Poisson loglinear modeling with linear constraints on the expected cell frequencies

TL;DR

This paper develops a unified framework for Poisson loglinear models with linear constraints, enabling inference and hypothesis testing for complex count data models, including multinomial and product multinomial cases.

Contribution

It introduces a general theory for Poisson loglinear models with linear constraints, encompassing multinomial models as special cases, and proposes inference methods and hypothesis testing procedures.

Findings

Simulation studies confirm the effectiveness of the proposed inference tools.

The framework unifies various count data models under a common theoretical approach.

Classical goodness-of-fit tests are adapted for the constrained models.

Abstract

In this paper we consider Poisson loglinear models with linear constraints (LMLC) on the expected table counts. Multinomial and product multinomial loglinear models can be obtained by considering that some marginal totals (linear constraints on the expected table counts) have been prefixed in a Poisson loglinear model. Therefore with the theory developed in this paper, multinomial and product multinomial loglinear models can be considered as a particular case. To carry out inferences on the parameters in the LMLC an information-theoretic approach is followed from which the classical maximum likelihood estimators and Pearson chi-square statistics for goodness-of fit are obtained. In addition, nested hypotheses are proposed as a general procedure for hypothesis testing. Through a simulation study the appropriateness of proposed inference tools is illustrated.