Multilevel structured additive regression
نویسندگان
چکیده
Models with structured additive predictor provide a very broad and rich framework for complex regression modeling. They can deal simultaneously with nonlinear covariate effects and time trends, unitor cluster-specific heterogeneity, spatial heterogeneity and complex interactions between covariates of different type. In this paper, we propose a hierarchical or multilevel version of regression models with structured additive predictor where the regression coefficients of a particular nonlinear term may obey another regression model with structured additive predictor. In that sense, the model is composed of a hierarchy of complex structured additive regression models. The proposed model may be regarded as an extended version of a multilevel model with nonlinear covariate terms in every level of the hierarchy. The model framework is also the basis for generalized random slope modeling based on multiplicative random effects. Inference is fully Bayesian and based on Markov chain Monte Carlo simulation techniques. We provide an in depth description of several highly efficient sampling schemes that allow to estimate complex models with several hierarchy levels and a large number of observations within a couple of minutes (often even seconds). We demonstrate the practicability of the approach in a complex appliS. Lang ( ) · N. Umlauf · P. Wechselberger Department of Statistics, University of Innsbruck, Universitätsstraße 15, 6020 Innsbruck, Austria e-mail: [email protected] K. Harttgen NADEL, ETH Zürich, Voltastrasse 24, 8092 Zurich, Switzerland T. Kneib Faculty of Economic Sciences, University of Göttingen, Platz der Göttinger Sieben 5, 37073 Göttingen, Germany cation on childhood undernutrition with large sample size and three hierarchy levels.
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عنوان ژورنال:
- Statistics and Computing
دوره 24 شماره
صفحات -
تاریخ انتشار 2014