Structured additive regression for multicategorical space-time data: a mixed model approach

Arbeitspapier

4208 In many practical situations, simple regression models suffer from the fact that the dependence of responses on covariates can not be sufficiently described by a purely parametric predictor. For example effects of continuous covariates may be nonlinear or complex interactions between covariates may be present. A specific problem of space-time data is that observations are in general spatially and/or temporally correlated. Moreover, unobserved heterogeneity between individuals or units may be present. While, in recent years, there has been a lot of work in this area dealing with univariate response models, only limited attention has been given to models for multicategorical space-time data. We propose a general class of structured additive regression models (STAR) for multicategorical responses, allowing for a flexible semiparametric predictor. This class includes models for multinomial responses with unordered categories as well as models for ordinal responses. Non-linear effects of continuous covariates, time trends and interactions between continuous covariates are modelled through Bayesian versions of penalized splines and flexible seasonal components. Spatial effects can be estimated based on Markov random fields, stationary Gaussian random fields or two-dimensional penalized splines. We present our approach from a Bayesian perspective, allowing to treat all functions and effects within a unified general framework by assigning appropriate priors with different forms and degrees of smoothness. Inference is performed on the basis of a multicategorical linear mixed model representation. This can be viewed as posterior mode estimation and is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to inverse smoothing parameters, are then estimated by using restricted maximum likelihood. Numerically efficient algorithms allow computations even for fairly large data sets. As a typical example we present results on an analysis of data from a forest health survey.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Discussion Paper ; No. 377

Klassifikation und Themen

• Thema: Multicategorical space-time data ; generalized linear mixed models ; restricted maximum likelihood ; stationary Gaussian random fields ; P-splines

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Kneib, Thomas ; Fahrmeir, Ludwig
• Ereignis: Veröffentlichung
• (wer): Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen
• (wo): München
• (wann): 2004

Weitere Informationen

• DOI: doi:10.5282/ubm/epub.1748
• Handle: http://hdl.handle.net/10419/31075
• URN: urn:nbn:de:bvb:19-epub-1748-9
• Letzte Aktualisierung: 10.03.2025, 11:43 MEZ