fda (version 2.4.0)

df.residual.fRegress: Degress of Freedom for Residuals from a Functional Regression

Description

Effective degrees of freedom for residuals, being the trace of the idempotent hat matrix transforming observations into residuals from the fit.

Usage

## S3 method for class 'fRegress':
df.residual(object, ...)

Arguments

object

Object of class inheriting from fRegress

...

additional arguments for other methods

Value

• The numeric value of the residual degrees-of-freedom extracted from object with the following attributes:
• nobs
  number of observations
• df.model
  effective degrees of freedom for the model, being the trace of the idempotent linear projection operator transforming the observations into their predictions per the model. This includes the intercept, so the 'degrees of freedom for the model' for many standard purposes that compare with a model with an estimated mean will be 1 less than this number.

Details

1. Determine N = number of observations

2. df.model <- object$df

3. df.residual <- (N - df.model)

4. Add attributes

References

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York. Hastie, Trevor, Tibshirani, Robert, and Friedman, Jerome (2001) The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, New York.

See Also

fRegress df.residual

Examples

##
## 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)
dfr.D9 <- df.residual(fRegress.D9)

# Check the answer manually
lm.D9 <- lm(weight ~ group)
dfr.D9l <- df.residual(lm.D9)
attr(dfr.D9l, 'nobs') <- length(predict(lm.D9))
attr(dfr.D9l, 'df.model') <- 2
stopifnot(
all.equal(dfr.D9, dfr.D9l)
)

##
## functional response with (concurrent) functional explanatory variable
##
# *** NOT IMPLEMENTED YET FOR FUNCTIONAL RESPONSE
#     BUT WILL EVENTUALLY USE THE FOLLOWING EXAMPLE:

(gaittime <- as.numeric(dimnames(gait)[[1]])*20)
gaitrange <- c(0,20)
gaitbasis <- create.fourier.basis(gaitrange, nbasis=21)
harmaccelLfd <- vec2Lfd(c(0, (2*pi/20)^2, 0), rangeval=gaitrange)
gaitfd <- smooth.basisPar(gaittime, gait,
       gaitbasis, Lfdobj=harmaccelLfd, lambda=1e-2)$fd
hipfd  <- gaitfd[,1]
kneefd <- gaitfd[,2]

knee.hip.f <- fRegress(kneefd ~ hipfd)

#knee.hip.dfr <- df.residual(knee.hip.f)


# Check the answer
#kh.dfr <- knee.hip.f$df ???