scam (version 1.1-1)

extrapolate.uni.scam: Extrapolation from the fitted SCAM model

Description

This function does extrapolations of the response variable values to the right-hand side of the data in case of a single univariate shape constrained term. It takes a fitted scam object produced by scam() and produces extrapolations given a new set of values for the model covariates to the ``right'' of the data set. It also produces predictions given a new set of values within the range of the model covariate or the original values used for the model fit. Extrapolations are accompanied by standard errors, based on the posterior distribution of the model coefficients. For predictions only see predict.scam.

Usage

extrapolate.uni.scam(object, newdata)

Arguments

object

a fitted scam object as produced by scam().

newdata

A data frame or list containing the values of the model covariates at which extrapolations are required.

Value

• A list is returned with the following items:
• fit
  Extrapolations of the response variable.
• se
  standard error estimates of extrapolated values.

References

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

See Also

scam, predict.scam

Examples

library(scam)
#########################################################
## Example on extrapolating a single univariate monotone increasing smooth...
##########################################################

set.seed(12)
   n <- 100
   x <- sort(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)

   b <- scam(y~s(x,k=15,bs="mpi",m=2),family=poisson(link="log"),
       data=dat,sp=NULL)

   plot(x,y,xlab="x",ylab="y")
   lines(x,exp(f))      ## the true function
   lines(x,b$fitted.values,col=2)  ## monotone fit

   newd <- data.frame(x=c(3.2,3.3,3.6))
   fe <- extrapolate.uni.scam(b,newd)

   plot(c(x,newd[[1]]),c(y,NA,NA,NA))
   lines(c(x,newd[[1]]),c(b$fitted,exp(fe$fit)),col=2)

### passing observed data + new data...
   newd <- data.frame(x=c(x,3.2,3.3,3.6))
   fe <- extrapolate.uni.scam(b,newd)

   plot(newd[[1]],c(y,NA,NA,NA))
   lines(newd[[1]],exp(fe$fit),col=2)


## Gaussian model ....
   ## simulating data...
 set.seed(2)
 n <- 200
 x <- sort(runif(n)*4-1)
 f <- exp(4*x)/(1+exp(4*x)) # monotone increasing smooth
 y <- f+rnorm(n)*0.1
 dat <- data.frame(x=x,y=y)
 b <- scam(y~ s(x,k=25,bs="mpi",m=2),family=gaussian(link="identity"),data=dat)

 newd <- data.frame(x=c(3.2,3.3,3.6))
 fe <- extrapolate.uni.scam(b,newd)

 plot(c(x,newd[[1]]),c(y,NA,NA,NA))
 lines(c(x,newd[[1]]),c(b$fitted,fe$fit),col=2)

### passing observed data + new data...
   newd <- data.frame(x=c(x,3.2,3.3,3.6))
   fe <- extrapolate.uni.scam(b,newd)

   plot(newd[[1]],c(y,NA,NA,NA))
   lines(newd[[1]],fe$fit,col=2)
   lines(newd[[1]],fe$fit+2*fe$se,col=3)
   lines(newd[[1]],fe$fit-2*fe$se,col=4)

###########################################################
## Example on extrapolating a single univariate monotone increasing and concave smooth...
##########################################################
  
set.seed(3)
   n <- 100
   x <- sort(runif(n)*99+1)
   f1 <- log(x)
   f <- (f1-min(f1))/(max(f1)-min(f1))
   y <- f+rnorm(n)*0.10
   dat <- data.frame(x=x,y=y)
 ## fit model ...
   b <- scam(y~s(x,k=15,bs="micv",m=2),family=gaussian(link="identity"),data=dat)

   newd <- data.frame(x=c(100,101,113))
   fe <- extrapolate.uni.scam(b,newd)

   plot(c(x,newd[[1]]),c(y,NA,NA,NA),ylim=c(min(y),max(c(y,fe$fit))))
   lines(c(x,newd[[1]]),c(b$fitted,fe$fit),col=2)
 
###########################################################
## Example on extrapolating a single univariate monotone decreasing smooth...
##########################################################

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


newd <- data.frame(x=c(2.3,2.7,3.2))
fe <- extrapolate.uni.scam(b,newd)

ylim<- c(min(y,exp(fe$fit)),max(y,exp(fe$fit)))
plot(c(x,newd[[1]]),c(y,NA,NA,NA),ylim=ylim)
lines(c(x,newd[[1]]),c(b$fitted,exp(fe$fit)),col=2)

### passing observed data + new data...
newd <- data.frame(x=c(x,2.3,2.7,3.2))
fe <- extrapolate.uni.scam(b,newd)

plot(newd[[1]],c(y,NA,NA,NA),ylim=ylim)
lines(newd[[1]],exp(fe$fit),col=2)

## Gaussian model ....
set.seed(3)
n <- 100
x <- sort(runif(n)*3-1)
f <- exp(-1.3*x)
y <- f+rnorm(n)*0.3
dat <- data.frame(x=x,y=y)
b <- scam(y~s(x,k=15,bs="mpd",m=2),family=gaussian,
       data=dat,sp=NULL)


newd <- data.frame(x=c(2.3,2.7,3.2))
fe <- extrapolate.uni.scam(b,newd)

ylim<- c(min(y,fe$fit),max(y,fe$fit))
plot(c(x,newd[[1]]),c(y,NA,NA,NA),ylim=ylim)
lines(c(x,newd[[1]]),c(b$fitted,fe$fit),col=2)


###########################################################
## Example on extrapolating a single univariate convex smooth...
##########################################################
  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)

newd <- data.frame(x=c(1.1,1.2,1.3))
fe <- extrapolate.uni.scam(b,newd)

ylim<- c(min(y,fe$fit),max(y,fe$fit))
plot(c(x,newd[[1]]),c(y,NA,NA,NA),ylim=ylim)
lines(c(x,newd[[1]]),c(b$fitted,fe$fit),col=2)

### passing observed data + new data...
newd <- data.frame(x=c(x,1.1,1.2,1.3))
fe <- extrapolate.uni.scam(b,newd)

plot(newd[[1]],c(y,NA,NA,NA),ylim=ylim)
lines(newd[[1]],fe$fit,col=2)