The GAMLSS library and datasets

Description

This a collection of functions to fit Generalized Additive Models for Location Scale and Shape(GAMLSS) and handled gamlss objects.

GAMLSS were introduced by Rigby and Stasinopoulos (2005). GAMLSS is a general framework for univariate regression type statistical problems using new ways of dealing with overdispersion, skewness and kurtosis in the response variable. 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 other parameters of the distribution of the response variable as linear parametric, nonlinear parametric or additive non-parametric functions of explanatory variables and/or random effects terms. Maximum (penalized) likelihood estimation is used to fit the models.

Details

This package allow the user to model the distribution of the response variable using a variety of one, two, three and four parameter families of distributions. The distributions implemented currently can be found in gamlss.family. Other distributions can be easily added. In the current implementation of GAMLSS several additive terms have been implemented including regression splines, smoothing splines, penalized splines, varying coefficients, fractional polynomials and random effects. Other additive terms can be easily added.

Author(s)

Mikis Stasinopoulos <d.stasinopoulos@londonmet.ac.uk>, Bob Rigby <r.rigby@londonmet.ac.uk> with contributions from Calliope Akantziliotou.

Maintainer: Mikis Stasinopoulos <d.stasinopoulos@londonmet.ac.uk>

References

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

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

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Examples

data(abdom)
mod<-gamlss(y~pb(x),sigma.fo=~pb(x),family=BCT, data=abdom, method=mixed(1,20))
plot(mod)
rm(mod)