UC Riverside

We propose a class of multiplicative models to describe the dependence of the response count on the effects of the explanatory variables and their interactions in a contingency table. The proposed models are motivated by loglinear models for contingency tables. Under these models, every cell count and/ or probability is the product of effects of the categorical variables used as explanatory variables. Such models are useful in analyzing complete as well as incomplete tables. We present a connection between these models and graphical probability models in describing conditional independence structures among the explanatory variables.

We extend the standard unsaturated log-linear models to a complete model retaining the conditional independence structure. We characterize the extension of the unsaturated model to the standard saturated model. We also compare the estimates of the unknown parameters in these two saturated representations. Necessary and sufficient conditions for the equivalence of the estimates of unknown parameters in these two models are given. We propose a criterion function for model selection based on the extensions of the unsaturated models. We discuss uniqueness and sum to zero properties of these extensions. We illustrate model building, estimation and selection methods with a auto-accident data set (Agresti, 2001). We also study the performance comparison of the newly proposed method with the standard methods that are commonly used in practice.