Generalized Additive Models for Location Scale and Shape (GAMLSS) in R

By D. Stasinopoulos, Robert A. Rigby. 2007

1,568 citations recorded by the source corpus.

GAMLSS is a general framework for fitting regression type models where the distribution of the response variable does not have to belong to the exponential family and includes highly skew and kurtotic continuous and discrete distribution. GAMLSS allows all the parameters of the distribution of the response variable to be modelled as linear/non-linear or smooth functions of the explanatory variables. This paper starts by defining the statistical framework of GAMLSS, then describes the current implementation of GAMLSS in R and finally gives four different data examples to demonstrate how GAMLSS can be used for statistical modelling.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1a81bee0a45ccc39a737068c28c0ffd755fa7077

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

1. Raydonal Ospina
2. Thomas Kneib
3. Silvia L. P. Ferrari
4. Raffaella Calabrese
5. Stefan Lang
6. N. Klein
7. Achim Zeileis
8. Rodrigo Rossetto Pescim

In Statistics and Probability

1. Thomas Kneib
2. N. Klein
3. Achim Zeileis
4. Torsten Hothorn
5. Stefan Lang
6. Francisco Cribari‐Neto
7. Silvia L. P. Ferrari
8. Raydonal Ospina

Citations in the corpus

• Most Likely Transformations (2015, methodology): “Stasinopoulos and Rigby (2007) fitted a growth curve to head circumferences (HC) of 7040 boys using a GAMLSS model with a Box-Cox t distribution describing the first four moments of head circumference conditionally on age.”
• Visualizing Count Data Regressions Using Rootograms (2016, neutral): “There are further methods available, currently for univariate distributions fitted via fitdistr() (to objects of class ‘numeric’, Venables and Ripley 2002), zero-inflated models (objects of class ‘zeroinfl’, Zeileis, Kleiber, and Jackman 2008), zero-truncated models (objects of class ‘zerotrunc’, as”
• Distributional regression forests for probabilistic precipitation forecasting in complex terrain (2018, methodology): “All functions can either be used with GAMLSS family objects from the R package gamlss.dist (Stasinopoulos and Rigby 2007, version 5.0.6) or with custom lists containing all required information about the distribution family.”
• Beta Regression in R (2010, methodology): “There are various models with implementations in R that have similar features, in particular including the family of models implemented in gamlss (Stasinopoulos and Rigby 2007), also providing beta regression, albeit with a different approach for modeling the variance.”
• The new class of Kummer beta generalized distributions: theory and applications (2013, methodology): “Numerical maximization of the log-likelihood above was accomplished by using the RS method (Rigby and Stasinopoulos, 2005) available in the R contributed gamlss package (Stasinopoulos and Rigby, 2007; R Development Core Team, 2009).”
• Distributions for Modeling Location, Scale, and Shape (2019, background): “3.4 Mixed distributions in GAMLSS . . . . . . . . . . . . . . . . . . 62 3.5 Generating GAMLSS family distributions . . . . . . . . . . . . . 63 3.5.1 New gamlss.family distribution . . . . . . . . . . . . . . 64 3.5.2 New log and logit versions from a continuous gamlss.family on (−∞,∞) . . . . . . ”
• Grip Strength across the Life Course: Normative Data from Twelve British Studies (2014, positive): “We produced genderspecific cross-sectional centiles for grip strength using the Box-Cox Cole and Green (BCCG) distribution (also known as the LMS method [27]) implemented in the Generalised Additive Models for Location, Scale and Shape (GAMLSS) library [28] for the statistical program, R [29].”
• Generalized beta-generated distributions (2012, neutral): “Adopting the parametrization in Stasinopoulos and Rigby (2007), the pdf and cdf of the inverse Gaussian (IG) distribution are f(x) = 1√ 2πσ2x3 exp { − 1 2µ2σ2x (x− µ)2 } , x, µ, σ > 0 (a) (b) (c) and F (x) = Φ ( 1√ σ2x ( x µ − 1 )) + exp ( 2 µσ2 ) Φ ( − 1√ σ2x ( x µ + 1 )) .”
• GAMLSS: A distributional regression approach (2018, methodology): “The basic ideas of GAMLSS, see Stasinopoulos et al. (2017), have been implemented in R in a series of packages, see Stasinopoulos and Rigby (2007).”
• Designating Market Maker Behaviour in Limit Order Book Markets (2015, methodology): “Indeed, the supporting R package used in this paper [Stasinopoulos and Rigby, 2007] enables the modelling of more than 80 parametric distributions.”
• Flexible Imputation of Missing Data (2012, background): “The gamlss package (Stasinopoulos and Rigby, 2007) contains over 60 built-in distributions.”