scam (version 1.2-18)

smooth.construct.tescv.smooth.spec: Tensor product smoothing constructor for a bivariate function concave in the second covariate

Description

This is a special method function for creating tensor product bivariate smooths concave in the second covariate which is built by the mgcv constructor function for smooth terms, smooth.construct. It is constructed from a pair of single penalty marginal smooths. This tensor product is specified by model terms such as s(x1,x2,k=c(q1,q2),bs="tescv",m=c(2,2)), where the basis for the first marginal smooth is specified in the second element of bs.

Usage

# S3 method for tescv.smooth.spec
smooth.construct(object, data, knots)

Value

An object of class "tescv.smooth". In addition to the usual elements of a smooth class documented under smooth.construct of the mgcv library, this object contains:

p.ident

A vector of 0's and 1's for model parameter identification: 1's indicate parameters which will be exponentiated, 0's - otherwise.

Zc

A matrix of identifiability constraints.

Arguments

object

A smooth specification object, generated by an s term in a GAM formula.

data

A data frame or list containing the values of the elements of object$term, with names given by object$term.

knots

An optional list containing the knots corresponding to object$term. If it is NULL then the knot locations are generated automatically.

Author

Natalya Pya <[e-mail]>

References

Pya, N. and Wood, S.N. (2015) Shape constrained additive models. Statistics and Computing, 25(3), 543-559

See Also

smooth.construct.temicv.smooth.spec smooth.construct.temicx.smooth.spec

smooth.construct.tedecv.smooth.spec smooth.construct.tedecx.smooth.spec

smooth.construct.tescx.smooth.spec

Examples

 if (FALSE) {
## tensor product `tescv' example 
require(scam)
simu <- function(x,z) { sin(2*x) - 4*z^2 } 
xs <-seq(0,1,length=30); zs <- seq(-1,1,length=30)
pr <- data.frame(x=rep(xs,30),z=rep(zs,rep(30,30)))
truth <- matrix(simu(pr$x,pr$z),30,30)
   
set.seed(5)
n <- 500
x <- runif(n)
z <- 2*runif(n)-1
f <- simu(x,z)
y <- f + rnorm(n)*.2
## fit model ...
b <- scam(y~s(x,z,bs="tescv"))
summary(b)
old.par <- par(mfrow=c(2,2),mar=c(4,4,2,2))
plot(b,se=TRUE)
plot(b,pers=TRUE,theta = 50, phi = 20);title("tescv")
plot(y,b$fitted.values,xlab="Simulated data",ylab="Fitted data",pch=".",cex=3)
persp(xs,zs,truth,theta = 50, phi = 20);title("truth")
par(old.par)  
vis.scam(b,theta = 50, phi = 20) 
 }