PLS_beta function

Partial least squares beta regression models

This function implements Partial least squares beta regression models on complete or incomplete datasets.

PLS_beta(
  dataY,
  dataX,
  nt = 2,
  limQ2set = 0.0975,
  dataPredictY = dataX,
  modele = "pls",
  family = NULL,
  typeVC = "none",
  EstimXNA = FALSE,
  scaleX = TRUE,
  scaleY = NULL,
  pvals.expli = FALSE,
  alpha.pvals.expli = 0.05,
  MClassed = FALSE,
  tol_Xi = 10^(-12),
  weights,
  method,
  sparse = FALSE,
  sparseStop = TRUE,
  naive = FALSE,
  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

• 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.

• typeVC: type of leave one out cross validation. For back compatibility purpose.

  • list("none"): no cross validation
  • list("standard"): no cross validation
  • list("missingdata"): no cross validation
  • list("adaptative"): no cross validation

• EstimXNA: only for modele="pls". Set whether the missing X values have to be estimated.

• 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 not always possible for glm responses.

• pvals.expli: should individual p-values be reported to tune model selection ?

• alpha.pvals.expli: level of significance for predictors when pvals.expli=TRUE

• MClassed: number of missclassified cases, should only be used for binary responses

• tol_Xi: minimal value for Norm2(Xi) and $det(pp'*pp)$ 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: the link function for pls-glm-polr, logistic, probit, complementary log-log or cauchit (corresponding to a Cauchy latent variable).

• sparse: should the coefficients of non-significant predictors (<alpha.pvals.expli) be set to 0

• sparseStop: should component extraction stop when no significant predictors (<alpha.pvals.expli) are found

• naive: use the naive estimates for the Degrees of Freedom in plsR? Default is FALSE.

• 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 ?

Returns

Depends on the model that was used to fit the model.

Details

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.

The default estimator for Degrees of Freedom is the Kramer and Sugiyama's one which only works for classical plsR models. For these models, Information criteria are computed accordingly to these estimations. Naive Degrees of Freedom and Information Criteria are also provided for comparison purposes. For more details, see Kraemer, N., Sugiyama M. (2010). "The Degrees of Freedom of Partial Least Squares Regression". preprint, http://arxiv.org/abs/1002.4112.

Note

Use plsRbeta instead.

Examples

data("GasolineYield",package="betareg")
yGasolineYield <- GasolineYield$yield
XGasolineYield <- GasolineYield[,2:5]
modpls <- PLS_beta(yGasolineYield,XGasolineYield,nt=3,modele="pls-beta")
modpls$pp
modpls$Coeffs
modpls$Std.Coeffs
modpls$InfCrit
modpls$PredictY[1,]
rm("modpls")

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. http://publications-sfds.math.cnrs.fr/index.php/J-SFdS/article/view/215

See Also

PLS_beta_wvc and PLS_beta_kfoldcv

Author(s)

Frédéric Bertrand

frederic.bertrand@utt.fr

https://fbertran.github.io/homepage/