# Prediction for MFPLM `predict` method for the multi-functional partial linear model (MFPLM) fitted using `PVS.kernel.fit` or `PVS.kNN.fit`. ```r ## S3 method for class 'PVS.kernel' predict(object, newdata.x = NULL, newdata.z = NULL, y.test = NULL, option = NULL, ...) ## S3 method for class '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, ...) ``` ## 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`. ## 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 $k$. ## Returns 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. ## Author(s) German Aneiros Perez german.aneiros@udc.es Silvia Novo Diaz snovo@est-econ.uc3m.es ## See Also `PVS.kernel.fit`, `sfpl.kernel.fit` and `predict.sfpl.kernel` or `PVS.kNN.fit`, `sfpl.kNN.fit` and `predict.sfpl.kNN`. ## Examples ```r 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) ```

predict.mfplm function