Generalized additive models for location, scale and shape

By Robert A. Rigby, D. Stasinopoulos. 2005

3,158 citations recorded by the source corpus.

Summary. A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y, as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random‐effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton–Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b8dc8aeaf943d59b5db8846d680d8d023c5b3b01

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

A comparison of three approaches to non-stationary flood frequency analysis (2017, methodology): “GAMLSS models were proposed by Rigby and Stasinopoulos (2005).”
Variational Inference for Heteroscedastic Semiparametric Regression (2015, methodology): “Models of this type have a small literature with Rigby & Stasinopoulos (2005) being a key reference.”
Bayesian structured additive distributional regression for multivariate responses (2015, methodology): “So far, most publications on regression analyses for multivariate responses have focused on one specific distribution such as the multivariate normal distribution in seemingly unrelated regression models (Zellner, 1962; Greene, 2011) or distributions for categorical outcomes and count data; see for ”
Distributions for Modeling Location, Scale, and Shape (2019, background): “very informative graph and statisticians use instead histograms or a smooth version of the plot called a nonparametric density estimator (see Silverman [1988] or Wand and Jones [1999] for the theory or section ?? for R functions).”
Generalized Additive Models for Location Scale and Shape (GAMLSS) in R (2007, methodology): “GAMLSS were introduced by Rigby and Stasinopoulos (2001, 2005) and Akantziliotou, Rigby, and Stasinopoulos (2002) as a way of overcoming some of the limitations associated with the popular generalized linear models, GLM, and generalized additive models, GAM (see Nelder and Wedderburn 1972; Hastie…”
Flexible Regression and Smoothing: Using Gamlss in R (2017, background): “At the end of this chapter, some notes refer the reader to Rigby and Stasinopoulos 2005, Appendix A.1 where the authors explain, with mathematical expressions, the GAMLSS algorithms based on maximum (penalized) likelihood.”
Beyond mean regression (2013, positive): “…the simplest example of a generalized additive model for location, scale and shape (GAMLSS, in fact without an effect on the shape) as introduced by Rigby and Stasinopoulos (2005) as a comprehensive class of models where different parameters of the response distribution are related to regression…”
Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape (2013, methodology): “More details on how the penalized log likelihood is maximized are given in Rigby and Stasinopoulos (2005).”
Negative Deceptive Opinion Spam (2013, methodology): “6We use the R package GAMLSS (Rigby and Stasinopoulos, 2005) to fit a log-normal distribution (left truncated at 150 characters) to the lengths of the deceptive reviews.”
Visualizing Count Data Regressions Using Rootograms (2016, background): “…in countreg), generalized additive models (objects of class ‘gam’, Wood 2006), and for selected count distributions falling within the framework of generalized additive models for location, scale, and shape (objects of class ‘gamlss’, Rigby and Stasinopoulos 2005; Stasinopoulos and Rigby 2007).”
Comparison of methods for non-stationary hydrologic frequency analysis: Case study using annual maximum daily precipitation in Taiwan (2017, methodology): “To apply IDT, we used probabilities of distribution function with time-dependent parameters to describe non-stationarity in hydrological time series (Strupczewski et al., 2001; Rigby and Stasinopoulos, 2005; Villarini et al., 2009; Lee and You, 2013).”
Parametric quantile regression based on the generalized gamma distribution (2013, methodology): “We must also mention the generalized additive models for location, scale and shape package GAMLSS (Rigby and Stasinopoulos, 2005; Stasinopoulos and Rigby, 2007; GAMLSS Team, 2011) which allows the fitting of regression models with a huge variety of parametric conditional distributions (including GG)”
Bayesian structured additive distributional regression with an application to regional income inequality in Germany (2015, methodology): “refore considerably expands the common exponential family framework. Distributional regression is closely related to generalised additive models for location, scale and shape (GAMLSS) as suggested by Rigby and Stasinopoulos (2005). We prefer the notion of distributional regression for our approach s”
Linear quantile mixed models (2013, methodology): “Also, other approaches might involve modeling the moments of a distribution function using a parametric family (e.g., Rigby and Stasinopoulos 2005) and deriving the quantiles of the response by inversion.”
Bayesian Item Response Modeling in R with brms and Stan (2019, background): “In a regression context, such models are often referred to as distributional regression models or as regression models of location, scale, and shape (Rigby and Stasinopoulos 2005; Stasinopoulos and Rigby 2007) to stress the fact that all parameters of the distribution can be predicted, not just a si”
Phytoplankton growth and the interaction of light and temperature: A synthesis at the species and community level (2016, methodology): “In preliminary analyses, we also fit nonparametric curves to the 90th percentile of the data (using GAMLSS, generalized additive models for location, scale, and shape; Rigby and Stasinopoulos 2005) and to the mean of the data (using a generalized additive model, GAM).”
A new family of generalized distributions (2011, methodology): “Numerical maximization of the log-likelihood above is accomplished by using the RS method 18 available in the gamlss package 14 in R Development Core Team 19 .”