fda.usc (version 2.1.0)

influence.fregre.fd: Functional influence measures

Description

Once estimated the functional regression model with scalar response, influence.fregre.fd function is used to obtain the functional influence measures.

Usage

# S3 method for fregre.fd
influence(model, ...)

Value

Return:

• DCP Cook's Distance for Prediction.

• DCE Cook's Distance for Estimation.

• DP \(\mbox{Pe}\tilde{\mbox{n}}\mbox{a's} \) Distance.

Arguments

model

fregre.pc, fregre.basis or fregre.basis.cv object.

...

Further arguments passed to or from other methods.

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente

Details

Identify influential observations in the functional linear model in which the predictor is functional and the response is scalar. Three statistics are introduced for measuring the influence: Distance Cook Prediction DCP, Distance Cook Estimation DCE and Distance \(\mbox{pe}\tilde{\mbox{n}}\mbox{a} \) DP respectively.

References

Febrero-Bande, M., Galeano, P. and Gonzalez-Manteiga, W. (2010). Measures of influence for the functional linear model with scalar response. Journal of Multivariate Analysis 101, 327-339.

Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. https://www.jstatsoft.org/v51/i04/

See Also

See Also as: fregre.pc, fregre.basis, influence_quan

Examples

if (FALSE) {
data(tecator)
x=tecator$absorp.fdata[1:129]
y=tecator$y$Fat[1:129]

res1=fregre.pc(x,y,1:5)  
# time consuming
res.infl1=influence(res1)  
res2=fregre.basis(x,y)  
res.infl2=influence(res2)  

res<-res1
res.infl<-res.infl1
mat=cbind(y,res$fitted.values,res.infl$DCP,res.infl$DCE,res.infl$DP)
colnames(mat)=c("Resp.","Pred.","DCP","DCE","DP")
pairs(mat)
}