Summary
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.
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© 1996 Physica-Verlag Heidelberg
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Rigby, R.A., Stasinopoulos, M.D. (1996). Mean and Dispersion Additive Models. In: Härdle, W., Schimek, M.G. (eds) Statistical Theory and Computational Aspects of Smoothing. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-48425-4_16
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DOI: https://doi.org/10.1007/978-3-642-48425-4_16
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-0930-5
Online ISBN: 978-3-642-48425-4
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