fsemipar (version 1.1.1)

predict.mfplm.PVS: Prediction for MFPLM

Description

predict method for the multi-functional partial linear model (MFPLM) fitted using PVS.kernel.fit or PVS.kNN.fit.

Usage

# S3 method for PVS.kernel
predict(object, newdata.x = NULL, newdata.z = NULL,
  y.test = NULL, option = NULL, ...)
# S3 method for PVS.kNN
predict(object, newdata.x = NULL, newdata.z = NULL, 
  y.test = NULL, option = NULL, knearest.n = object$knearest, 
  min.knn.n = object$min.knn, max.knn.n = object$max.knn.n, 
  step.n = object$step, ...)

Value

The function returns the predicted values of the response (y) for newdata.x and newdata.z. If !is.null(y.test), it also provides the mean squared error of prediction (MSEP) computed as mean((y-y.test)^2). If option=3, two sets of predictions (and two MSEPs) are provided, corresponding to the items a) and b) mentioned in the section Details.

If is.null(newdata.x) or is.null(newdata.z), then the function returns the fitted values.

Arguments

object

Output of the functions mentioned in the Description (i.e. an object of the class PVS.kernel or PVS.kNN).

newdata.x

A matrix containing new observations of the functional covariate in the functional nonparametric component, collected by row.

newdata.z

Matrix containing the new observations of the scalar covariates derived from the discretisation of a curve, collected by row.

y.test

(optional) A vector containing the new observations of the response.

option

Allows the selection among the choices 1, 2 and 3 for PVS.kernel objects, and 1, 2, 3, and 4 for PVS.kNN objects. The default setting is 1. See the section Details.

...

Further arguments.

knearest.n

Only used for objects PVS.kNN if option=2, option=3 or option=4: sequence in which the number of nearest neighbours k.opt is selected. The default is object$knearest.

min.knn.n

Only used for objects PVS.kNN if option=2, option=3 or option=4: minumum value of the sequence in which the number of nearest neighbours k.opt is selected (thus, this number must be smaller than the sample size). The default is object$min.knn.

max.knn.n

Only used for objects PVS.kNN if option=2, option=3 or option=4: maximum value of the sequence in which the number of nearest neighbours k.opt is selected (thus, this number must be larger than min.kNN and smaller than the sample size). The default is object$max.knn.

step.n

Only used for objects PVS.kNN if option=2, option=3 or option=4: positive integer used to build the sequence of k-nearest neighbours in the following way: min.knn, min.knn + step.n, min.knn + 2*step.n, min.knn + 3*step.n,.... The default is object$step.

Author

German Aneiros Perez

Silvia Novo Diaz

Details

To obtain the predictions of the response for newdata.x and newdata.z, the following options are provided:

• If option=1, we maintain all the estimates (k.opt or h.opt and beta.est) to predict the functional nonparametric component of the model. As we use the estimates of the second step of the algorithm, only the train.2 is used as training sample to predict. Then, it should be noted that k.opt or h.opt may not be suitable to predict the functional nonparametric component of the model.

• If option=2, we maintain beta.est, while the tuning parameter (\(h\) or \(k\)) is selected again to predict the functional nonparametric component of the model. This selection is performed using the leave-one-out cross-validation (LOOCV) criterion in the associated functional nonparametric model and the complete training sample (i.e. train=c(train.1,train.2)), obtaining a global selection for \(h\) or \(k\). As we use the entire training sample (not just a subsample of it), the sample size is modified and, as a consequence, the parameters knearest, min.knn, max.knn, and step given to the function IASSMR.kNN.fit may need to be provided again to compute predictions. For that, we add the arguments knearest.n, min.knn.n, max.knn.n and step.mn.

• If option=3, we maintain only the indexes of the relevant variables selected by the IASSMR. We estimate again the linear coefficients using sfpl.kernel.fit or sfpl.kNN.fit, respectively, without penalisation (setting lambda.seq=0) and using the entire training sample (train=c(train.1,train.2)). The method provides two predictions (and MSEPs):

  • a) The prediction associated with option=1 for sfpl.kernel or sfpl.kNN class.

  • b) The prediction associated with option=2 for sfpl.kernel or sfpl.kNN class.

  (see the documentation of the functions predict.sfpl.kernel and predict.sfpl.kNN)

• If option=4 (an option only available for the class PVS.kNN) we maintain beta.est, while the tuning parameter \(k\) is selected again to predict the functional nonparametric component of the model. This selection is performed using LOOCV criterion in the functional nonparametric model associated and the complete training sample (i.e. train=c(train.1,train.2)), obtaining a local selection for \(k\).

See Also

PVS.kernel.fit, sfpl.kernel.fit and predict.sfpl.kernel or PVS.kNN.fit, sfpl.kNN.fit and predict.sfpl.kNN.

Examples

# \donttest{
data(Sugar)

y<-Sugar$ash
x<-Sugar$wave.290
z<-Sugar$wave.240

#Outliers
index.y.25 <- y > 25
index.atip <- index.y.25
(1:268)[index.atip]

#Dataset to model
x.sug <- x[!index.atip,]
z.sug<- z[!index.atip,]
y.sug <- y[!index.atip]

train<-1:216
test<-217:266

#Fit
fit.kernel<- PVS.kernel.fit(x=x.sug[train,],z=z.sug[train,], 
              y=y.sug[train],train.1=1:108,train.2=109:216,
              lambda.min.h=0.03,lambda.min.l=0.03,
              max.q.h=0.35, nknot=20,criterion="BIC",
              max.iter=5000)
fit.kNN<- PVS.kNN.fit(x=x.sug[train,],z=z.sug[train,], y=y.sug[train],
            train.1=1:108,train.2=109:216,lambda.min.h=0.07, 
            lambda.min.l=0.07, nknot=20,criterion="BIC",
            max.iter=5000)

#Preditions
predict(fit.kernel,newdata.x=x.sug[test,],newdata.z=z.sug[test,],y.test=y.sug[test],option=2)
predict(fit.kNN,newdata.x=x.sug[test,],newdata.z=z.sug[test,],y.test=y.sug[test],option=2)
# }