predict.scam {scam}

Prediction from fitted SCAM model

Description

This function is a clone of the mgcv library code predict.gam with some modifications to adopt shape preserving smooth terms. It takes a fitted scam object produced by scam() and produces predictions given a new set of values for the model covariates or the original values used for the model fit. Predictions can be accompanied by standard errors, based on the posterior distribution of the model coefficients.

It now alows prediction outside the range of knots, and use linear extrapolation in this case.

Usage

## S3 method for class 'scam'
predict(object,newdata,type="link",se.fit=FALSE,terms=NULL,exclude=NULL,
    block.size=NULL,newdata.guaranteed=FALSE,na.action=na.pass,...)

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 predictions are required. If this is not provided then predictions corresponding to the original data are returned. If newdata is provided then it should contain all the variables needed for prediction: a warning is generated if not.

type

When this has the value "link" (default) the linear predictor (possibly with associated standard errors) is returned. When type="terms" each component of the linear predictor is returned seperately (possibly with standard errors): this includes parametric model components, followed by each smooth component, but excludes any offset and any intercept. type="iterms" is the same, except that any standard errors returned for unconstrained smooth components will include the uncertainty about the intercept/overall mean. When type="response" predictions on the scale of the response are returned (possibly with approximate standard errors). When type="lpmatrix" then a matrix is returned which yields the values of the linear predictor (minus any offset) when postmultiplied by the parameter vector (in this case se.fit is ignored). The latter option is most useful for getting variance estimates for quantities derived from the model: for example integrated quantities, or derivatives of smooths. A linear predictor matrix can also be used to implement approximate prediction outside R (see example code, below).

se.fit

when this is TRUE (not default) standard error estimates are returned for each prediction.

terms

if type=="terms" then only results for the terms given in this array will be returned.

exclude

if type=="terms" or type="iterms" then terms (smooth or parametric) named in this array will not be returned. Otherwise any smooth terms named in this array will be set to zero. If NULL then no terms are excluded.

block.size

maximum number of predictions to process per call to underlying code: larger is quicker, but more memory intensive. Set to < 1 to use total number of predictions as this.

newdata.guaranteed

Set to TRUE to turn off all checking of newdata except for sanity of factor levels: this can speed things up for large prediction tasks, but newdata must be complete, with no NA values for predictors required in the model.

na.action

what to do about NA values in newdata. With the default na.pass, any row of newdata containing NA values for required predictors, gives rise to NA predictions (even if the term concerned has no NA predictors). na.exclude or na.omit result in the dropping of newdata rows, if they contain any NA values for required predictors. If newdata is missing then NA handling is determined from object$na.action.

...

other arguments.

Details

See predict.gam for details.

Value

If type=="lpmatrix" then a matrix is returned which will give a vector of linear predictor values (minus any offest) at the supplied covariate values, when applied to the model coefficient vector. Otherwise, if se.fit is TRUE then a 2 item list is returned with items (both arrays) fit and se.fit containing predictions and associated standard error estimates, otherwise an array of predictions is returned. The dimensions of the returned arrays depends on whether type is "terms" or not: if it is then the array is 2 dimensional with each term in the linear predictor separate, otherwise the array is 1 dimensional and contains the linear predictor/predicted values (or corresponding s.e.s). The linear predictor returned termwise will not include the offset or the intercept.

newdata can be a data frame, list or model.frame: if it's a model frame then all variables must be supplied.

Author(s)

Natalya Pya <[e-mail]> based partly on mgcv by Simon Wood

References

Chambers and Hastie (1993) Statistical Models in S. Chapman & Hall.

Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

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

scam, plot.scam

Examples

## Not run: 
library(scam)
set.seed(2)
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)*0.2
dat <- data.frame(x1=x1,x2=x2,y=y)
b <- scam(y~s(x1,k=15,bs="cr")+s(x2,k=30,bs="mpi"),data=dat)

newd <- data.frame(x1=seq(-3,3,length.out=20),x2=seq(-1,3,length.out=20))
pred <- predict(b,newd)
pred
predict(b,newd,type="terms",se=TRUE)

## prediction on the original data...
pr <- predict(b,type="terms")
x<-sort(x1,index=TRUE)
old.par <- par(mfrow=c(2,2))
plot(x$x,(pr[,1])[x$ix],type="l",col=3,xlab="x1")
z<-sort(x2,index=TRUE)
plot(z$x,(pr[,2])[z$ix],type="l",col=3,xlab="x2")
plot(b,select=1,scale=0,se=FALSE)
plot(b,select=2,scale=0,se=FALSE)
par(old.par)

## linear extrapolation with predict.scam()...
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"),family=poisson(link="log"),data=dat)
newd <- data.frame(x=c(2.3,2.7,3.2))
fe <- predict(b,newd,type="link",se=TRUE)
ylim<- c(min(y,exp(fe$fit)),max(y,exp(fe$fit)))
plot(c(x,newd[[1]]),c(y,NA,NA,NA),ylim=ylim,ylab="y",xlab="x")
lines(c(x,newd[[1]]),c(b$fitted,exp(fe$fit)),col=3)

## prediction on the original data...
pr <- predict(b)
plot(x,y)
lines(x,exp(pr),col=3)


## 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"),data=dat)
 newd <- data.frame(x=c(3.2,3.3,3.6))
 fe <- predict(b,newd)
 plot(c(x,newd[[1]]),c(y,NA,NA,NA),ylab="y",xlab="x")
 lines(c(x,newd[[1]]),c(b$fitted,fe),col=3)

### passing observed data + new data...
 newd <- data.frame(x=c(x,3.2,3.3,3.6))
 fe <- predict(b,newd,se=TRUE)
 plot(newd[[1]],c(y,NA,NA,NA),ylab="y",xlab="x")
 lines(newd[[1]],fe$fit,col=2)
 lines(newd[[1]],fe$fit+2*fe$se.fit,col=3)
 lines(newd[[1]],fe$fit-2*fe$se.fit,col=4)

## prediction with CI...
 newd <- data.frame(x=seq(-1.2,3.5,length.out=100))
 fe <- predict(b,newd,se=TRUE)
 ylim<- c(min(y,fe$se.fit),max(y,fe$se.fit))
 plot(newd[[1]],fe$fit,type="l",ylim=ylim,ylab="y",xlab="x")
 lines(newd[[1]],fe$fit+2*fe$se.fit,lty=2)
 lines(newd[[1]],fe$fit-2*fe$se.fit,lty=2)
 
## prediction on the original data...
pr <- predict(b)
plot(x,y)
lines(x,pr,col=3)

## bivariate example...
   set.seed(2)
   n <- 30
   x1 <- sort(runif(n));  x2 <- sort(runif(n)*4-1)
   f <- matrix(0,n,n)
   for (i in 1:n) for (j in 1:n) 
        f[i,j] <- 2*sin(pi*x1[i]) +exp(4*x2[j])/(1+exp(4*x2[j]))
   f <- as.vector(t(f));  
   y <- f+rnorm(length(f))*0.1
   x11 <-  matrix(0,n,n); x11[,1:n] <- x1;  x11 <- as.vector(t(x11))
   x22 <- rep(x2,n)
   dat <- list(x1=x11,x2=x22,y=y)
   b <- scam(y~s(x1,x2,k=c(10,10),bs="tesmi2"),data=dat,optimizer="efs")
   par(mfrow=c(2,2),mar=c(4,4,2,2))
   plot(b,se=TRUE);   plot(b,pers=TRUE,theta = 80, phi = 40)

   n.out <- 20
   xp <- seq(0,1.4,length.out=n.out) 
   zp <- seq(-1,3.4,length.out=n.out)
   xp1 <-  matrix(0,n.out,n.out);   xp1[,1:n.out] <- xp
   xp1 <- as.vector(t(xp1));   xp2 <- rep(zp,n.out)
   newd <- data.frame(x1=xp1,x2=xp2)
   fe <- predict(b,newd)
   fc <- t(matrix(fe,n.out,n.out))
   persp(xp,zp,fc,expand= 0.85,ticktype = "simple",xlab="x1",
     ylab="x2",zlab="f^",main="", theta = 80, phi = 40)


## obtaining a 'prediction matrix'...
newd <- data.frame(x1=c(-2,-1),x2=c(0,1))
Xp <- predict(b,newdata=newd,type="lpmatrix")
fv <- Xp%*% b$beta.t
fv
 
## End(Not run)