fregre.pls: Functional Penalized PLS regression with scalar response

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/fregre.pc.R

Description

Computes functional linear regression between functional explanatory variable X(t) and scalar response Y using penalized Partial Least Squares (PLS)

Y=<\tilde{X},β>+ε

where <.,.> denotes the inner product on L_2 and ε are random errors with mean zero , finite variance σ^2 and E[X(t)ε]=0.
ν_1,...,ν_∞ orthonormal basis of PLS to represent the functional data as X(t)=∑_(k=1:∞) γ_k ν_k.

Usage

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fregre.pls(fdataobj, y = NULL, l = NULL, lambda = 0, P = c(0, 0, 1), ...)

Arguments

fdataobj

fdata class object.

y

Scalar response with length n.

l

Index of components to include in the model.

lambda

Amount of penalization. Default value is 0, i.e. no penalization is used.

P

If P is a vector: P are coefficients to define the penalty matrix object. By default P=c(0,0,1) penalize the second derivative (curvature) or acceleration. If P is a matrix: P is the penalty matrix object.

...

Further arguments passed to or from other methods.

Details

Functional (FPLS) algorithm maximizes the covariance between X(t) and the scalar response Y via the partial least squares (PLS) components. The functional penalized PLS are calculated in fdata2pls by alternative formulation of the NIPALS algorithm proposed by Kraemer and Sugiyama (2011).
Let {ν_k}_k=1:∞ the functional PLS components and X_i(t)=∑{k=1:∞} γ_{ik} ν_k and β(t)=∑{k=1:∞} β_k ν_k. The functional linear model is estimated by:

y.est=< X,β.est > \approx ∑{k=1:k_n} γ_k β_k


The response can be fitted by:

Value

Return:

Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es

References

Preda C. and Saporta G. PLS regression on a stochastic process. Comput. Statist. Data Anal. 48 (2005): 149-158.

N. Kraemer, A.-L. Boulsteix, and G. Tutz (2008). Penalized Partial Least Squares with Applications to B-Spline Transformations and Functional Data. Chemometrics and Intelligent Laboratory Systems, 94, 60 - 69. http://dx.doi.org/10.1016/j.chemolab.2008.06.009

Martens, H., Naes, T. (1989) Multivariate calibration. Chichester: Wiley.

Kraemer, N., Sugiyama M. (2011). The Degrees of Freedom of Partial Least Squares Regression. Journal of the American Statistical Association. Volume 106, 697-705.

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. http://www.jstatsoft.org/v51/i04/

See Also

See Also as: P.penalty and fregre.pls.cv.
Alternative method: fregre.pc.

Examples

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## Not run: 
data(tecator)
x<-tecator$absorp.fdata
y<-tecator$y$Fat
res=fregre.pls(x,y,c(1:8),lambda=10)
summary(res)

## End(Not run)

Example output

Loading required package: fda
Loading required package: splines
Loading required package: Matrix
Loading required package: fds
Loading required package: rainbow
Loading required package: MASS
Loading required package: pcaPP
Loading required package: RCurl

Attaching package:fdaThe following object is masked frompackage:graphics:

    matplot

Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-33. For overview type 'help("mgcv-package")'.
----------------------------------------------------------------------------------
 Functional Data Analysis and Utilities for Statistical Computing
 fda.usc version 2.0.2 (built on 2020-02-17) is now loaded
 fda.usc is running sequentially usign foreach package
 Please, execute ops.fda.usc() once to run in local parallel mode
 Deprecated functions: min.basis, min.np, anova.hetero, anova.onefactor, anova.RPm
 New functions: optim.basis, optim.np, fanova.hetero, fanova.onefactor, fanova.RPm
----------------------------------------------------------------------------------

Warning message:
In if (class(Minv) != "try-error") { :
  the condition has length > 1 and only the first element will be used
 *** Summary Functional Regression with Partial Least Squares*** 

-Call: fregre.pls(fdataobj = x, y = y, l = c(1:8), lambda = 10)

              Estimate Std. Error   t value      Pr(>|t|)
(Intercept) 18.1423256  0.1899909 95.490516 1.225261e-171
PLS1        -0.8147606  0.1206244 -6.754528  1.456586e-10
PLS2         8.6253070  0.3260360 26.455075  5.914682e-68
PLS3         5.7642481  0.2327310 24.767859  1.738403e-63
PLS4         6.3763077  0.4174746 15.273523  1.194715e-35
PLS5        19.7023847  1.8253711 10.793632  8.690502e-22
PLS6         9.6759513  2.8464063  3.399357  8.119417e-04
PLS7        24.0614833  3.6205276  6.645850  2.680142e-10
PLS8        53.6760792  2.3935314 22.425475  5.023804e-57

-R squared:  0.9542937
-Residual variance:  7.760754 on  204.5715  degrees of freedom
-Names of possible atypical curves: 43 44 
-Names of possible influence curves: 34 35 86 89 140 180 181 

fda.usc documentation built on Feb. 18, 2020, 1:07 a.m.