Low‐Rank Scale‐Invariant Tensor Product Smooths for Generalized Additive Mixed Models

By Simon N. Wood. Biometrics, 2006

619 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/273b4a995715faa8c684ece4be56f12c1622df1d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Distributed lag non-linear models (2010, background): “This issue represents an opportunity for further development, and could benefit from the research already carried out on penalized tensor-product smoothers [25, 36].”
Spatial fisheries ecology: Recent progress and future prospects (2008, methodology): “The error terms ei are generally assumed to be independent and identically distributed with zero mean and common variance, but in very recent applications it is possible to generalize the model to allow for (spatially) correlated errors (Wood, 2004b).”
Generalized Additive Models for Exceedances of High Thresholds With an Application to Return Level Estimation for U.S. Wind Gusts (2019, background): “…are restricted to regression splines here, such as thin plate or Duchon splines (Duchon 1977; Wood 2003) for continuous two-dimensional variation, natural cubic and P-splines for continuous one-dimensional variation, and tensor products (De Boor 1978; Wood 2006b) for smoothly varying interactions.”
A general framework for functional regression modelling (2017, methodology): “Such a constraint can be incorporated by appropriately modifying the design matrix (cf. Wood (2006a); see Brockhaus et al. (2015b) on how to preserve the Kronecker structure for tensor product bases as in expansion (3.2)).”
P-spline ANOVA-type interaction models for spatio-temporal smoothing (2011, methodology): “There are other alternatives to avoid the identifiability problems: (i) add a ridge penalty on the system of equations in (2.3) as in Marx and Eilers (1998) or (ii) identify and impose the constraints numerically (see Wood, 2006a).”
Smoothing Parameter and Model Selection for General Smooth Models (2015, methodology): “(w)+f 3(h,w). The smooth interaction term f 3 can readily be constructed in a way that excludes the main effects of wand h, by constructing its basis using the usual tensor product construction (e.g. Wood, 2006b), but based on marginal bases into which the constraints P i f 1(hi) = 0 and P i f 2(wi)”
Making better biogeographical predictions of species’ distributions (2006, methodology): “VGAM, Yee & Wild 1996; GAMM, Wood 2004 ).”