predict.bigtps {bigsplines}

Predicts for "bigtps" Objects

Description

Get fitted values and standard error estimates for thin-plate splines.

Usage

## S3 method for class 'bigtps'
predict(object,newdata=NULL,se.fit=FALSE,
        effect=c("all","0","lin","non"),
        design=FALSE,smoothMatrix=FALSE,...)

Arguments

object

Object of class "bigtps", which is output from bigtps.

newdata

Vector or matrix containing new data points for prediction. See Details and Example. Default of newdata=NULL uses original data in object input.

se.fit

Logical indicating whether the standard errors of the fitted values should be estimated. Default is se.fit=FALSE.

effect

Which effect to estimate: effect="all" gives full \hat{y}, effect="0" gives the intercept (constant) portion of \hat{y}, effect="lin" gives linear portion of \hat{y}, and effect="non" gives nonlinear portion of \hat{y}.

design

Logical indicating whether the design matrix should be returned.

smoothMatrix

Logical indicating whether the smoothing matrix should be returned.

...

Ignored.

Details

Uses the coefficient and smoothing parameter estimates from a fit thin-plate spline (estimated by bigtps) to predict for new data.

Value

If se.fit=FALSE, design=FALSE, and smoothMatrix=FALSE, returns vector of fitted values.

Otherwise returns list with elements:

fit

Vector of fitted values

se.fit

Vector of standard errors of fitted values (if se.fit=TRUE)

X

Design matrix used to create fitted values (if design=TRUE)

ix

Index vector such that fit=X%*%object$coef[ix] (if design=TRUE)

S

Smoothing matrix corresponding to fitted values (if smoothMatrix=TRUE)

Author(s)

Nathaniel E. Helwig <[e-mail]>

References

Gu, C. (2013). Smoothing spline ANOVA models, 2nd edition. New York: Springer.

Helwig, N. E. (2017). Regression with ordered predictors via ordinal smoothing splines. Frontiers in Applied Mathematics and Statistics, 3(15), 1-13.

Helwig, N. E. and Ma, P. (2015). Fast and stable multiple smoothing parameter selection in smoothing spline analysis of variance models with large samples. Journal of Computational and Graphical Statistics, 24, 715-732.

Helwig, N. E. and Ma, P. (2016). Smoothing spline ANOVA for super-large samples: Scalable computation via rounding parameters. Statistics and Its Interface, 9, 433-444.

Examples

##########   EXAMPLE 1   ##########

# define univariate function and data
set.seed(773)
myfun <- function(x){ 2 + x + sin(2*pi*x) }
x <- runif(10^4)
y <- myfun(x) + rnorm(10^4)

# fit thin-plate spline (default 1 dim: 30 knots)
tpsmod <- bigtps(x,y)
crossprod( predict(tpsmod) - myfun(x) )/10^4

# define new data for prediction
newdata <- data.frame(x=seq(0,1,length.out=100))

# get fitted values and standard errors for new data
yc <- predict(tpsmod,newdata,se.fit=TRUE)

# plot results with 95% Bayesian confidence interval
plot(newdata$x,yc$fit,type="l")
lines(newdata$x,yc$fit+qnorm(.975)*yc$se.fit,lty=3)
lines(newdata$x,yc$fit-qnorm(.975)*yc$se.fit,lty=3)

# predict constant, linear, and nonlinear effects
yc0 <- predict(tpsmod,newdata,se.fit=TRUE,effect="0")
ycl <- predict(tpsmod,newdata,se.fit=TRUE,effect="lin")
ycn <- predict(tpsmod,newdata,se.fit=TRUE,effect="non")
crossprod( yc$fit - (yc0$fit + ycl$fit + ycn$fit) )

# plot results with 95% Bayesian confidence intervals
par(mfrow=c(1,2))
plot(newdata$x,ycl$fit,type="l",main="Linear effect")
lines(newdata$x,ycl$fit+qnorm(.975)*ycl$se.fit,lty=3)
lines(newdata$x,ycl$fit-qnorm(.975)*ycl$se.fit,lty=3)
plot(newdata$x,ycn$fit,type="l",main="Nonlinear effect")
lines(newdata$x,ycn$fit+qnorm(.975)*ycn$se.fit,lty=3)
lines(newdata$x,ycn$fit-qnorm(.975)*ycn$se.fit,lty=3)


##########   EXAMPLE 2   ##########

# function with two continuous predictors
set.seed(773)
myfun <- function(x1v,x2v){
  sin(2*pi*x1v) + log(x2v+.1) + cos(pi*(x1v-x2v))
}
x <- cbind(runif(10^4),runif(10^4))
y <- myfun(x[,1],x[,2]) + rnorm(10^4)

# fit thin-plate spline (default 2 dim: 100 knots)
tpsmod <- bigtps(x,y)

# define new data
newdata <- as.matrix(expand.grid(seq(0,1,length=50),seq(0,1,length=50)))

# get fitted values for new data
yp <- predict(tpsmod,newdata)

# plot results
imagebar(seq(0,1,length=50),seq(0,1,length=50),matrix(yp,50,50),
         xlab=expression(italic(x)[1]),ylab=expression(italic(x)[2]),
         zlab=expression(hat(italic(y))))

# predict linear and nonlinear effects
yl <- predict(tpsmod,newdata,effect="lin")
yn <- predict(tpsmod,newdata,effect="non")

# plot results
par(mfrow=c(1,2))
imagebar(seq(0,1,length=50),seq(0,1,length=50),matrix(yl,50,50),
         main="Linear effect",xlab=expression(italic(x)[1]),
         ylab=expression(italic(x)[2]),zlab=expression(hat(italic(y))))
imagebar(seq(0,1,length=50),seq(0,1,length=50),matrix(yn,50,50),
         main="Nonlinear effect",xlab=expression(italic(x)[1]),
         ylab=expression(italic(x)[2]),zlab=expression(hat(italic(y))))