Abstract

Generalized Additive Models for Location, Scale and Shape (GAMLSS) were introduced by Rigby and Stasinopoulos (2005). They refer to a very general regression type model in which both the systematic and random parts of the model are highly flexible and where the fitting algorithm is fast enough to allow the rapid exploration of very large and complex data sets. GAMLSS is a general framework for univariate regression type statistical problems. In GAMLSS the exponential family distribution assumption used in Generalized Linear Model (GLM) and Generalized Additive Model (GAM), (see Nelder and Wedderburn, 1972 and Hastie and Tibshirani, 1990, respectively) is relaxed and replaced by a very general distribution family including highly skew and kurtotic discrete and continuous distributions. The systematic part of the model is expanded to allow modelling not only the mean (or location) but all the other parameters of the distribution of y as linear parametric, non-linear parametric and/or additive (smoothing) non-parametric functions of explanatory variables and/or random effects terms. Maximum (penalized) likelihood estimation is used to fit the models. For medium to large size data, GAMLSS allow flexibility in statistical modelling far beyond other currently available methods. The GAMLSS framework is implemented in R.

The most important application of GAMLSS up to now is its use by the Department of Nutrition for Health and Development of the World Health Organization to construct the worldwide standard growth centile curves, see WHO . The range of possible applications for GAMLSS is very wide and examples will be given of its usefulness in modelling data. In the talk we will describe the GAMLSS model, the variety of different (two, three and four parameter) distributions that are implemented within the R GAMLSS package and the variety of different additive (smoothing) terms that can be used. New distributions and new additive terms can be added easily to the R package. The use of censored data, truncate distributions and finite mixture of distributions within the GAMLSS framework, will also be described.

References

Hastie, T.J., and Tibshirani, R.J. (1990) Generalized Additive Models. London: Chapman & Hall.

Ihaka, R., and Gentleman, R. (1996), A Language for Data Analysis and Graphics, Journal of Computational and Graphical Statistics, 5,3,299-314.

Nelder, J.A. and Wedderburn, R.W.M. (1972) Generalized Linear Models. J. R. Statist. Soc. A, 135, 370-384.

Rigby, R.A. and Stasinopoulos, D.M. (2005) Generalized Additive Models for Location, Scale and Shape (with discussion). Appl. Statist., 54, 1-38.

WHO Multicentre Growth Reference Study Group (2006) WHO Child Growth Standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age: Methods and development. Geneva: World Health Organization.