smooth.construct.teid.smooth.spec: Tensor product smoothing constructor for bivariate functions...

In scam: Shape Constrained Additive Models

Tensor product smoothing constructor for bivariate functions with monotonicity constraints: increasing in the first covariate and decreasing in the second

Description

This is a special method function for constructing tensor product bivariate smooths that are monotonically increasing in the first covariate and monotonically decreasing in the second.

The smooths are specified using model terms such as s(x1, x2, k = c(q1, q2), bs = "teid", m = c(2, 2)), where q1 and q2 denote the basis dimensions of the marginal smooths, which are represented using B-spline basis functions. The order of the marginal B-spline basis is given by m_j + 1.

Usage

## S3 method for class 'teid.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 "teid.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.tedmd.smooth.spec, smooth.construct.tedmi.smooth.spec, smooth.construct.tedi.smooth.spec,

Examples

 
## tensor product `teid' example 
require(scam)
simu <- function(x,z) {exp(4*x)/(1+exp(4*x))-exp(2*z)/(1+exp(2*z)) } 
xs <- zs <- seq(-1,3,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(2)
n <- 500
x <- runif(n)*4-1
z <- runif(n)*4-1
f <- simu(x,z)
y <- f + rnorm(n)*.1
## fit model ...
b <- scam(y~s(x,z,k=c(10,10),bs="teid"))
summary(b)
old.par <- par(mfrow=c(2,2),mar=c(4,4,2,2))
plot(b,se=TRUE)
plot(b,pers=TRUE,theta = 60, phi = 40);title("teid")
plot(y,b$fitted.values,xlab="Simulated data",ylab="Fitted data",pch=".",cex=3)
persp(xs,zs,truth,theta = 60, phi = 40);title("truth")
par(old.par)  
vis.scam(b,theta = 50, phi = 40)         
 

scam documentation built on Oct. 17, 2026, 1:07 a.m.