This function implements Partial least squares Regression generalized linear models complete or incomplete datasets.

plsRbeta(x, …)
# S3 method for default
plsRbetamodel(dataY,dataX,nt=2,limQ2set=.0975,
dataPredictY=dataX,modele="pls",family=NULL,typeVC="none",EstimXNA=FALSE,
scaleX=TRUE,scaleY=NULL,pvals.expli=FALSE,alpha.pvals.expli=.05,
MClassed=FALSE,tol_Xi=10^(-12),weights,method,sparse=FALSE,sparseStop=TRUE,
# S3 method for formula
plsRbetamodel(formula,data=NULL,nt=2,limQ2set=.0975,
dataPredictY,modele="pls",family=NULL,typeVC="none",EstimXNA=FALSE,
scaleX=TRUE,scaleY=NULL,pvals.expli=FALSE,alpha.pvals.expli=.05,
MClassed=FALSE,tol_Xi=10^(-12),weights,subset,start=NULL,etastart,
mustart,offset,method="glm.fit",control= list(),contrasts=NULL,
verbose=TRUE)

## Arguments

x a formula or a response (training) dataset response (training) dataset predictor(s) (training) dataset an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under 'Details'. an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which plsRbeta is called. number of components to be extracted limit value for the Q2 predictor(s) (testing) dataset 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. 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. type of leave one out cross validation. For back compatibility purpose. noneno cross validation standardno cross validation missingdatano cross validation adaptativeno cross validation only for modele="pls". Set whether the missing X values have to be estimated. scale the predictor(s) : must be set to TRUE for modele="pls" and should be for glms pls. scale the response : Yes/No. Ignored since non always possible for glm responses. should individual p-values be reported to tune model selection ? level of significance for predictors when pvals.expli=TRUE number of missclassified cases, should only be used for binary responses minimal value for Norm2(Xi) and $$\mathrm{det}(pp' \times pp)$$ if there is any missing value in the dataX. It defaults to $$10^{-12}$$ an optional vector of 'prior weights' to be used in the fitting process. Should be NULL or a numeric vector. an optional vector specifying a subset of observations to be used in the fitting process. starting values for the parameters in the linear predictor. starting values for the linear predictor. starting values for the vector of means. this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases. One or more offset terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See model.offset. the method to be used in fitting the model. The default method "glm.fit" uses iteratively reweighted least squares (IWLS). User-supplied fitting functions can be supplied either as a function or a character string naming a function, with a function which takes the same arguments as glm.fit. a list of parameters for controlling the fitting process. For glm.fit this is passed to glm.control. an optional list. See the contrasts.arg of model.matrix.default. should the coefficients of non-significant predictors (<alpha.pvals.expli) be set to 0 should component extraction stop when no significant predictors (<alpha.pvals.expli) are found Use the naive estimates for the Degrees of Freedom in plsR? Default is FALSE. 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. character specification of the type of estimator. Currently, maximum likelihood ("ML"), ML with bias correction ("BC"), and ML with bias reduction ("BR") are supported. should info messages be displayed ? arguments to pass to plsRmodel.default or to plsRmodel.formula

## Details

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

"pls"

ordinary pls models

"pls-glm-Gamma"

glm gaussian with inverse link pls models

"pls-glm-gaussian"

glm gaussian with identity link pls models

"pls-glm-inverse-gamma"

glm binomial with square inverse link pls models

"pls-glm-logistic"

glm binomial with logit link pls models

"pls-glm-poisson"

glm poisson with log link pls models

"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 gaussian family

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

The binomial family

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

The Gamma family

accepts the links inverse, identity and log.

The poisson family

accepts the links log, identity, and sqrt.

The inverse.gaussian family

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

The quasi family

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

The function power

can be used to create a power link function.

A typical predictor has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with any duplicates removed.

A specification of the form first:second indicates the the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first + second + first:second.

The terms in the formula will be re-ordered so that main effects come first, followed by the interactions, all second-order, all third-order and so on: to avoid this pass a terms object as the formula.

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.

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.

## Value

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

## 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

## Note

Use plsRbeta instead.

plsR and plsRglm

## Examples


data("GasolineYield",package="betareg")
modpls <- plsRbeta(yield~.,data=GasolineYield,nt=3,modele="pls-beta")#> ____************************************************____
#>
#> Model: pls-beta
#>
#>
#>
#> Type: ML
#>
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Predicting X without NA neither in X or Y____
#> ****________________________________________________****
#> modpls$pp#> Comp_ 1 Comp_ 2 Comp_ 3 #> gravity 0.37895923 -0.42864981 0.50983922 #> pressure 0.61533000 -0.41618828 -0.01737302 #> temp10 -0.50627633 0.47379983 -0.47750566 #> temp 0.30248369 0.60751756 0.28239621 #> batch1 0.50274128 -0.30221156 -0.25801764 #> batch2 -0.14241033 -0.13859422 0.80068659 #> batch3 -0.04388172 -0.17303214 0.48564161 #> batch4 0.11299471 -0.08302689 0.04755182 #> batch5 0.23341035 0.08396326 -0.51238456 #> batch6 0.07974302 0.07209943 -0.30710455 #> batch7 -0.37365392 -0.02133356 0.81852001 #> batch8 -0.12891598 0.16967195 -0.06904725 #> batch9 -0.02230288 0.19425476 -0.57189134 #> batch10 -0.25409429 0.28587553 -0.61277072modpls$Coeffs#>                    [,1]
#> Intercept -4.1210566077
#> gravity    0.0157208676
#> pressure   0.0305159627
#> temp10    -0.0074167766
#> temp       0.0108057945
#> batch1     0.0910284843
#> batch2     0.1398537354
#> batch3     0.2287070465
#> batch4    -0.0008124326
#> batch5     0.1018679027
#> batch6     0.1147971957
#> batch7    -0.1005469609
#> batch8    -0.0447907428
#> batch9    -0.0706292318
#> batch10   -0.1984703429modpls$Std.Coeffs#> [,1] #> Intercept -1.5526788976 #> gravity 0.0885938394 #> pressure 0.0799466278 #> temp10 -0.2784359925 #> temp 0.7537685874 #> batch1 0.0305865495 #> batch2 0.0414169259 #> batch3 0.0677303525 #> batch4 -0.0002729861 #> batch5 0.0301676274 #> batch6 0.0339965674 #> batch7 -0.0337848600 #> batch8 -0.0132645358 #> batch9 -0.0173701781 #> batch10 -0.0587759166modpls$InfCrit#>                  AIC        BIC Chi2_Pearson_Y      RSS_Y pseudo_R2_Y      R2_Y
#> Nb_Comp_0  -52.77074  -49.83927       30.72004 0.35640772          NA        NA
#> Nb_Comp_1  -87.96104  -83.56383       31.31448 0.11172576   0.6879757 0.6865226
#> Nb_Comp_2 -114.10269 -108.23975       33.06807 0.04650238   0.8671800 0.8695248
#> Nb_Comp_3 -152.71170 -145.38302       30.69727 0.01138837   0.9526757 0.9680468modpls$PredictY[1,]#> gravity pressure temp10 temp batch1 batch2 batch3 #> 2.0495333 1.6866554 -1.3718198 -1.8219769 2.6040833 -0.3165683 -0.3165683 #> batch4 batch5 batch6 batch7 batch8 batch9 batch10 #> -0.3720119 -0.3165683 -0.3165683 -0.3720119 -0.3165683 -0.2541325 -0.3165683 rm("modpls") data("GasolineYield",package="betareg") yGasolineYield <- GasolineYield$yield
XGasolineYield <- GasolineYield[,2:5]
modpls <- plsRbeta(yGasolineYield,XGasolineYield,nt=3,modele="pls-beta")#> ____************************************************____
#>
#> Model: pls-beta
#>
#>
#>
#> Type: ML
#>
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#> modpls$pp#> Comp_ 1 Comp_ 2 Comp_ 3 #> gravity 0.4590380 -0.4538663 -2.5188256 #> pressure 0.6395524 -0.4733525 0.6488823 #> temp10 -0.5435643 0.5292108 -1.3295905 #> temp 0.5682795 0.5473174 -0.2156423modpls$Coeffs#>                   [,1]
#> Intercept -3.324462301
#> gravity    0.001577508
#> pressure   0.072027686
#> temp10    -0.008398771
#> temp       0.010365973modpls$Std.Coeffs#> [,1] #> Intercept -1.547207760 #> gravity 0.008889933 #> pressure 0.188700277 #> temp10 -0.315301400 #> temp 0.723088387modpls$InfCrit#>                  AIC        BIC Chi2_Pearson_Y      RSS_Y pseudo_R2_Y      R2_Y
#> Nb_Comp_0  -52.77074  -49.83927       30.72004 0.35640772          NA        NA
#> Nb_Comp_1 -112.87383 -108.47662       30.57369 0.05211039   0.8498691 0.8537900
#> Nb_Comp_2 -136.43184 -130.56889       30.97370 0.02290022   0.9256771 0.9357471
#> Nb_Comp_3 -139.08440 -131.75572       31.08224 0.02022386   0.9385887 0.9432564modpls\$PredictY[1,]#>   gravity  pressure    temp10      temp
#>  2.049533  1.686655 -1.371820 -1.821977 rm("modpls")