Generalized Additive Models for Location Scale and Shape (GAMLSS) inR

Abstract

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.

The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data

“…Both models were estimated using the GAMLSS Library of R Package (Stasinopoulos and Rigby, 2007). Secondly, the PIG model showed better GOF than the NB model, as expected, and models with varying dispersion parameters exhibited a slightly better fit than the fixeddispersion model, as noted by Miaou and Lord (2003).…”

“…In fact, a few studies in areas such as medicine and motor insurance have suggested the PIG as an alternative to the NB model for modeling count data distribution since the PIG distribution has slightly longer tails and larger kurtosis (Willmot, 1987, Shoukri et al, 2004, Dean et al, 1989, Jagger and Elsner, 2012. Besides, the likelihood function can be easily obtained and has nicely closed form, which indicates the estimation of parameters will be quite simple and almost take no time (Stasinopoulos and Rigby, 2012). Despite these nice properties, the application of the PIG model in highway safety (e.g.…”

Reproductive activity of the tropical arrow squid Doryteuthis plei around São Sebastião Island (SE Brazil) based on a 10-year fisheries monitoring

“…The GAMLSS procedure was used with a cubic spline smoothing function (cs) (Stasinopoulos and Rigby, 2007). Models were applied to analyze the correlations between body measurements and reproductive structures and with the spatial and temporal factors of the small-scale fisheries.…”

Estimating total claim size in the auto insurance industry: a comparison between tweedie and zero-adjusted inverse gaussian distribution

“…The ZAIG model was estimated by the GAMLSS package (Stasinopoulos & Rigby, 2007;Stasinopoulos, Rigby, & Akantziliotou, 2008) for the R system (R Development Core Team, 2007). The Tweedie model was estimated using the SPSS package (version 16.0).…”