# Prediction for SFPLSIM and MFPLSIM (using FASSMR) `predict` S3 method for: * Semi-functional partial linear single-index model (SFPLSIM) fitted using `sfplsim.kernel.fit` or `sfplsim.kNN.fit`. * Multi-functional partial linear single-index model (MFPLSIM) fitted using `FASSMR.kernel.fit` or `FASSMR.kNN.fit`. ```r ## S3 method for class 'sfplsim.kernel' predict(object, newdata.x = NULL, newdata.z = NULL, y.test = NULL, option = NULL, ...) ## S3 method for class 'sfplsim.kNN' predict(object, newdata.x = NULL, newdata.z = NULL, y.test = NULL, option = NULL, ...) ## S3 method for class 'FASSMR.kernel' predict(object, newdata.x = NULL, newdata.z = NULL, y.test = NULL, option = NULL, ...) ## S3 method for class 'FASSMR.kNN' predict(object, newdata.x = NULL, newdata.z = NULL, y.test = NULL, option = NULL, ...) ``` ## Arguments - `object`: Output of the functions mentioned in the `Description` (i.e. an object of the class `sfplsim.kernel`, `sfplsim.kNN`, `FASSMR.kernel` or `FASSMR.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 (SFPLSIM) or of the scalar covariates coming from the discretisation of a curve (MFPLSIM), collected by row. - `y.test`: (optional) A vector containing the new observations of the response. - `option`: Allows the choice between 1 and 2. The default is 1. See the section `Details`. - ``...``: Further arguments passed to or from other methods. ## Details Two options are provided to obtain the predictions of the response for `newdata.x` and `newdata.z`: * If `option=1`, we maintain all the estimations (`k.opt` or `h.opt`, `theta.est` and `beta.est`) 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 associated functional single-index model. ## 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 `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 `sfplsim.kernel.fit`, `sfplsim.kNN.fit`, `FASSMR.kernel.fit` or `FASSMR.kNN.fit`. ## Examples ```r data("Tecator") y<-Tecator$fat X<-Tecator$absor.spectra2 z1<-Tecator$protein z2<-Tecator$moisture #Quadratic, cubic and interaction effects of the scalar covariates. z.com<-cbind(z1,z2,z1^2,z2^2,z1^3,z2^3,z1*z2) train<-1:160 test<-161:215 #SFPLSIM fit. Convergence errors for some theta are obtained. s.fit.kernel<-sfplsim.kernel.fit(x=X[train,], z=z.com[train,], y=y[train], max.q.h=0.35,lambda.min.l=0.01, factor.pn=2, nknot.theta=4, criterion="BIC", range.grid=c(850,1050), nknot=20, max.iter=5000) s.fit.kNN<-sfplsim.kNN.fit(y=y[train],x=X[train,], z=z.com[train,], max.knn=20,lambda.min.l=0.01, factor.pn=2, nknot.theta=4, criterion="BIC",range.grid=c(850,1050), nknot=20, max.iter=5000) predict(s.fit.kernel,newdata.x=X[test,],newdata.z=z.com[test,], y.test=y[test],option=2) predict(s.fit.kNN,newdata.x=X[test,],newdata.z=z.com[test,], y.test=y[test],option=2) 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 m.fit.kernel <- FASSMR.kernel.fit(x=x.sug[train,],z=z.sug[train,], y=y.sug[train], nknot.theta=2, lambda.min.l=0.03, max.q.h=0.35,num.h = 10, nknot=20,criterion="BIC", max.iter=5000) m.fit.kNN<- FASSMR.kNN.fit(x=x.sug[train,],z=z.sug[train,], y=y.sug[train], nknot.theta=2, lambda.min.l=0.03, max.knn=20,nknot=20,criterion="BIC",max.iter=5000) predict(m.fit.kernel,newdata.x=x.sug[test,],newdata.z=z.sug[test,], y.test=y.sug[test],option=2) predict(m.fit.kNN,newdata.x=x.sug[test,],newdata.z=z.sug[test,], y.test=y.sug[test],option=2) ```

predict.sfplsim.FASSMR function