predict.fRegress: Predict method for Functional Regression

Description

Model predictions for object of class fRegress.

Usage

# S3 method for fRegress
predict(object, newdata=NULL, se.fit = FALSE,
     interval = c("none", "confidence", "prediction"),
     level = 0.95, ...)

Arguments

object

Object of class inheriting from fRegress

newdata

Either NULL or a list matching object\$xfdlist.

If(is.null(newdata)) predictions <- object\$yhatfdobj

If newdata is a list, predictions = the sum of either

newdata[i] * betaestfdlist[i] if object\$yfdobj has class fd

inprod(newdata[i], betaestfdlist[i]) if class(object\$yfdobj) = numeric.

se.fit

a switch indicating if standard errors of predictions are required

NOTE: se.fit = TRUE is NOT IMPLEMENTED YET.

interval

type of prediction (response or model term)

NOTE: Only "interval = 'none'" has been implemented so far.

level

Tolerance/confidence level

…

additional arguments for other methods

Value

The predictions produced by predict.fRegress are either a vector or a functional parameter (class fdPar) object, matching the class of object\$y.

If interval is not "none", the predictions will be multivariate for object\$y and the requested lwr and upr bounds. If object\$y is a scalar, these predictions are returned as a matrix; otherwise, they are a multivariate functional parameter object (class fdPar).

If se.fit is TRUE, predict.fRegress returns a list with the following components:

fit

vector or matrix or univariate or multivariate functional parameter object depending on the value of interval and the class of object\$y.

se.fit

standard error of predicted means

Details

1. Without newdata, fit <- object\$yhatfdobj.

2. With newdata, if(class(object\$y) == 'numeric'), fit <- sum over i of inprod(betaestlist[i], newdata[i]). Otherwise, fit <- sum over i of betaestlist[i] * newdata[i].

3. If(se.fit | (interval != 'none')) compute se.fit, then return whatever is desired.

Examples

Run this code

# NOT RUN {
###
###
### vector response with functional explanatory variable
### vector response with vector explanatory variable
###
###
##
## example from help('lm')
##
ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
group <- gl(2,10,20, labels=c("Ctl","Trt"))
weight <- c(ctl, trt)
fRegress.D9 <- fRegress(weight ~ group)

pred.fR.D9 <- predict(fRegress.D9)
#  Now compare with 'lm'
lm.D9 <- lm(weight ~ group)
pred.lm.D9 <- predict(lm.D9)

# }
# NOT RUN {
all.equal(as.vector(pred.fR.D9), as.vector(pred.lm.D9))
# }
# NOT RUN {
##
## vector response with functional explanatory variable
##
annualprec <- log10(apply(CanadianWeather$dailyAv[,,
                   "Precipitation.mm"], 2,sum))
smallbasis  <- create.fourier.basis(c(0, 365), 25)
tempfd <- smooth.basis(day.5,
   CanadianWeather$dailyAv[,,"Temperature.C"], smallbasis)$fd
precip.Temp.f <- fRegress(annualprec ~ tempfd)

precip.Temp.p <- predict(precip.Temp.f)

# plot response vs. fitted 
plot(annualprec, precip.Temp.p)

# }