predict.bigspline: Predicts for "bigspline" Objects

In taylerablake/thin-plate-splines: Smoothing Splines for Large Samples

Description

Get fitted values and standard error estimates for cubic smoothing splines.

Usage

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

Arguments

object	Object of class "bigspline", which is output from bigspline.
newdata	Vector 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 cubic smoothing spline (estimated by bigspline) 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. (2013). Fast and stable smoothing spline analysis of variance models for large samples with applications to electroencephalography data analysis. Unpublished doctoral dissertation. University of Illinois at Urbana-Champaign.

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 cubic spline model
cubmod <- bigspline(x,y)
crossprod( predict(cubmod) - 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(cubmod,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(cubmod,newdata,se.fit=TRUE,effect="0")
ycl <- predict(cubmod,newdata,se.fit=TRUE,effect="lin")
ycn <- predict(cubmod,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   ##########

# define (same) 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 a different cubic spline model
cubamod <- bigspline(x,y,type="cub0")
crossprod( predict(cubamod) - myfun(x) )/10^4

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

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

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

# predict constant, linear, and nonlinear effects
ya0 <- predict(cubamod,newdata,se.fit=TRUE,effect="0")
yal <- predict(cubamod,newdata,se.fit=TRUE,effect="lin")
yan <- predict(cubamod,newdata,se.fit=TRUE,effect="non")
crossprod( ya$fit - (ya0$fit + yal$fit + yan$fit) )

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

taylerablake/thin-plate-splines documentation built on May 8, 2019, 11:16 p.m.