Non-parametric tilted bootstrap for PLS beta regression models

Provides a wrapper for the bootstrap function tilt.boot from the boot R package.
Implements non-parametric tilted bootstrap for PLS beta regression models by case resampling : the tilt.boot function will run an initial bootstrap with equal resampling probabilities (if required) and will use the output of the initial run to find resampling probabilities which put the value of the statistic at required values. It then runs an importance resampling bootstrap using the calculated probabilities as the resampling distribution.

Usage

tilt.bootplsbeta(
  object,
  typeboot = "plsmodel",
  statistic = coefs.plsRbeta,
  R = c(499, 250, 250),
  alpha = c(0.025, 0.975),
  sim = "ordinary",
  stype = "i",
  index = 1,
  stabvalue = 1e+06
)

Arguments

object: An object of class plsRbetamodel to bootstrap
typeboot: The type of bootstrap. Either (Y,X) boostrap (typeboot="plsmodel") or (Y,T) bootstrap (typeboot="fmodel_np"). Defaults to (Y,T) resampling.
statistic: A function which when applied to data returns a vector containing the statistic(s) of interest. statistic must take at least two arguments. The first argument passed will always be the original data. The second will be a vector of indices, frequencies or weights which define the bootstrap sample. Further, if predictions are required, then a third argument is required which would be a vector of the random indices used to generate the bootstrap predictions. Any further arguments can be passed to statistic through the ... argument.
R: The number of bootstrap replicates. Usually this will be a single positive integer. For importance resampling, some resamples may use one set of weights and others use a different set of weights. In this case R would be a vector of integers where each component gives the number of resamples from each of the rows of weights.
alpha: The alpha level to which tilting is required. This parameter is ignored if R[1] is 0 or if theta is supplied, otherwise it is used to find the values of theta as quantiles of the initial uniform bootstrap. In this case R[1] should be large enough that min(c(alpha, 1-alpha))*R[1] > 5, if this is not the case then a warning is generated to the effect that the theta are extreme values and so the tilted output may be unreliable.
sim: A character string indicating the type of simulation required. Possible values are "ordinary" (the default), "balanced", "permutation", or "antithetic".
stype: A character string indicating what the second argument of statistic represents. Possible values of stype are "i" (indices - the default), "f" (frequencies), or "w" (weights).
index: The index of the statistic of interest in the output from statistic. By default the first element of the output of statistic is used.
stabvalue: A value to hard threshold bootstrap estimates computed from atypical resamplings.

Value

An object of class "boot".

References

Frédéric Bertrand, Nicolas Meyer, Michèle Beau-Faller, Karim El Bayed, Izzie-Jacques Namer, Myriam Maumy-Bertrand (2013). Régression Bêta PLS. Journal de la Société Française de Statistique, 154(3):143-159. https://ojs-test.apps.ocp.math.cnrs.fr/index.php/J-SFdS/article/view/215

Author

Frédéric Bertrand
frederic.bertrand@lecnam.net
https://fbertran.github.io/homepage/

Examples

# \donttest{
data("GasolineYield",package="betareg")
yGasolineYield <- GasolineYield$yield
XGasolineYield <- GasolineYield[,2:5]
modplsRbeta <- plsRbeta(yGasolineYield, XGasolineYield, nt=3, 
modele="pls-beta")
#> ____************************************************____
#> 
#> Model: pls-beta 
#> 
#> Link: logit 
#> 
#> Link.phi: 
#> 
#> Type: ML 
#> 
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#> 
# GazYield.tilt.boot <- tilt.bootplsbeta(modplsRbeta,
# statistic=coefs.plsRbeta, R=c(499, 100, 100), 
# alpha=c(0.025, 0.975), sim="balanced", stype="i", index=1)
# boxplots.bootpls(GazYield.tilt.boot,1:2)
# }