Estimable Functions in Log-Linear Models

Abstract

Since Goodman's introduction of log-linear models to social scientists in 1972, the technique has become a basic tool. Applications have been limited, however, by a serious misunderstanding of the interpretation of parameters in log-linear models. The problem arises from attempts to interpret the parameters as though they are similar to regression coefficients, rather than as similar to ANOVA coefficients. More technically, the problem arises from a failure to understand the concept of estimability and its application to log-linear analysis. This article defines the concept of estimability for log-linear models, indicates the implications of this concept for the interpretation of parameters in log-linear models, and provides rules for determining the estimability of linear functions of parameters.