Quasi-Binomial Regression Model for the Analysis of Data with Extra-Binomial Variation

Mohamed M Shoukri,Maha M Aleid

doi:10.4236/ojs.2022.121001

Abstract

Objectives: Developing inference procedures on the quasi-binomial distribution and the regression model. Methods: Score testing and the method of maximum likelihood for regression parameters estimation. Data: Several examples are included, based on published data. Results: A quasi-binomial model is used to model binary response data which exhibit extra-binomial variation. A partial score test on the binomial hypothesis versus the quasi-binomial alternative is developed and illustrated on three data sets. The extended logit transformation on the binomial parameter is introduced and the large sample dispersion matrix of the estimated parameters is derived. The Nonlinear Mixed Procedure (NLMIXED) in SAS is shown to be very appropriate for the estimation of nonlinear regression.

Highlights

In many biological and toxicological experiments, the variable of interest is in the form of counts resulting from binary responses
The Nonlinear Mixed Procedure (NLMIXED) in SAS is shown to be very appropriate for the estimation of nonlinear regression
It has long been presumed that an inherent characteristic of data from these types of studies is the tendency for individual experimental units to respond more alike than individuals from other groups, which is commonly known as the “group effect”

Summary

Introduction

In many biological and toxicological experiments, the variable of interest is in the form of counts resulting from binary responses In such experiments the data may sometimes exhibit greater heterogeneity (variation) than the binomial model. Altham [1] proposed that the analysis of such experiments be based on two-parameter generalizations of the binomial model which allows for the presence of dependent responses within groups and gave two models. The quasi-binomial (QBD) model has two parameters p and φ. We shall formulate a C (α ) test for testing the binomial model against the QBD alternative. This can be done by testing the null hypothesis H0 : φ = 0 against its negation in the presence of the nuisance parameter p. The above statistic provides a C (α ) a binomial score test which is asymptotically optimal against the quasi-binomial alternative

Examples

Quasi-Binomial Regression Model

Applications of the QBD Regression

Discussion