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Light version of PLS_beta for cross validation purposes

Source: R/PLS_beta_wvc.R
PLS_beta_wvc.Rd

Light version of PLS_beta for cross validation purposes either on complete or incomplete datasets.

Usage

PLS_beta_wvc(
  dataY,
  dataX,
  nt = 2,
  dataPredictY = dataX,
  modele = "pls",
  family = NULL,
  scaleX = TRUE,
  scaleY = NULL,
  keepcoeffs = FALSE,
  keepstd.coeffs = FALSE,
  tol_Xi = 10^(-12),
  weights,
  method = "logistic",
  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

dataPredictY

predictor(s) (testing) dataset

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.

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

whether the coefficients of the linear fit on link scale of unstandardized eXplanatory variables should be returned or not.

keepstd.coeffs

whether the coefficients of the linear fit on link scale of standardized eXplanatory variables should be returned or not.

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).

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.

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

valsPredict

nrow(dataPredictY) * nt matrix of the predicted values

list("coeffs")

If the coefficients of the eXplanatory variables were requested:
i.e. keepcoeffs=TRUE.
ncol(dataX) * 1 matrix of the coefficients of the the eXplanatory variables

Details

This function is called by PLS_beta_kfoldcv_formula in order to perform cross validation either on complete or incomplete datasets.

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.

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

PLS_beta for more detailed results, PLS_beta_kfoldcv for cross validating models and PLS_lm_wvc for the same function dedicated to plsR models

Author

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

Examples



data("GasolineYield",package="betareg")
yGasolineYield <- GasolineYield$yield
XGasolineYield <- GasolineYield[,2:5]
modpls <- PLS_beta_wvc(yGasolineYield,XGasolineYield,nt=3,modele="pls-beta")
#> ____************************************************____
#> 
#> Model: pls-beta 
#> 
#> Link: logit 
#> 
#> Link.phi: 
#> 
#> Type: ML 
#> 
#> ____Predicting X without NA neither in X nor in Y____
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ****________________________________________________****
#> 
modpls
#> $valsPredict
#>          [,1]       [,2]       [,3]
#> 1  0.18187561 0.11903943 0.10952240
#> 2  0.28144600 0.21696140 0.20261811
#> 3  0.40832135 0.36230655 0.34425424
#> 4  0.53264139 0.51765777 0.49957441
#> 5  0.09146549 0.06943426 0.07502378
#> 6  0.13577318 0.11596641 0.12544647
#> 7  0.22233799 0.21890398 0.23599703
#> 8  0.10602196 0.07790980 0.07966260
#> 9  0.16157484 0.13521897 0.13883717
#> 10 0.25042473 0.23903046 0.24599354
#> 11 0.11891955 0.09303271 0.09654273
#> 12 0.18591623 0.16653971 0.17329467
#> 13 0.27871743 0.28018396 0.29138506
#> 14 0.35738689 0.38179969 0.39599093
#> 15 0.17161846 0.15752793 0.15803548
#> 16 0.25185901 0.25707499 0.25904081
#> 17 0.29688709 0.31561682 0.31849155
#> 18 0.11068533 0.09850211 0.10778989
#> 19 0.20894958 0.22098448 0.24058365
#> 20 0.27062891 0.30383939 0.32869099
#> 21 0.06553811 0.05499223 0.05039617
#> 22 0.08837118 0.08064164 0.07436527
#> 23 0.15947909 0.17048346 0.15961238
#> 24 0.23275612 0.27146324 0.25733075
#> 25 0.08053348 0.07770608 0.07413182
#> 26 0.14334064 0.16067020 0.15503960
#> 27 0.24074422 0.30093955 0.29386264
#> 28 0.12150336 0.13720602 0.13615557
#> 29 0.19979036 0.25165193 0.25145287
#> 30 0.09173971 0.11343104 0.10618428
#> 31 0.10162505 0.12869524 0.12076561
#> 32 0.14395482 0.19625333 0.18584054
#> 
#> $valsPredictPhis
#>        [,1]     [,2]     [,3]
#> 1  89.08427 199.6073 231.1113
#> 2  89.08427 199.6073 231.1113
#> 3  89.08427 199.6073 231.1113
#> 4  89.08427 199.6073 231.1113
#> 5  89.08427 199.6073 231.1113
#> 6  89.08427 199.6073 231.1113
#> 7  89.08427 199.6073 231.1113
#> 8  89.08427 199.6073 231.1113
#> 9  89.08427 199.6073 231.1113
#> 10 89.08427 199.6073 231.1113
#> 11 89.08427 199.6073 231.1113
#> 12 89.08427 199.6073 231.1113
#> 13 89.08427 199.6073 231.1113
#> 14 89.08427 199.6073 231.1113
#> 15 89.08427 199.6073 231.1113
#> 16 89.08427 199.6073 231.1113
#> 17 89.08427 199.6073 231.1113
#> 18 89.08427 199.6073 231.1113
#> 19 89.08427 199.6073 231.1113
#> 20 89.08427 199.6073 231.1113
#> 21 89.08427 199.6073 231.1113
#> 22 89.08427 199.6073 231.1113
#> 23 89.08427 199.6073 231.1113
#> 24 89.08427 199.6073 231.1113
#> 25 89.08427 199.6073 231.1113
#> 26 89.08427 199.6073 231.1113
#> 27 89.08427 199.6073 231.1113
#> 28 89.08427 199.6073 231.1113
#> 29 89.08427 199.6073 231.1113
#> 30 89.08427 199.6073 231.1113
#> 31 89.08427 199.6073 231.1113
#> 32 89.08427 199.6073 231.1113
#> 
rm("modpls")