Extensions in the Use of Log-Multiplicative Scaled Association Models in Multiway Contingency Tables

The proposed iterative macro program to estimate linear and quadratic constraints on the intrinsic association (φ) not only satisfies the condition of simultaneous estimation and yields efficient estimates but also has the flexibility to incorporate other log-linear effects.

Abstract

This article extends the use of log-multiplicative scaled association models to multiway cross-classifications with complex constraints in the partial homogeneous models. It proposes a special class of conditional association models with linear and quadratic constraints on the intrinsic association (φ) when the layer (group) variable indexes temporal order. For multiway cross-classifications with more than one group variable, another class of conditional association models with additive and interactive constraints on the intrinsic association (φ) with the group variables is provided. The proposed iterative macro program to estimate these constraints not only satisfies the condition of simultaneous estimation and yields efficient estimates but also has the flexibility to incorporate other log-linear effects.