Generalized Additive Models for Location, Scale and Shape

2005/04/14 by Robert A. Rigby, R. A. Rigby, D. M. Stasinopoulos +1 · 23 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Optimal Experimental Design Methods #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.1111/j.1467-9876.2005.00510.x

crossref issued 2005/04/14 · crossref published 2005/04/14 · crossref published-online 2005/04/14 · openalex publication_date 2005/04/14 · crossref created 2005/04/14 · crossref published-print 2005/06/01 · crossref deposited 2024/12/31 · openalex created_date 2025/10/10 · crossref indexed 2026/08/03 · openalex updated_date 2026/08/03

Abstract

Summary A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y, as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton–Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.

Citations

• Conditional Heteroskedasticity in Asset Returns: A New Approach
• A Generalization of the Gamma Distribution
• Autoregressive Conditional Density Estimation
• Bayes Factors and BIC
• Smoothing reference centile curves: The lms method and penalized likelihood
• Generalized Linear Models

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