plsRglm: Partial least squares Regression generalized linear models

In plsRglm: Partial Least Squares Regression for Generalized Linear Models

Partial least squares Regression generalized linear models

Description

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

Usage

plsRglm(object, ...)
## Default S3 method:
plsRglmmodel(object,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,
sparse=FALSE,sparseStop=TRUE,naive=FALSE,verbose=TRUE,...)
## S3 method for class 'formula'
plsRglmmodel(object,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,sparse=FALSE,sparseStop=TRUE,naive=FALSE,verbose=TRUE,...)
PLS_glm(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=FALSE, naive=FALSE,verbose=TRUE)
PLS_glm_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,start=NULL,etastart,mustart,offset,method,
control= list(),contrasts=NULL,sparse=FALSE,sparseStop=FALSE,naive=FALSE,verbose=TRUE)

Arguments

object	response (training) dataset or 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'.
dataY	response (training) dataset
dataX	predictor(s) (training) dataset
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 from environment(formula), typically the environment from which plsRglm is called.
nt	number of components to be extracted
limQ2set	limit value for the Q2
dataPredictY	predictor(s) (testing) dataset
modele	name of the PLS glm model to be fitted ("pls", "pls-glm-Gamma", "pls-glm-gaussian", "pls-glm-inverse.gaussian", "pls-glm-logistic", "pls-glm-poisson", "pls-glm-polr"). 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. none 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 non 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.
start	starting values for the parameters in the linear predictor.
etastart	starting values for the linear predictor.
mustart	starting values for the vector of means.
offset	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.
method	For a glm model (modele="pls-glm-family"), 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. For a polr model (modele="pls-glm-polr"), logistic or probit or (complementary) log-log (loglog or cloglog) or cauchit (corresponding to a Cauchy latent variable).
control	a list of parameters for controlling the fitting process. For glm.fit this is passed to glm.control.
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.
verbose	Should details 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 N. Kraemer and M. Sugiyama. (2011). The Degrees of Freedom of Partial Least Squares Regression. Journal of the American Statistical Association, 106(494), 697-705, 2011.

Value

Depends on the model that was used to fit the model. You can generally at least find these items.

nr	Number of observations
nc	Number of predictors
nt	Number of requested components
ww	raw weights (before L2-normalization)
wwnorm	L2 normed weights (to be used with deflated matrices of predictor variables)
wwetoile	modified weights (to be used with original matrix of predictor variables)
tt	PLS components
pp	loadings of the predictor variables
CoeffC	coefficients of the PLS components
uscores	scores of the response variable
YChapeau	predicted response values for the dataX set
residYChapeau	residuals of the deflated response on the standardized scale
RepY	scaled response vector
na.miss.Y	is there any NA value in the response vector
YNA	indicatrix vector of missing values in RepY
residY	deflated scaled response vector
ExpliX	scaled matrix of predictors
na.miss.X	is there any NA value in the predictor matrix
XXNA	indicator of non-NA values in the predictor matrix
residXX	deflated predictor matrix
PredictY	response values with NA replaced with 0
RSS	residual sum of squares (original scale)
RSSresidY	residual sum of squares (scaled scale)
R2residY	R2 coefficient value on the standardized scale
R2	R2 coefficient value on the original scale
press.ind	individual PRESS value for each observation (scaled scale)
press.tot	total PRESS value for all observations (scaled scale)
Q2cum	cumulated Q2 (standardized scale)
family	glm family used to fit PLSGLR model
ttPredictY	PLS components for the dataset on which prediction was requested
typeVC	type of leave one out cross-validation used
dataX	predictor values
dataY	response values
weights	weights of the observations
computed_nt	number of components that were computed
AIC	AIC vs number of components
BIC	BIC vs number of components
Coeffsmodel_vals
ChisqPearson
CoeffCFull	matrix of the coefficients of the predictors
CoeffConstante	value of the intercept (scaled scale)
Std.Coeffs	Vector of standardized regression coefficients
Coeffs	Vector of regression coefficients (used with the original data scale)
Yresidus	residuals of the PLS model
residusY	residuals of the deflated response on the standardized scale
InfCrit	table of Information Criteria: AIC AIC vs number of components BIC BIC vs number of components MissClassed Number of miss classed results Chi2_Pearson_Y Q2 value (standardized scale) RSS residual sum of squares (original scale) R2 R2 coefficient value on the original scale R2residY R2 coefficient value on the standardized scale RSSresidY residual sum of squares (scaled scale)
Std.ValsPredictY	predicted response values for supplementary dataset (standardized scale)
ValsPredictY	predicted response values for supplementary dataset (original scale)
Std.XChapeau	estimated values for missing values in the predictor matrix (standardized scale)
FinalModel	final GLR model on the PLS components
XXwotNA	predictor matrix with missing values replaced with 0
call	call
AIC.std	AIC.std vs number of components (AIC computed for the standardized model

Note

Use cv.plsRglm to cross-validate the plsRglm models and bootplsglm to bootstrap them.

Author(s)

Frederic Bertrand
[e-mail]
https://fbertran.github.io/homepage/

References

Nicolas Meyer, Myriam Maumy-Bertrand et Frederic Bertrand (2010). Comparaison de la regression PLS et de la regression logistique PLS : application aux donnees d'allelotypage. Journal de la Societe Francaise de Statistique, 151(2), pages 1-18. http://publications-sfds.math.cnrs.fr/index.php/J-SFdS/article/view/47

See Also

See also plsR.

Examples

data(Cornell)
XCornell<-Cornell[,1:7]
yCornell<-Cornell[,8]

modplsglm <- plsRglm(yCornell,XCornell,10,modele="pls-glm-gaussian")

#To retrieve the final GLR model on the PLS components
finalmod <- modplsglm$FinalModel
#It is a glm object.
plot(finalmod)


#Cross validation
cv.modplsglm<-cv.plsRglm(Y~.,data=Cornell,6,NK=100,modele="pls-glm-gaussian", verbose=FALSE)
res.cv.modplsglm<-cvtable(summary(cv.modplsglm))
plot(res.cv.modplsglm)

#If no model specified, classic PLSR model
modpls <- plsRglm(Y~.,data=Cornell,6)
modpls
modpls$tt
modpls$uscores
modpls$pp
modpls$Coeffs

#rm(list=c("XCornell","yCornell",modpls,cv.modplsglm,res.cv.modplsglm))


data(aze_compl)
Xaze_compl<-aze_compl[,2:34]
yaze_compl<-aze_compl$y
plsRglm(yaze_compl,Xaze_compl,nt=10,modele="pls",MClassed=TRUE, verbose=FALSE)$InfCrit
modpls <- plsRglm(yaze_compl,Xaze_compl,nt=10,modele="pls-glm-logistic",
MClassed=TRUE,pvals.expli=TRUE, verbose=FALSE)
modpls
colSums(modpls$pvalstep)
modpls$Coeffsmodel_vals

plot(plsRglm(yaze_compl,Xaze_compl,4,modele="pls-glm-logistic")$FinalModel)
plsRglm(yaze_compl[-c(99,72)],Xaze_compl[-c(99,72),],4,
modele="pls-glm-logistic",pvals.expli=TRUE)$pvalstep
plot(plsRglm(yaze_compl[-c(99,72)],Xaze_compl[-c(99,72),],4,
modele="pls-glm-logistic",pvals.expli=TRUE)$FinalModel)
rm(list=c("Xaze_compl","yaze_compl","modpls"))


data(bordeaux)
Xbordeaux<-bordeaux[,1:4]
ybordeaux<-factor(bordeaux$Quality,ordered=TRUE)
modpls <- plsRglm(ybordeaux,Xbordeaux,10,modele="pls-glm-polr",pvals.expli=TRUE)
modpls
colSums(modpls$pvalstep)


XbordeauxNA<-Xbordeaux
XbordeauxNA[1,1] <- NA
modplsNA <- plsRglm(ybordeaux,XbordeauxNA,10,modele="pls-glm-polr",pvals.expli=TRUE)
modpls
colSums(modpls$pvalstep)
rm(list=c("Xbordeaux","XbordeauxNA","ybordeaux","modplsNA"))


data(pine)
Xpine<-pine[,1:10]
ypine<-pine[,11]
modpls1 <- plsRglm(ypine,Xpine,1)
modpls1$Std.Coeffs
modpls1$Coeffs
modpls4 <- plsRglm(ypine,Xpine,4)
modpls4$Std.Coeffs
modpls4$Coeffs
modpls4$PredictY[1,]
plsRglm(ypine,Xpine,4,dataPredictY=Xpine[1,])$PredictY[1,]

XpineNAX21 <- Xpine
XpineNAX21[1,2] <- NA
modpls4NA <- plsRglm(ypine,XpineNAX21,4)
modpls4NA$Std.Coeffs
modpls4NA$YChapeau[1,]
modpls4$YChapeau[1,]
modpls4NA$CoeffC
plsRglm(ypine,XpineNAX21,4,EstimXNA=TRUE)$XChapeau
plsRglm(ypine,XpineNAX21,4,EstimXNA=TRUE)$XChapeauNA

# compare pls-glm-gaussian with classic plsR
modplsglm4 <- plsRglm(ypine,Xpine,4,modele="pls-glm-gaussian")
cbind(modpls4$Std.Coeffs,modplsglm4$Std.Coeffs)

# without missing data
cbind(ypine,modpls4$ValsPredictY,modplsglm4$ValsPredictY)

# with missing data
modplsglm4NA <- plsRglm(ypine,XpineNAX21,4,modele="pls-glm-gaussian")
cbind((ypine),modpls4NA$ValsPredictY,modplsglm4NA$ValsPredictY)
rm(list=c("Xpine","ypine","modpls4","modpls4NA","modplsglm4","modplsglm4NA"))

data(fowlkes)
Xfowlkes <- fowlkes[,2:13]
yfowlkes <- fowlkes[,1]
modpls <- plsRglm(yfowlkes,Xfowlkes,4,modele="pls-glm-logistic",pvals.expli=TRUE)
modpls
colSums(modpls$pvalstep)
rm(list=c("Xfowlkes","yfowlkes","modpls"))


if(require(chemometrics)){
data(hyptis)
yhyptis <- factor(hyptis$Group,ordered=TRUE)
Xhyptis <- as.data.frame(hyptis[,c(1:6)])
options(contrasts = c("contr.treatment", "contr.poly"))
modpls2 <- plsRglm(yhyptis,Xhyptis,6,modele="pls-glm-polr")
modpls2$Coeffsmodel_vals
modpls2$InfCrit
modpls2$Coeffs
modpls2$Std.Coeffs

table(yhyptis,predict(modpls2$FinalModel,type="class"))
rm(list=c("yhyptis","Xhyptis","modpls2"))
}

dimX <- 24
Astar <- 6
dataAstar6 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ysimbin1 <- dicho(dataAstar6)[,1]
Xsimbin1 <- dicho(dataAstar6)[,2:(dimX+1)]
modplsglm <- plsRglm(ysimbin1,Xsimbin1,10,modele="pls-glm-logistic")
modplsglm

simbin=data.frame(dicho(dataAstar6))
cv.modplsglm <- suppressWarnings(cv.plsRglm(Y~.,data=simbin,nt=10,
modele="pls-glm-logistic",NK=100, verbose=FALSE))
res.cv.modplsglm <- cvtable(summary(cv.modplsglm,MClassed=TRUE,
verbose=FALSE))
plot(res.cv.modplsglm) #defaults to type="CVMC"

rm(list=c("dimX","Astar","dataAstar6","ysimbin1","Xsimbin1","modplsglm","cv.modplsglm",
"res.cv.modplsglm"))

plsRglm documentation built on March 31, 2023, 11:10 p.m.