Automatic smoothing parameter selection in GAMLSS with an application to centile estimation. (August 2014)

• Record Type: Journal Article
• Authors: Rigby, Robert A; Stasinopoulos, Dimitrios M
• Other Names: Eilers Paul HC guest-editor.
• Is Part Of: Statistical methods in medical research. Volume 23:Number 4(2014:Aug.)
• Page Start: 318
• Page End: 332
• Publication Date: 2014-08
• Subjects: Box–Cox power exponential distribution -- Box–Cox t distribution -- lambda–mu–sigma method -- P-splines -- quantile estimation; Medicine -- Research -- Statistical methods -- Periodicals; Research -- Periodicals; Review Literature -- Periodicals; Statistics -- methods -- Periodicals; Médecine -- Recherche -- Méthodes statistiques -- Périodiques; 610.727
• DOI: 10.1177/0962280212473302
• Languages: English
• ISSNs: 0962-2802

Abstract

A method for automatic selection of the smoothing parameters in a generalised additive model for location, scale and shape (GAMLSS) model is introduced. The method uses a P-spline representation of the smoothing terms to express them as random effect terms with an internal (or local) maximum likelihood estimation on the predictor scale of each distribution parameter to estimate its smoothing parameters. This provides a fast method for estimating multiple smoothing parameters. The method is applied to centile estimation where all four parameters of a distribution for the response variable are modelled as smooth functions of a transformed explanatory variable x . This allows smooth modelling of the location, scale, skewness and kurtosis parameters of the response variable distribution as functions of x .