” The general approach for dichotomous variables is illustrated here using data from the study of “The American Soldier” by Stouffer et al. We also illustrate how the ECTA program can be used to estimate nested models, and show the equivalence between a particular class of nested models and the model of quasi-independence.