scam (version 1.1-1)

smooth.construct.cx.smooth.spec: Constructor for convex P-splines in SCAMs

Description

This is a special method function for creating smooths subject to convexity constraint which is built by the mgcv constructor function for smooth terms, smooth.construct. It is constructed using the mixed constrained P-splines. This smooth is specified via model terms such as s(x,k,bs="cx",m=2), where k denotes the basis dimension and m+1 is the order of the B-spline basis.

Usage

## S3 method for class 'cx.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 data required by this term, with names given by object$term. The by variable is the last element.

knots

An optional list containing the knots supplied for basis setup. If it is NULL then the knot locations are generated automatically.

Value

• An object of class "cx.smooth".

References

Pya, N. and Wood, S.N. (2014) Shape constrained additive models. Statistics and Computing, DOI 10.1007/s11222-013-9448-7 Pya, N. (2010) Additive models with shape constraints. PhD thesis. University of Bath. Department of Mathematical Sciences

See Also

smooth.construct.cv.smooth.spec, smooth.construct.mpi.smooth.spec, smooth.construct.mdcv.smooth.spec, smooth.construct.mdcx.smooth.spec, smooth.construct.micv.smooth.spec, smooth.construct.mpd.smooth.spec

Examples

## Convex P-splines example 
  ## simulating data...
   set.seed(1)
   n <- 100
   x <- sort(2*runif(n)-1)
   f <- 4*x^2
   y <- f + rnorm(n)*0.4
   dat <- data.frame(x=x,y=y)
   b <- scam(y~s(x,k=15,bs="cx",m=2),family=gaussian,data=dat)
   # UNCONSTRAINED FIT *****************
   b1 <- scam(y~s(x,k=15,bs="cr",m=2),family=gaussian, data=dat)

## plot results ...
   plot(x,y,xlab="x",ylab="y")
   lines(x,f)      ## the true function
   lines(x,b$fitted,col=2)  ## constrained fit 
   lines(x,b1$fitted,col=3) ## unconstrained fit 

## Poisson version...
   y <- rpois(n,exp(f))
   dat <- data.frame(x=x,y=y)
 ## fit model ...
   b <- scam(y~s(x,k=15,bs="cx",m=2),family=poisson(link="log"),data=dat)

# UNCONSTRAINED FIT *****************
   b1 <- scam(y~s(x,k=15,bs="cr",m=2),family=poisson(link="log"), data=dat)

## plot results ...
   plot(x,y,xlab="x",ylab="y")
   lines(x,exp(f))      ## the true function
   lines(x,b$fitted,col=2)  ## constrained fit 
   lines(x,b1$fitted,col=3) ## unconstrained fit