bigsplines (version 1.1-1)

predict.bigtps: Predicts for "bigtps" Objects

Description

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

Usage

# S3 method for 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.

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)

Details

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

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

# NOT RUN {
##########   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))))

# }