Partial least squares regression beta models with kfold cross validation

This function implements kfold cross validation on complete or incomplete datasets for partial least squares beta regression models

Usage

PLS_beta_kfoldcv(
  dataY,
  dataX,
  nt = 2,
  limQ2set = 0.0975,
  modele = "pls",
  family = NULL,
  K = nrow(dataX),
  NK = 1,
  grouplist = NULL,
  random = FALSE,
  scaleX = TRUE,
  scaleY = NULL,
  keepcoeffs = FALSE,
  keepfolds = FALSE,
  keepdataY = TRUE,
  keepMclassed = FALSE,
  tol_Xi = 10^(-12),
  weights,
  method,
  link = NULL,
  link.phi = NULL,
  type = "ML",
  verbose = TRUE
)

Arguments

dataY

response (training) dataset

dataX

predictor(s) (training) dataset

nt

number of components to be extracted

limQ2set

limit value for the Q2

modele

name of the PLS glm or PLS beta model to be fitted ("pls", "pls-glm-Gamma", "pls-glm-gaussian", "pls-glm-inverse.gaussian", "pls-glm-logistic", "pls-glm-poisson", "pls-glm-polr", "pls-beta"). Use "modele=pls-glm-family" to enable the family option.

family

a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See family for details of family functions.) To use the family option, please set modele="pls-glm-family". User defined families can also be defined. See details.

K

number of groups

NK

number of times the group division is made

grouplist

to specify the members of the K groups

random

should the K groups be made randomly

scaleX

scale the predictor(s) : must be set to TRUE for modele="pls" and should be for glms pls.

scaleY

scale the response : Yes/No. Ignored since non always possible for glm responses.

keepcoeffs

shall the coefficients for each model be returned

keepfolds

shall the groups' composition be returned

keepdataY

shall the observed value of the response for each one of the predicted value be returned

keepMclassed

shall the number of miss classed be returned (unavailable)

tol_Xi

minimal value for Norm2(Xi) and \(\mathrm{det}(pp' \times pp)\) if there is any missing value in the dataX. It defaults to \(10^{-12}\)

weights

an optional vector of 'prior weights' to be used in the fitting process. Should be NULL or a numeric vector.

method

logistic, probit, complementary log-log or cauchit (corresponding to a Cauchy latent variable).

link

character specification of the link function in the mean model (mu). Currently, "logit", "probit", "cloglog", "cauchit", "log", "loglog" are supported. Alternatively, an object of class "link-glm" can be supplied.

link.phi

character specification of the link function in the precision model (phi). Currently, "identity", "log", "sqrt" are supported. The default is "log" unless formula is of type y~x where the default is "identity" (for backward compatibility). Alternatively, an object of class "link-glm" can be supplied.

type

character specification of the type of estimator. Currently, maximum likelihood ("ML"), ML with bias correction ("BC"), and ML with bias reduction ("BR") are supported.

verbose

should info messages be displayed ?

Value

results_kfolds

list of NK. Each element of the list sums up the results for a group division:

list

of K matrices of size about nrow(dataX)/K * nt with the predicted values for a growing number of components

list()

...

list

of K matrices of size about nrow(dataX)/K * nt with the predicted values for a growing number of components

folds

list of NK. Each element of the list sums up the informations for a group division:

list

of K vectors of length about nrow(dataX) with the numbers of the rows of dataX that were used as a training set

list()

...

list

of K vectors of length about nrow(dataX) with the numbers of the rows of dataX that were used as a training set

dataY_kfolds

list of NK. Each element of the list sums up the results for a group division:

list

of K matrices of size about nrow(dataX)/K * 1 with the observed values of the response

list()

...

list

of K matrices of size about nrow(dataX)/K * 1 with the observed values of the response

call

the call of the function

Details

Predicts 1 group with the K-1 other groups. Leave one out cross validation is thus obtained for K==nrow(dataX).

There are seven different predefined models with predefined link functions available :

list("\"pls\"")

ordinary pls models

list("\"pls-glm-Gamma\"")

glm gaussian with inverse link pls models

list("\"pls-glm-gaussian\"")

glm gaussian with identity link pls models

list("\"pls-glm-inverse-gamma\"")

glm binomial with square inverse link pls models

list("\"pls-glm-logistic\"")

glm binomial with logit link pls models

list("\"pls-glm-poisson\"")

glm poisson with log link pls models

list("\"pls-glm-polr\"")

glm polr with logit link pls models

Using the "family=" option and setting "modele=pls-glm-family" allows changing the family and link function the same way as for the glm function. As a consequence user-specified families can also be used.

The

accepts the links (as names) identity, log and inverse.

list("gaussian")

accepts the links (as names) identity, log and inverse.

family

accepts the links (as names) identity, log and inverse.

The

accepts the links logit, probit, cauchit, (corresponding to logistic, normal and Cauchy CDFs respectively) log and cloglog (complementary log-log).

list("binomial")

accepts the links logit, probit, cauchit, (corresponding to logistic, normal and Cauchy CDFs respectively) log and cloglog (complementary log-log).

family

accepts the links logit, probit, cauchit, (corresponding to logistic, normal and Cauchy CDFs respectively) log and cloglog (complementary log-log).

The

accepts the links inverse, identity and log.

list("Gamma")

accepts the links inverse, identity and log.

family

accepts the links inverse, identity and log.

The

accepts the links log, identity, and sqrt.

list("poisson")

accepts the links log, identity, and sqrt.

family

accepts the links log, identity, and sqrt.

The

accepts the links 1/mu^2, inverse, identity and log.

list("inverse.gaussian")

accepts the links 1/mu^2, inverse, identity and log.

family

accepts the links 1/mu^2, inverse, identity and log.

The

accepts the links logit, probit, cloglog, identity, inverse, log, 1/mu^2 and sqrt.

list("quasi")

accepts the links logit, probit, cloglog, identity, inverse, log, 1/mu^2 and sqrt.

family

accepts the links logit, probit, cloglog, identity, inverse, log, 1/mu^2 and sqrt.

The function

can be used to create a power link function.

list("power")

can be used to create a power link function.

Non-NULL weights can be used to indicate that different observations have different dispersions (with the values in weights being inversely proportional to the dispersions); or equivalently, when the elements of weights are positive integers w_i, that each response y_i is the mean of w_i unit-weight observations.

Note

Works for complete and incomplete datasets.

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

See also

kfolds2coeff, kfolds2Pressind, kfolds2Press, kfolds2Mclassedind, kfolds2Mclassed and kfolds2CVinfos_beta to extract and transform results from kfold cross validation.

Author

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

Examples

if (FALSE) { # \dontrun{
data("GasolineYield",package="betareg")
yGasolineYield <- GasolineYield$yield
XGasolineYield <- GasolineYield[,2:5]
bbb <- PLS_beta_kfoldcv(yGasolineYield,XGasolineYield,nt=3,modele="pls-beta")
kfolds2CVinfos_beta(bbb)
} # }