ScholarLens Back to search
1996•Contributions to statisticsRequires access

Mean and Dispersion Additive Models

Robert A. Rigby, Mikis D. Stasinopoulos

Open publisher page 50 citations

Abstract

This paper presents a flexible model for the mean and variance of a dependent variable. The variance is modelled as a product of a dispersion parameter and a known variance function of the mean. The dependence of each of the mean and dispersion parameter on explanatory variables is modelled using a semi-parametric additive model. We call this model the ’Mean and Dispersion Additive Model’ or ’MADAM’. The MADAM is fitted either by maximisation of the penalised extended Quasi-likelihood or by pseudo-maximization of the penalised Normal likelihood. A successive relaxation fitting algorithm is described and is implemented in GLIM4 allowing flexible and interactive modelling of both the mean and dispersion of a dependent variable. Two examples are given to demonstrate the use of the MADAM for modelling overdispersion in each of Poisson regression model and a Binomial logistic regression model.

About this research paper

What this paper is about

This paper presents a flexible model for the mean and variance of a dependent variable. The variance is modelled as a product of a dispersion parameter and a known variance function of the mean. The dependence of each of the mean and dispersion parameter on explanatory variables is modelled using a semi-parametric additive model. We call this model the ’Mean and Dispersion Additive Model’ or ’MADAM’. The MADAM is fitted either by maximisation of the penalised extended Quasi-likelihood or by pseudo-maximization of the penalised Normal likelihood. A successive relaxation fitting algorithm is described and is implemented in GLIM4 allowing flexible and interactive modelling of both the mean and dispersion of a dependent variable. Two examples are given to demonstrate the use of the MADAM for modelling overdispersion in each of Poisson regression model and a Binomial logistic regression model.

Why it matters

OpenAlex reports 50 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

This paper presents a flexible model for the mean and variance of a dependent variable. The variance is modelled as a product of a dispersion parameter and a known variance function of the mean. The dependence of each of the mean and dispersion parameter on explanatory variables is modelled using a semi-parametric additive model. We call this model the ’Mean and Dispersion Additive Model’ or ’MADAM’. The MADAM is fitted either by maximisation of the penalised extended Quasi-likelihood or by pseudo-maximization of the penalised Normal likelihood. A successive relaxation fitting algorithm is described and is implemented in GLIM4 allowing flexible and interactive modelling of both the mean and dispersion of a dependent variable. Two examples are given to demonstrate the use of the MADAM for modelling overdispersion in each of Poisson regression model and a Binomial logistic regression model.

Key concepts: Overdispersion, Mathematics, Dispersion (optics), Quasi-likelihood, Statistics, Binomial regression, Zero-inflated model, Regression analysis

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Mean and Dispersion Additive Models — Research Paper | ScholarLens