CONDITIONAL INDEPENDENCE AND LOG LINEAR MODELS FOR MULTI-DIMENSIONAL CONTINGENCY TABLES.

The article comments on conditional independence and log linear models for multi-dimensional contingency tables. Frequency data in the form described by a contingency table occur in many different fields of research, as indicated by the abundant literature available. The approach to their analysis varies from the relatively ad hoc application of the Chi-square tests for various relationships of independence to the specification of a model for which parameter estimates of effects, as well as tests, may be used. A number of features may be listed for the log linear model which make it convenient, at least if no theoretically more acceptable model is available. The log linear model is the simplest form of model which automatically fills the boundary conditions that all predicted proportions for all cells of the table lie in the interval. It is the only model for which the parameters can be estimated in a situation of inverse sampling, i.e., when random samples are taken from each sub-population corresponding to a value of the dependent variable. In addition, since it is directly analogous to the linear models of normal theory, the statistical theory of inference-making is relatively simple, primarily because sufficient statistics exist for all the parameters.