P-spline Varying Coefficient Models for Complex Data

Brian D. Marx ()
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Brian D. Marx: Louisiana State University, Department of Experimental Statistics

A chapter in Statistical Modelling and Regression Structures, 2010, pp 19-43 from Springer

Abstract: Abstract Although the literature on varying coefficient models (VCMs) is vast, we believe that there remains room to make these models more widely accessible and provide a unified and practical implementation for a variety of complex data settings. The adaptive nature and strength of P-spline VCMs allow a full range of models: from simple to additive structures, from standard to generalized linear models, from one-dimensional coefficient curves to two-dimensional (or higher) coefficient surfaces, among others, including bilinear models and signal regression. As P-spline VCMs are grounded in classical or generalized (penalized) regression, fitting is swift and desirable diagnostics are available. We will see that in higher dimensions, tractability is only ensured if efficient array regression approaches are implemented. We also motivate our approaches through several examples, most notably the German deep drill data, to highlight the breadth and utility of our approach.

Keywords: Tensor Product; Effective Dimension; Smooth Term; Difference Penalty; Cataclastic Rock (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2413-1_2

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DOI: 10.1007/978-3-7908-2413-1_2

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