scam (version 1.0)

smooth.construct.mpd.smooth.spec: Constructor for monotone decreasing P-splines in SCAMs

Description

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

Usage

smooth.construct.mpd.smooth.spec(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 "mpd.smooth".

References

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

See Also

smooth.construct.mpi.smooth.spec, smooth.construct.mdcv.smooth.spec, smooth.construct.mdcx.smooth.spec, smooth.construct.micv.smooth.spec, smooth.construct.micx.smooth.spec

Examples

## Monotone decreasing P-splines example 
  ## simulating data...
   set.seed(3)
   n <- 100
   x <- runif(n)*3-1
   f <- exp(-1.3*x)
   y <- rpois(n,exp(f))
   dat <- data.frame(x=x,y=y)
 ## fit model ...
   b <- scam(y~s(x,k=15,bs="mpd",m=2),family=poisson(link="log"),
       data=dat,sp=NULL)

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

## plot results ...
   plot(x,y,xlab="x",ylab="y")
   x1 <- sort(x,index=TRUE)
   lines(x1$x,exp(f)[x1$ix])      ## the true function
   lines(x1$x,b$fitted.values[x1$ix],col=2)  ## monotone fit 
   lines(x1$x,b1$fitted.values[x1$ix],col=3) ## unconstrained fit