Thin plate regression splines

By Simon N. Wood. 2003

2,464 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f1d3d313a723c9eaeef496244edcfefeae237feb

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 Computational Mechanics

In Statistics and Probability

Citations in the corpus

Temporal Dynamics of the Human Vaginal Microbiota (2012, methodology): “We have also built models with the same structure as model (1), but where s(t) was set to be either a thin plate regression spline (30, 31) or a polynomial of normalized menstrual time.”
Bivariate Binomial Spatial Modeling of Loa loa Prevalence in Tropical Africa (2008, methodology): “Our method is similar in spirit to the geoadditive models of Kammann and Wand (2003) or the thin-plate regression splines of Wood (2003).”
Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK (2005, methodology): “Obvious competitors include spline smoothing methods (Wood, 2003) and hierarchical stochastic models in which the set of underlying type-specific probability surfaces are modelled as a realization of a latent multivariate spatial stochastic process, so extending to the multivariate setting the…”
Water quality of the Great Barrier Reef: distributions, effects on reef biota and trigger values for the protection of ecosystem health (2008, methodology): “Statistical methods The water quality and benthic variables were each modelled spatially (Chapters 3 & 4) using generalised additive models (GAMs) and smoothing splines (Wood 2003).”
Econometric modelling of the regional knowledge production function in Europe (2015, methodology): “Penalized Regression Splines are adopted as a basis to represent the univariate smooth terms (Wood, 2003, 2006a, 2006b), whereas for bivariate smooth functions such as fðRDr;t;HKr;tÞ, we use the scale-invariant tensor product smooths proposed by Wood (2006c) (Augustin et al., 2009; Longhi et al.,…”
Analyzing dynamic phonetic data using generalized additive mixed modeling: A tutorial focusing on articulatory differences between L1 and L2 speakers of English (2018, neutral): “The adjusted r(2) represents the amount of variance explained by the regression (corrected to use unbiased estimators; see Wood, 2006, p. 29). The deviance explained is a generalization of r(2) and will be very similar to the actual r(2) value for Gaussian models (Wood, 2006, p. 84). The REML (restr”
Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models (2011, methodology): “with respect to β, where D is the model deviance, defined as the saturated log-likelihood minus the log-likelihood, all multiplied by 2φ (D is a useful GLM analogue of the residual sum of squares of a linear model, and working in terms of D will allow the direct use of some results from Wood (2008))”
Spatial and temporal density dependence regulates the condition of central Baltic Sea clupeids: compelling evidence using an extensive international acoustic survey (2011, positive): “The following additive formulation was used: ConditionY ;SD ¼ aþ sðViÞY ;SD þ þ sðVnÞY ;SD þ e; where a is the intercept, s is the thin-plate smoothing spline function (Wood 2003), Vi; . . .;Vn are the predictors, and e is the random error.”
Bivariate Penalized Splines for Regression (2013, methodology): “We also included a fast (lowrank approximation) version TPS2 (Wood (2003)) using the function gam() in R package mgcv.”
Smoothing Parameter and Model Selection for General Smooth Models (2015, methodology): “he rank 8 basis approximation gives visible approximation errors for φ 6...φ 8, which have vanished for the rank 16 approximation. (Actually if we use the rank 8 thin plate regression spline basis of Wood (2003) then the approximation is accurate to graphical accuracy.) In summary each increase in r”
Fast bivariate P‐splines: the sandwich smoother (2010, methodology): “, the thin plate regression splines (Wood, 2003).”
Causal inference in partially linear structural equation models (2016, methodology): “In order to estimate the residuals in step 5 of computeGDPX, we use additive model fitting based on the R-package mgcv with default settings [29, 30].”
Leaf form-climate relationships on the global stage: an ensemble of characters (2015, methodology): “This is achieved by penalized thin plate regression splines (see Wood, 2003, for details) in the multidimensional smoothings.”