Tps {fields}  R Documentation 
Fits a thin plate spline surface to irregularly spaced data. The smoothing parameter is chosen by generalized crossvalidation. The assumed model is additive Y = f(X) +e where f(X) is a d dimensional surface. This is a special case of the spatial process estimate.
Tps(x, Y, m = NULL, p = NULL, scale.type = "range", ...)
To be helpful, a more complete list of arguments are described that are the same as those for the Krig function.
x 
Matrix of independent variables. Each row is a location or a set of independent covariates. 
Y 
Vector of dependent variables. 
m 
A polynomial function of degree (m1) will be included in the model as the drift (or spatial trend) component. Default is the value such that 2md is greater than zero where d is the dimension of x. 
p 
Exponent for radial basis functions. Default is 2md. 
scale.type 
The independent variables and knots are scaled to the specified scale.type. By default the scale type is "range", whereby the locations are transformed to the interval (0,1) by forming (xmin(x))/range(x) for each x. Scale type of "user" allows specification of an x.center and x.scale by the user. The default for "user" is mean 0 and standard deviation 1. Scale type of "unscaled" does not scale the data. 
... 
Any argument that is valid for the Krig function. Some of the main ones
are listed below.

A thin plate spline is result of minimizing the residual sum of squares subject to a constraint that the function have a certain level of smoothness (or roughness penalty). Roughness is quantified by the integral of squared mth order derivatives. For one dimension and m=2 the roughness penalty is the integrated square of the second derivative of the function. For two dimensions the roughness penalty is the integral of
(Dxx(f))**22 + 2(Dxy(f))**2 + (Dyy(f))**22
(where Duv denotes the second partial derivative with respect to u and v.) Besides controlling the order of the derivatives, the value of m also determines the base polynomial that is fit to the data. The degree of this polynomial is (m1).
The smoothing parameter controls the amount that the data is smoothed. In the usual form this is denoted by lambda, the Lagrange multiplier of the minimization problem. Although this is an awkward scale, lambda =0 corresponds to no smoothness constraints and the data is interpolated. lambda=infinity corresponds to just fitting the polynomial base model by ordinary least squares.
This estimator is implemented by passing the right generalized covariance function based on radial basis functions to the more general function Krig. One advantage of this implementation is that once a Tps/Krig object is created the estimator can be found rapidly for other data and smoothing parameters provided the locations remain unchanged. This makes simulation within R efficient (see example below). Tps does not currenty support the knots argument where one can use a reduced set of basis functions. This is mainly to simplify and a good alternative using knots would be to use a valid covariance from the Matern family and a large range parameter.
A list of class Krig. This includes the predicted surface of fitted.values and the residuals. The results of the grid search minimizing the generalized cross validation function is returned in gcv.grid. Please see the documentation on Krig for details of the returned arguments.
See "Nonparametric Regression and Generalized Linear Models" by Green and Silverman. See "Additive Models" by Hastie and Tibshirani.
Krig, summary.Krig, predict.Krig, predict.se.Krig, plot.Krig,
surface.Krig
,
sreg
#2d example fit< Tps(ozone$x, ozone$y) # fits a surface to ozone measurements. set.panel(2,2) plot(fit) # four diagnostic plots of fit and residuals. set.panel() summary(fit) # predict onto a grid that matches the ranges of the data. out.p<predict.surface( fit) image( out.p) surface(out.p) # perspective and contour plots of GCV spline fit # predict at different effective # number of parameters out.p<predict.surface( fit,df=10) #1d example out<Tps( rat.diet$t, rat.diet$trt) # lambda found by GCV plot( out$x, out$y) lines( out$x, out$fitted.values) # # compare to the ( much faster) one spline algorithm # sreg(rat.diet$t, rat.diet$trt) # # Adding a covariate to the fixed part of model # Note: this is a fairly big problem numerically (850+ locations) Tps( RMprecip$x,RMprecip$y, Z=RMprecip$elev)> out surface( out, drop.Z=TRUE) US( add=TRUE, col="grey") # # simulation reusing Tps/Krig object # fit< Tps( rat.diet$t, rat.diet$trt) true< fit$fitted.values N< length( fit$y) temp< matrix( NA, ncol=50, nrow=N) sigma< fit$shat.GCV for ( k in 1:50){ ysim< true + sigma* rnorm(N) temp[,k]< predict(fit, y= ysim) } matplot( fit$x, temp, type="l") # #4d example fit< Tps(BD[,1:4],BD$lnya,scale.type="range") # plots fitted surface and contours # default is to hold 3rd and 4th fixed at median values surface(fit)