Impact points selection of functional predictor and regression using local maxima distance correlation (LMDC)

LMDC.select function selects impact points of functional predictior using local maxima distance correlation (LMDC) for a scalar response given.
LMDC.regre function fits a multivariate regression method using the selected impact points like covariates for a scalar response.

Usage

LMDC.select(
  y,
  covar,
  data,
  tol = 0.06,
  pvalue = 0.05,
  plot = FALSE,
  local.dc = TRUE,
  smo = FALSE,
  verbose = FALSE
)

LMDC.regre(
  y,
  covar,
  data,
  newdata,
  pvalue = 0.05,
  method = "lm",
  par.method = NULL,
  plot = FALSE,
  verbose = FALSE
)

Arguments

y: name of the response variable.
covar: vector with the names of the covaviables (or points of impact) with length p.
data: data frame with length n rows and at least p + 1 columns, containing the scalar response and the potencial p covaviables (or points of impact) in the model.
tol: Tolerance value for distance correlation and imapct point.
pvalue: pvalue of bias corrected distance correlation t-test.
plot: logical value, if TRUE plots the distance correlation curve for each covariate in multivariate case and in each discretization points (argvals) in the functional case.
local.dc: Compute local distance correlation.
smo: logical. If TRUE, the curve of distance correlation computed in the impact points is smoothed using B-spline representation with a suitable number of basis elements.
verbose: print iterative and relevant steps of the procedure.
newdata: An optional data frame in which to look for variables with which to predict.
method: Name of regression method used, see details. This argument is used in do.call function like "what" argument.
par.method: List of parameters used to call the method. This argument is used in do.call function like "args" argument.

Value

LMDC.select: function returns a list of two elements:
cor: the value of distance correlation for each covariate.
maxLocal: index or locations of local maxima distance correlations.
LMDC.regre: function returns a list of folowing elements:
model: object corresponding to the estimated method using the selected variables.
xvar: names of selected variables (impact points).
edf: effective degrees of freedom.
nvar: number of selected variables (impact points).

Details

String of characters corresponding to the name of the regression method called. Model available options:

"lm": Step-wise lm regression model (uses lm function, stats package). Recommended for linear models, test linearity using. flm.test function.
"gam": Step-wise gam regression model (uses gam function, mgcv package). Recommended for non-linear models.

Models that use the indicated function of the required package:

"svm": Support vector machine (svm function, e1071 package).
"knn": k-nearest neighbor regression (knnn.reg function, FNN package).
"lars": Least Angle Regression using Lasso (lars function, lars package).
"glmnet": Lasso and Elastic-Net Regularized Generalized Linear Models (glmnet and cv.glmnet function, glmnet package).
"rpart": Recursive partitioning for regression a (rpart function, rpart package).
"flam": Fit the Fused Lasso Additive Model for a Sequence of Tuning Parameters (flam function, flam package).
"novas": NOnparametric VAriable Selection (code available in
https://www.math.univ-toulouse.fr/~ferraty/SOFTWARES/NOVAS/novas-routines.R).
"cosso": Fit Regularized Nonparametric Regression Models Using COSSO Penalty (cosso function, cosso package).
"npreg": kernel regression estimate of a one (1) dimensional dependent variable on p-variate explanatory data (npreg function, np package).
"mars": Multivariate adaptive regression splines (mars function, mda package).
"nnet": Fit Neural Networks (nnet function, nnet package).
"lars": Fits Least Angle Regression, Lasso and Infinitesimal Forward Stagewise regression models (lars function, lars package).

References

Ordonez, C., Oviedo de la Fuente, M., Roca-Pardinas, J., Rodriguez-Perez, J. R. (2018). Determining optimum wavelengths for leaf water content estimation from reflectance: A distance correlation approach. Chemometrics and Intelligent Laboratory Systems. 173,41-50 doi:10.1016/j.chemolab.2017.12.001 .

Author

Manuel Oviedo de la Fuente manuel.oviedo@udc.es

Examples

if (FALSE) { # \dontrun{
data(tecator)
absorp=fdata.deriv(tecator$absorp.fdata,2)
ind=1:129
x=absorp[ind,]
y=tecator$y$Fat[ind]
newx=absorp[-ind,]
newy=tecator$y$Fat[-ind]

## Functional PC regression
res.pc=fregre.pc(x,y,1:6)
pred.pc=predict(res.pc,newx)

# Functional regression with basis representation
res.basis=fregre.basis.cv(x,y)
pred.basis=predict(res.basis[[1]],newx)

# Functional nonparametric regression
res.np=fregre.np.cv(x,y)
pred.np=predict(res.np,newx)

dat    <- data.frame("y"=y,x$data)
newdat <- data.frame("y"=newy,newx$data)

res.gam=fregre.gsam(y~s(x),data=list("df"=dat,"x"=x))
pred.gam=predict(res.gam,list("x"=newx))

dc.raw <- LMDC.select("y",data=dat, tol = 0.05, pvalue= 0.05,
                      plot=F, smo=T,verbose=F)
covar <- paste("X",dc.raw$maxLocal,sep="")                      
# Preselected design/impact points 
covar
ftest<-flm.test(dat[,-1],dat[,"y"], B=500, verbose=F,
    plot.it=F,type.basis="pc",est.method="pc",p=4,G=50)
    
if (ftest$p.value>0.05) { 
  # Linear relationship, step-wise lm is recommended
  out <- LMDC.regre("y",covar,dat,newdat,pvalue=.05,
              method ="lm",plot=F,verbose=F)
} else {
 # Non-Linear relationship, step-wise gam is recommended
  out <- LMDC.regre("y",covar,dat,newdat,pvalue=.05,
              method ="gam",plot=F,verbose=F) }  
             
# Final  design/impact points
out$xvar

# Predictions
mean((newy-pred.pc)^2)                
mean((newy-pred.basis)^2) 
mean((newy-pred.np)^2)              
mean((newy-pred.gam)^2) 
mean((newy-out$pred)^2)
} # }