Mean and Dispersion Additive Models: Applications and Diagnostics

This paper presents further applications and diagnostics of the ‘Mean and Dispersion Additive Model’ or ‘MADAM’. This is a flexible model for the mean and variance of a dependent variable in which the variance is modelled as a product of the dispersion parameter and a known variance function of the mean, and the mean and dispersion parameters are each modelled as functions of explanatory variables using a semi-parametric Additive model. MADAM’s are fitted using a successive relaxation algorithm which alternates between mean and dispersion model fits until convergence, providing diagnostics for each model. It is shown in the appendix that the algorithm maximises the penalised extended quasi-likelihood of the MADAM.