fpca {dfrr}

Functional principal component analysis (fpca) of a dfrr fit

Description

fpca() returns estimations of the smooth principal components/eigen-functions and the corresponding eigen-values of the residual function in the dfrr model. The result is a named list containing the vector of eigen-values and the matrix of Fourier coefficients. See Details.

Usage

fpca(object, standardized = NULL, unstandardized = !standardized)

Arguments

object

a fitted dfrr-object obtained from invoking the function dfrr.

standardized, unstandardized

a boolean indicating whether stanadrdized/unstandardized pricipal components/eigen-functions are reported. Only standardized pricipal components/eigen-functions are identifiable, thus the arugment is defaults to standardized=TRUE.

Details

Fourier coefficients which are reported are based on the a set of basis which can be determined by basis(dfrr_fit). Thus the evaluation of pricipal component/eigen-function on the set of time points specified by vector time, equals to fpca(dfrr_fit)%*%t(eval.basis(time,basis(dfrr_fit))).

Consider that the unstandardized estimations are not identifiable. So, it is recommended to extract and report the standardized estimations.

Value

fpca(dfrr_fit) returns a list containtng the following components:

values

a vector containing the eigen-values of the standaridized/unstandardized covariance operator of the residual function term in dfrr model, sorted in decreasing order.

vectors

a matrix whose columns contain the Fourier coefficients of the principal components/eigen-functions of the standaridized/unstandardized covariance operator of the residual function term in dfrr model, sorted based on the corresponding eigen-values.

See Also

plot.fpca.dfrr

Examples

set.seed(2000)
N<-50;M<-24

X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)

#The argument T_E indicates the number of EM algorithm.
#T_E is set to 1 for the demonstration purpose only.
#Remove this argument for the purpose of converging the EM algorithm.
dfrr_fit<-dfrr(Y~X,yind=time,T_E=1)
fpcs<-fpca(dfrr_fit)
plot(fpcs,plot.eigen.functions=TRUE,plot.contour=TRUE,plot.3dsurface = TRUE)