scam (version 1.2-5)

smooth.construct.mpi.smooth.spec: Constructor for monotone increasing P-splines in SCAMs

Description

This is a special method function for creating smooths subject to a monotone increasing constraint 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 suach as s(x,k,bs="mpi",m=2), where k denotes the basis dimension and m+1 is the order of the B-spline basis.

Usage

# S3 method for mpi.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 "mpi.smooth".

Details

The constructor is not called directly, but as with gam(mgcv) is used internally.

If the knots of the spline are not supplied, then they are placed evenly throughout the covariate values. If the knots are supplied, then the number of supplied knots should be k+m+2, and the range of the middle k-m knots must include all the covariate values.

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.mpd.smooth.spec, smooth.construct.cv.smooth.spec, smooth.construct.cx.smooth.spec, smooth.construct.mdcv.smooth.spec, smooth.construct.mdcx.smooth.spec, smooth.construct.micv.smooth.spec, smooth.construct.micx.smooth.spec

Examples

# NOT RUN {
 
## Monotone increasing P-splines example 
  ## simulating data...
   set.seed(12)
   n <- 100
   x <- runif(n)*4-1
   f <- 4*exp(4*x)/(1+exp(4*x))
   y <- rpois(n,exp(f))
   dat <- data.frame(x=x,y=y)
 ## fit model ...
   b <- scam(y~s(x,k=15,bs="mpi",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 

## example with supplied knots...
   knots <- list(x=c (-1.5,  -1.2, -.99, -.97, -.7, -.5, -.3, 0, 0.7,  
           0.9,1.1, 1.22,1.5,2.2,2.77,2.93,2.99, 3.2,3.6))
   b2 <- scam(y~s(x,k=15,bs="mpi",m=2),knots=knots, 
          family=poisson(link="log"), data=dat)
   summary(b2)
   plot(b2)

# }
# NOT RUN {
## example with two terms...
   set.seed(0)
   n <- 200
   x1 <- runif(n)*6-3
   f1 <- 3*exp(-x1^2) # unconstrained term
   x2 <- runif(n)*4-1;
   f2 <- exp(4*x2)/(1+exp(4*x2)) # monotone increasing smooth
   f <- f1+f2
   y <- f+rnorm(n)*0.1
   dat <- data.frame(x1=x1,x2=x2,y=y)
   knots <- list(x1=c(-4,-3.5,-2.99,-2.7,-2.5,-1.9,-1.1,-.9,-.3,0.3,.8,1.2,1.9,2.3,
2.7,2.99,3.5,4.1), x2=c(-1.5,-1.2,-1.1, -.89,-.69,-.5,-.3,0,0.7, 
0.9,1.1,1.22,1.5,2.2,2.77,2.99,3.1, 3.2,3.6))
   b3 <- scam(y~s(x1,k=15,bs="bs",m=2)+s(x2,bs="mpi", k=15,m=2), 
         knots=knots,data=dat)
  
## setting knots for f(x2) only...
   knots <- list(x2=c(-1.5,-1.2,-1.1, -.89,-.69,-.5,-.3,
   0,0.7,0.9,1.1,1.22,1.5,2.2,2.77,2.99,3.1, 3.2,3.6))
   b4 <- scam(y~s(x1,k=15,bs="bs")+s(x2,bs="mpi", k=15),
       knots=knots,data=dat)
 
# }