smooth.construct.tescv.smooth.spec {scam}

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 class 'tescv.smooth.spec'
smooth.construct(object, data, knots)

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.

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.

Author(s)

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

 ## Not run: 
## tensor product `tescv' example 
  ## simulating data...
   set.seed(5)
   n <- 30
   x1 <- sort(runif(n))
   x2 <- sort(2*runif(n)-1)
   f1 <- matrix(0,n,n)
   for (i in 1:n) for (j in 1:n) 
        f1[i,j] <- sin(2*x1[i]) - 4*x2[j]^2
   f1 <- as.vector(t(f1))
   f <- (f1-min(f1))/(max(f1)-min(f1))
   y <- f+rnorm(length(f))*0.1
   x11 <-  matrix(0,n,n)
   x11[,1:n] <- x1
   x11 <- as.vector(t(x11))
   x22 <- rep(x2,n)
   dat <- list(x1=x11,x2=x22,y=y)
## fit model ...
   b <- scam(y~s(x1,x2,k=c(10,10),bs="tescv",m=2),
            family=gaussian(), data=dat)
## plot results ...
   par(mfrow=c(2,2),mar=c(4,4,2,2))
   plot(b,se=TRUE)
   plot(b,pers=TRUE, theta = 50, phi = 20) 
   plot(y,b$fitted.values,xlab="Simulated data",ylab="Fitted data")
   x11()
   vis.scam(b, theta = 50, phi = 20)
   ## plotting the truth...
   x11()
   x1 <- seq(min(x1),max(x1),length.out=30)
   x2 <-  seq(min(x2),max(x2),length.out=30)
   f1 <- matrix(0,n,n)
   for (i in 1:n) for (j in 1:n) f1[i,j] <- sin(2*x1[i]) - 4*x2[j]^2
   persp(x1,x2,f1,theta = 50, phi = 20)  
 
## End(Not run)