smooth.construct.tesmd2.smooth.spec {scam}

Tensor product smoothing constructor for a bivariate function monotone decreasing in the second covariate

Description

This is a special method function for creating tensor product bivariate smooths monotone decreasing 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="tesmd2",m=c(2,2)). The default basis for the first marginal smooth is P-spline. Cyclic cubic regression spline ("cc") is implemented in addition to the P-spline. See an example below on how to call for it.

Usage

## S3 method for class 'tesmd2.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 "tesmd2.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.

margin.bs

A two letter character string indicating the (penalized) smoothing basis to use for the first unconstrained marginal smooth. (eg "ps" for P-splines).

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

Pya, N. (2010) Additive models with shape constraints. PhD thesis. University of Bath. Department of Mathematical Sciences

See Also

smooth.construct.tesmd1.smooth.spec

Examples

 ## Not run: 
## tensor product `tesmd2' example 
  ## simulating data...
   require(scam)
   set.seed(2)
   n <- 30
   x1 <- sort(runif(n)); x2 <- sort(runif(n)*4-1)
   f <- matrix(0,n,n)
   for (i in 1:n) for (j in 1:n) 
        f[i,j] <- 2*sin(pi*x1[i])-exp(4*x2[j])/(1+exp(4*x2[j]))
   f <- as.vector(t(f))
   y <- f+rnorm(length(f))*.2
   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,bs="tesmd2",k=10),data=dat)
## plot results ...
   old.par <- par(mfrow=c(2,2),mar=c(4,4,2,2))
   plot(b,se=TRUE)
   plot(b,scheme=1,theta = 30, phi = 40)
   plot(y,b$fitted.values,xlab="Simulated data",ylab="Fitted data")
   par(old.par)
   vis.scam(b,theta = 40, phi = 20)

## example with cyclic cubic regression spline along the 1st covariate...
   set.seed(4)
   n <- 30
   x1 <- sort(runif(n)); x2 <- sort(runif(n)*4-1) 
   f <- matrix(0,n,n)
   for (i in 1:n) for (j in 1:n) 
        f[i,j] <- sin(2*pi*x1[i])-exp(4*x2[j])/(1+exp(4*x2[j]))
   f <- as.vector(t(f))
   y <- f+rnorm(length(f))*.2
   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 ...
   b1 <- scam(y~s(x1,x2,bs="tesmd2",xt=list("cc"),k=10), data=dat)
## plot results ...
   old.par <-par(mfrow=c(2,2))
   plot(b1,se=TRUE)
   plot(b1,scheme=1,theta = 30, phi = 40)
   plot(y,b1$fitted.values,xlab="Simulated data",ylab="Fitted data")
   par(old.par)
   vis.scam(b1,theta=40,phi=20)
 
## End(Not run)