Analyzing Contingency Tables by Weighted Least Squares: An Alternative to the Goodman Approach

In recent years, social scientists have been introduced to a variety of new techniques for the analysis of qualita tive data. The approach described by Leo Goodman in a series of articles (1972a, 1972b, 1973) has been the one used most frequently. Goodman's technique involves the fitting of log-linear models to contingency tables by means of an iter ative proportional fitting algorithm (see Goodman, 1971)J From the expected frequencies this algorithm generates, one can obtain estimates of the parameters that represent the fitted model; these parameters are analogous to regression coefficients. This approach makes possible the analysis of multivariate relationships involving a set of nominal vari ables. However, there are several potential drawbacks to the Goodman approach. First the specific estimating algorithm used by Goodman imposes restrictions on the types of the models which can be fitted to the table being analyzed. Specifically, users of his technique are restricted to hier archical models. With hierarchical models, if interaction terms are included in the model, the main effects comprising the interactions must also be included. A further restric tion imposed by the estimating algorithm eliminates models involving nested or conditional effects (i.e., separate main effects of one variable within levels of another variable);