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Generalized Additive Models for Location, Scale and Shape

Statistical modelling at its best


What is GAMLSS

GAMLSS are univariate distributional regression models, where all the parameters of the assumed distribution for the response can be modelled as additive functions of the explanatory variables.


How to use GAMLSS

The GAMLSS framework of statistical modelling is implemented in a series of packages in R. The packages can be downloaded from the R library, CRAN. There is a fair amount of documentation on GAMLSS. The book `Flexible Regression and Smoothing:  Using  GAMLSS  in R', published on April 2017, serves as an introduction to R packages.


What distributions can be used within GAMLSS

GAMLSS provide over 100 continuous, discrete and mixed distributions for modelling the response variable. Truncated, censored, log and logit transformed and finite mixture versions of these distributions can be also used. The book `Distributions for Modelling Location, Scale, and Shape: Using GAMLSS in R, is a comprehensive review of the distributions. The draft version of the book `Distributions for Modelling Location, Scale and Shape: Using GAMLSS in R' is also a good source of information but rather out of date.


What additive terms can be used within GAMLSS

P-splines, Cubic splines, loess smoothing, ridge regression, lasso regression, simple random effects and varying coefficient models are some of the additive functions provided in the implementation. Appropriate interface is also provided so GAMLSS models can be used in combination with smoothers from the gam() function (of package mgcv), the neural network function nnet() (of package nnet) and decision threes (of package rpart).


Who's is using GAMLSS

GAMLSS has been used in a variety of fields including: actuarial science, biology, biosciences, energy economic, genomics, finance, fisheries, food consumption, growth curves estimation, marine research, medicine, meteorology, rainfalls, vaccines, e.t.c. The World Health Organisation (WHO), the International Monetary Fund (IMF), the European Bank and the Bank of England are among the organisations who use GAMLSS in their analysis.


How to learn more about GAMLSS

Books: i) `Flexible Regression and Smoothing:  Using  GAMLSS  in R'  (April 2017) ii) `Distributions for Modelling Location, Scale, and Shape: Using GAMLSS in R' (October 2019).
Articles: iii) 'GAMLSS' on the Journal of Statistical Software (2007) can be useful for a short introduction but a slightly out of date. iv) `GAMLSS: A Distributional Regression Approach' on the Statistical Modelling Journal (2018)

Blogs and Latest News
  • Dear GAMLSS friends and users Our previous website `’  hosted at Hostgator was hacked, so  we took the decision  to move our site to a new host and restart the web site under the old  `’  name.  We currently redirect all  `’ traffic to `’. On moving the site we lost some material. We apologise […]

  •  1. package: gamlss i) The function within gamlss() has a line added to prevent the iterative weighs wt to go to Inf. ii) The tp() function within lms() and quantSheets() has changed name and modified slightly iii) The vcoc.gamlss() has the warnings changed and allows if theinverse of the Hessian (R) fails to recalucated […]

  • Version 4.2-7 i) gamlss gamlssML(): now allows the fitting binomial data (sorry it never checked before) and the use of formula in the specification of the model (e.g, y~1) to be consistent with gamlss(). Note that explanatory variables will be ignored if used with gamlssML().  .gamlss.multin.list is now on NAMESPACE  the functions vcov.gamlss() and summary.gamlss() […]

  • This version is released on the 22–6-2013 and it is the first time that robust (sandwich) standard errors are introduce  in gamlss models.  Of course those standard errors apply to parametric GAMLSS models only. When non-parametric smoothing terms are used then  the (sandwich) standard errors can still be used with caution since they are not yet take […]

  •   Version 4.2-5 The most important change in this version of gamlss is the way that the standard errors are calculated. In  previous version the vcov() function was calculated using a final iteration to a non-linear maximisation procedure. This procedure failed in a lot of occasions and the result was that the reported standard errors […]

  • The new version of gamlss is 4.2-0. The following are the changes made:   package gamlss: The functions and prof.term() are improved. The argument step is not anymore compulsory and if not set the argument length is used instead. For most cases there is no need to have a fine grid since the function is approximated using splinefun(). The output is […]

  • The new features in version 2.1-2 are as follows: package gamlss: The function histSmo() is added for density estimation. The function histDist() now has the function gamlssML() as its main fitting function. The fitting function  gamlss() is only used if gamlssML() fails. The function gamlssML() has now an argument start.from. In the function fitDist(), the normal distribution NO() is added to the list of “.realline” so it also appears […]

What did they say
  • The GAMLSS team

    The type of statistical inference used may be less important to the conclusions than choosing a suitable model in the first place.

  • Occam’s Razor

    entities should not be multiplied beyond necessity

  • Richard Feynman

    no matter how beautiful your theory, no matter how clever you are or what your name is, if it disagrees with experiment, it’s wrong

  • John W. Tukey

    Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.

  • George Box

    All models are wrong but some are useful