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Generalized additive models for location, scale and shape for high dimensional data—a flexible approach based on boosting
Author(s) -
Mayr Andreas,
Fenske Nora,
Hofner Benjamin,
Kneib Thomas,
Schmid Matthias
Publication year - 2012
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2011.01033.x
Subject(s) - covariate , generalized additive model , boosting (machine learning) , feature selection , additive model , computer science , scale (ratio) , mathematics , model selection , mathematical optimization , algorithm , variable (mathematics) , data mining , statistics , econometrics , machine learning , physics , quantum mechanics , mathematical analysis
Summary. Generalized additive models for location, scale and shape (GAMLSSs) are a popular semiparametric modelling approach that, in contrast with conventional generalized additive models, regress not only the expected mean but also every distribution parameter (e.g. location, scale and shape) to a set of covariates. Current fitting procedures for GAMLSSs are infeasible for high dimensional data set‐ups and require variable selection based on (potentially problematic) information criteria. The present work describes a boosting algorithm for high dimensional GAMLSSs that was developed to overcome these limitations. Specifically, the new algorithm was designed to allow the simultaneous estimation of predictor effects and variable selection. The algorithm proposed was applied to Munich rental guide data, which are used by landlords and tenants as a reference for the average rent of a flat depending on its characteristics and spatial features. The net rent predictions that resulted from the high dimensional GAMLSSs were found to be highly competitive and covariate‐specific prediction intervals showed a major improvement over classical generalized additive models.