plsRglm (version 0.7.6)

PLS_lm_formula: Partial least squares Regression models with leave one out cross validation

Description

This function implements Partial least squares Regression models with leave one out cross validation for complete or incomplete datasets (formula specification of the model).

Usage

PLS_lm_formula(formula,data=NULL,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,subset,contrasts=NULL,sparse=FALSE,sparseStop=TRUE,naive=FALSE)

Arguments

formula

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'.

data

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 fro

nt

number of components to be extracted

limQ2set

limit value for the Q2

dataPredictY

predictor(s) (testing) dataset

modele

name of the PLS model to be fitted, only ("pls" available for this fonction.

family

for the present moment the family argument is ignored and set thanks to the value of modele.

typeVC

type of leave one out cross validation. Several procedures are available and may be forced. [object Object],[object Object],[object Object],[object Object]

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 $\mathrm{det}(pp' \times pp)$ 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.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

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.

Value

• nr
  Description of 'comp1'
• nc
  Description of 'comp2'
• nt
  Description of 'comp2'
• ww
  Description of 'comp2'
• wwnorm
  Description of 'comp2'
• wwetoile
  Description of 'comp2'
• tt
  Description of 'comp2'
• pp
  Description of 'comp2'
• CoeffC
  Description of 'comp2'
• uscores
  Description of 'comp2'
• YChapeau
  Description of 'comp2'
• residYChapeau
  Description of 'comp2'
• RepY
  Description of 'comp2'
• na.miss.Y
  Description of 'comp2'
• YNA
  Description of 'comp2'
• residY
  Description of 'comp2'
• ExpliX
  Description of 'comp2'
• na.miss.X
  Description of 'comp2'
• XXNA
  Description of 'comp2'
• residXX
  Description of 'comp2'
• PredictY
  Description of 'comp2'
• press.ind
  Description of 'comp2'
• press.tot
  Description of 'comp2'
• familly
  Description of 'comp2'
• ttPredictY
  Description of 'comp2'
• typeVC
  Description of 'comp2'
• dataY
  Description of 'comp2'
• computed_nt
  Description of 'comp2'
• CoeffCFull
  Description of 'comp2'
• CoeffConstante
  Description of 'comp2'
• Std.Coeffs
  Description of 'comp2'
• press.ind2
  Description of 'comp2'
• RSSresidY
  Description of 'comp2'
• Coeffs
  Description of 'comp2'
• Yresidus
  Description of 'comp2'
• RSS
  Description of 'comp2'
• residusY
  Description of 'comp2'
• AIC.std
  AIC.std vs number of components (AIC computed for the standardized model
• AIC
  AIC vs nber of components
• optional
  If the response is assumed to be binary: i.e. MClassed=TRUE. [object Object],[object Object],[object Object]
• ttPredictFittedMissingY
  Description of 'comp2'
• optional
  If cross validation was requested: i.e. typeVC="standard", typeVC="missingdata" or typeVC="adaptative". [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
• optional
  If no cross validation was requested : i.e. typeVC="none". [object Object]
• Std.ValsPredictY
  Description of 'comp2'
• ValsPredictY
  Description of 'comp2'
• Std.XChapeau
  Description of 'comp2'
• XXwotNA
  Description of 'comp2'

Details

There are several ways to deal with missing values that leads to different computations of leave one out cross validation criteria. 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. 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.

References

Nicolas Meyer, Myriam Maumy-Bertrand et Fr�d�ric{Fr'ed'eric} Bertrand (2010). Comparaison de la r�gression{r'egression} PLS et de la r�gression{r'egression} logistique PLS : application aux donn�es{donn'ees} d'all�lotypage{d'all'elotypage}. Journal de la Soci�t� Fran�aise de Statistique, 151(2), pages 1-18. http://smf4.emath.fr/Publications/JSFdS/151_2/pdf/sfds_jsfds_151_2_1-18.pdf

See Also

PLS_lm_wvc and PLS_lm_kfoldcv_formula

Examples

data(Cornell)
PLS_lm_formula(Y~.,data=Cornell,nt=10)$InfCrit
PLS_lm_formula(Y~.,data=Cornell,nt=10,typeVC="standard")$CVinfos
PLS_lm_formula(Y~.,data=Cornell,nt=6)$AIC 
PLS_lm_formula(Y~.,data=Cornell,nt=6)$AIC.std    

modpls <- PLS_lm_formula(Y~.,data=Cornell,nt=6,pvals.expli =TRUE) 
modpls2 <- PLS_lm_formula(Y~.,data=Cornell,nt=6,sparse=TRUE)    
modpls3 <- PLS_lm_formula(Y~.,data=Cornell,nt=6,sparse=TRUE,sparseStop=FALSE)    


data(aze_compl)
modpls <- PLS_lm_formula(y~.,data=aze_compl,nt=10,MClassed=TRUE)

modpls$AIC
modpls$AIC.std
modpls$MissClassed
modpls$Probs
modpls$Probs.trc
modpls$Probs-modpls$Probs.trc

modpls$InfCrit
PLS_lm_formula(y~.,data=aze_compl,nt=10)$InfCrit

PLS_lm_formula(y~.,data=aze_compl,nt=10,typeVC="standard")$CVinfos
PLS_lm_formula(y~.,data=aze_compl,nt=10,typeVC="standard",MClassed=TRUE)$CVinfos
rm(list=c("modpls"))


dimX <- 24
Astar <- 2
simul_data_UniYX(dimX,Astar)
dataAstar2 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ydataAstar2 <- dataAstar2[,1]
XdataAstar2 <- dataAstar2[,2:(dimX+1)]
ysimbin1 <- dicho(ydataAstar2)
Xsimbin1 <- dicho(XdataAstar2)
PLS_lm_formula(ysimbin1~Xsimbin1,nt=10,MClassed=TRUE)$Probs
PLS_lm_formula(ysimbin1~Xsimbin1,nt=10,MClassed=TRUE)$Probs.trc
PLS_lm_formula(ysimbin1~Xsimbin1,nt=10,MClassed=TRUE)$MissClassed
PLS_lm_formula(ysimbin1~Xsimbin1,nt=10,typeVC="standard",MClassed=TRUE)$CVinfos
PLS_lm_formula(ysimbin1~XdataAstar2,nt=10,typeVC="standard",MClassed=TRUE)$CVinfos
PLS_lm_formula(ydataAstar2~XdataAstar2,nt=10,typeVC="standard")$CVinfos
rm(list=c("dimX","Astar","dataAstar2","ysimbin1","Xsimbin1","ydataAstar2","XdataAstar2"))


dimX <- 6
Astar <- 4
dataAstar4 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ydataAstar4 <- dataAstar4[,1]
XdataAstar4 <- dataAstar4[,2:(dimX+1)]
modpls <- PLS_lm_formula(ydataAstar4~XdataAstar4,nt=10,typeVC="standard")
modpls$computed_nt
modpls$CVinfos
str(modpls)
rm(list=c("dimX","Astar","dataAstar4","modpls","ydataAstar4","XdataAstar4"))


dimX <- 24
Astar <- 2
dataAstar2 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ydataAstar2 <- dataAstar2[,1]
XdataAstar2 <- dataAstar2[,2:(dimX+1)]
modpls <- PLS_lm_formula(ydataAstar2~XdataAstar2,nt=10,typeVC="standard")
modpls$computed_nt
modpls$CVinfos
rm(list=c("dimX","Astar","dataAstar2","modpls","ydataAstar2","XdataAstar2"))


# Comparing the results with the plspm package and SIMCA results in Tenenhaus's book
library(plspm)

data(Cornell)
XCornell<-Cornell[,1:7]
yCornell<-Cornell[,8]
plsreg1(x=XCornell,y=as.vector(yCornell),nc=3)$coeffs
PLS_lm_formula(Y~.,data=Cornell,nt=3)$uscores
PLS_lm_formula(Y~.,data=Cornell,nt=3)$pp
PLS_lm_formula(Y~.,data=Cornell,nt=3)$Coeffs

plsreg1(x=XCornell,y=as.vector(yCornell),nc=4,cv=TRUE)
PLS_lm_formula(Y~.,data=Cornell,nt=4,typeVC="standard")$press.ind
PLS_lm_formula(Y~.,data=Cornell,nt=4,typeVC="standard")$press.tot
PLS_lm_formula(Y~.,data=Cornell,nt=4,typeVC="standard")$CVinfos
plsreg1(x=XCornell,y=as.vector(yCornell),nc=4,cv=TRUE)$Q2


data(pine)
PLS_lm_formula(log(x11)~.,data=pine,nt=4)$Std.Coeffs
plsreg1(x=Xpine,y=log(as.vector(ypine)),nc=4)$std.coef
PLS_lm_formula(log(x11)~.,data=pine,nt=4)$Coeffs
plsreg1(x=Xpine,y=log(as.vector(ypine)),nc=4)$coeffs
PLS_lm_formula(log(x11)~.,data=pine,nt=1)$Std.Coeffs
PLS_lm_formula(log(x11)~.,data=pine,nt=1)$Coeffs
plsreg1(x=Xpine,y=log(as.vector(ypine)),nc=10)$Q2
PLS_lm_formula(log(x11)~.,data=pine,nt=10,typeVC="standard")$CVinfos
plsreg1(x=Xpine,y=log(as.vector(ypine)),nc=4,cv=TRUE)$Q2


data(pine_full)
PLS_lm_formula(log(x11)~.,data=pine_full,1)$Std.Coeffs
PLS_lm_formula(log(x11)~.,data=pine_full,1)$Coeffs
plsreg1(x=Xpine_full,y=log(as.vector(ypine_full)),nc=4)$coeffs


pineNAX21 <- pine
pineNAX21[1,2] <- NA
PLS_lm_formula(log(x11)~.,data=pineNAX21,nt=4)$Std.Coeffs

PLS_lm_formula(log(x11)~.,data=pineNAX21,nt=4)$YChapeau[1,]
PLS_lm_formula(log(x11)~.,data=pine,nt=4)$YChapeau[1,]

PLS_lm_formula(log(x11)~.,data=pineNAX21,nt=4)$CoeffC

plsreg1(x=XpineNAX21,y=as.vector(log(ypine)),nc=4,cv=TRUE)
PLS_lm_formula(log(x11)~.,data=pineNAX21,nt=2,dataPredictY=pineNAX21[1,-11])$ValsPredictY

PLS_lm_formula(log(x11)~.,data=pine,10,typeVC="none")$InfCrit
PLS_lm_formula(log(x11)~.,data=pine,10,typeVC="standard")$CVinfos
PLS_lm_formula(log(x11)~.,data=pine,10,typeVC="adaptative")$CVinfos
PLS_lm_formula(log(x11)~.,data=pine,10,typeVC="missingdata")$CVinfos
PLS_lm_formula(log(x11)~.,data=pineNAX21,10,typeVC="none")$InfCrit
PLS_lm_formula(log(x11)~.,data=pineNAX21,10,typeVC="standard")$CVinfos
PLS_lm_formula(log(x11)~.,data=pineNAX21,10,typeVC="adaptative")$CVinfos
PLS_lm_formula(log(x11)~.,data=pineNAX21,10,typeVC="missingdata")$CVinfos

PLS_lm_formula(log(x11)~.,data=pineNAX21,4,EstimXNA=TRUE)$XChapeau
PLS_lm_formula(log(x11)~.,data=pineNAX21,4,EstimXNA=TRUE)$XChapeauNA
rm(list=c("XCornell","yCornell","XpineNAX21"))



dimX <- 24
Astar <- 3
dataAstar3 <- t(replicate(200,simul_data_UniYX(dimX,Astar)))
ydataAstar3 <- dataAstar3[,1]
XdataAstar3 <- dataAstar3[,2:(dimX+1)]
modpls <- PLS_lm_formula(ydataAstar3~XdataAstar3,,10,typeVC="standard")
modpls$computed_nt
modpls$CVinfos
rm(list=c("dimX","Astar","dataAstar3","modpls","ydataAstar3","XdataAstar3"))


dimX <- 24
Astar <- 4
dataAstar4 <- t(replicate(200,simul_data_UniYX(dimX,Astar)))
ydataAstar4 <- dataAstar4[,1]
XdataAstar4 <- dataAstar4[,2:(dimX+1)]
modpls <- PLS_lm_formula(ydataAstar4~XdataAstar4,,10,typeVC="standard")
modpls$computed_nt
modpls$CVinfos
rm(list=c("dimX","Astar","dataAstar4","modpls","ydataAstar4","XdataAstar4"))


dimX <- 24
Astar <- 5
dataAstar5 <- t(replicate(200,simul_data_UniYX(dimX,Astar)))
ydataAstar5 <- dataAstar5[,1]
XdataAstar5 <- dataAstar5[,2:(dimX+1)]
modpls <- PLS_lm_formula(ydataAstar5~XdataAstar5,nt=10,typeVC="standard")
modpls$computed_nt
modpls$CVinfos
rm(list=c("dimX","Astar","dataAstar5","modpls","ydataAstar5","XdataAstar5"))


dimX <- 24
Astar <- 6
dataAstar6 <- t(replicate(200,simul_data_UniYX(dimX,Astar)))
ydataAstar6 <- dataAstar6[,1]
XdataAstar6 <- dataAstar6[,2:(dimX+1)]
modpls <- PLS_lm_formula(ydataAstar6~XdataAstar6,nt=10,typeVC="standard")
modpls$computed_nt
modpls$CVinfos
rm(list=c("dimX","Astar","dataAstar6","modpls","ydataAstar6","XdataAstar6"))