smooth.construct.tesmi1.smooth.spec: Tensor product smoothing constructor for a bivariate function...

In scam: Shape Constrained Additive Models

Tensor product smoothing constructor for a bivariate function monotone increasing in the first covariate

Description

This is a special method function for creating tensor product bivariate smooths monotone increasing in the first 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="tesmi1",m=2). The basis for the second marginal smooth can be specified as a two letter character string of the argument xt (eg xt="cc" to specify cyclic cubic regression spline). See example below. The default basis for the second 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 'tesmi1.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 "tesmi1.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 second unconstrained marginal smooth. (eg "cc" for cyclic cubic regression spline).

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.tesmi2.smooth.spec

Examples

  ## Not run: 
## tensor product `tesmi1' example... 
  ## simulating data...
   require(scam)
   set.seed(2)
   n <- 30
   x1 <- sort(runif(n)*4-1)
   x2 <- sort(runif(n))
   f <- matrix(0,n,n)
   for (i in 1:n) for (j in 1:n) 
        f[i,j] <- exp(4*x1[i])/(1+exp(4*x1[i]))+2*sin(pi*x2[j])
   f <- as.vector(t(f))
   y <- f+rnorm(length(f))*.3
   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="tesmi1",k=c(10,10)), data=dat)
## plot results ...
   old.par<- par(mfrow=c(2,2))
   plot(b,se=TRUE)
   plot(b,pers=TRUE,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 second covariate...
   set.seed(2)
   n <- 30
   x1 <- sort(runif(n)*4-1)
   x2 <- sort(runif(n))
   f <- matrix(0,n,n)
   for (i in 1:n) for (j in 1:n) 
        f[i,j] <- exp(4*x1[i])/(1+exp(4*x1[i]))+sin(2*pi*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="tesmi1",xt=list("cc"),k=10), data=dat)
## plot results ...
   old.par<- par(mfrow=c(2,2))
   plot(b1,se=TRUE)
   plot(b1,pers=TRUE,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)

scam documentation built on June 22, 2024, 10:43 a.m.