predict.IASSMR {fsemipar}

Prediction for MFPLSIM

Description

predict method for the multi-functional partial linear single-index model (MFPLSIM) fitted using IASSMR.kernel.fit or IASSMR.kNN.fit.

Usage

## S3 method for class 'IASSMR.kernel'
predict(object, newdata.x = NULL, newdata.z = NULL,
  y.test = NULL, option = NULL, ...)
## S3 method for class 'IASSMR.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, ...)

Arguments

object

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

newdata.x

A matrix containing new observations of the functional covariate in the functional single-index 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 choice between 1, 2 and 3. The default is 1. See the section Details.

...

Further arguments.

knearest.n

Only used for objects IASSMR.kNN if option=2 or option=3: vector of positive integers containing the sequence in which the number of nearest neighbours k.opt is selected. The default is object$knearest.

min.knn.n

Only used for objects IASSMR.kNN if option=2 or option=3: minumum value of the sequence in which the number of 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 IASSMR.kNN if option=2 or option=3: maximum value of the sequence in which the number of 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 IASSMR.kNN if option=2 or option=3: positive integer used to build the sequence of k-nearest neighbours as follows: min.knn, min.knn + step.n, min.knn + 2*step.n, min.knn + 3*step.n,.... The default is object$step.

Details

Three options are provided to obtain the predictions of the response for newdata.x and newdata.z:

• If option=1, we maintain all the estimates (k.opt or h.opt, theta.est and beta.est) to predict the functional single-index 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 single-index component of the model.

• If option=2, we maintain theta.est and beta.est, while the tuning parameter (h or k) is selected again to predict the functional single-index component of the model. This selection is performed using the leave-one-out cross-validation criterion in the functional single-index model associated and the complete training sample (i.e. train=c(train.1,train.2)). 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, 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.n.

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

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

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

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

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), the function returns the fitted values.

Author(s)

German Aneiros Perez [e-mail]

Silvia Novo Diaz [e-mail]

See Also

sfplsim.kernel.fit, sfplsim.kNN.fit, IASSMR.kernel.fit, IASSMR.kNN.fit.

Examples

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

fit.kNN<- IASSMR.kNN.fit(x=x.sug[train,],z=z.sug[train,], y=y.sug[train],
          train.1=1:108,train.2=109:216,nknot.theta=2,lambda.min.h=0.07,
          lambda.min.l=0.07, max.knn=20, nknot=20,criterion="BIC",
          max.iter=5000)

#Predictions
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)