PLS_glm_formula: Partial least squares Regression generalized linear models

Description

This function implements Partial least squares Regression generalized linear models complete or incomplete datasets (formula specification of the model).

Usage

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=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

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"

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 fami

typeVC

type of leave one out cross validation. For back compatibility purpose. [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.

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

method

[object Object],[object Object]

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.

Value

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

Details

There are seven different predefined models with predefined link functions available : [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object] 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. [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object] 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.

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

Examples

Run this code

data(Cornell)
PLS_glm_formula(Y~.,data=Cornell,3)$uscores
PLS_glm_formula(Y~.,data=Cornell,3)$pp
PLS_glm_formula(Y~.,data=Cornell,3)$Coeffs
PLS_glm_formula(Y~.,data=Cornell,10)$InfCrit
PLS_glm_formula(Y~.,data=Cornell,10,modele="pls-glm-gaussian")$InfCrit
data.frame(pls=PLS_glm_formula(Y~.,data=Cornell,3)$Coeffs,PLS_glm_formula_gaussian=PLS_glm_formula(Y~.,data=Cornell,10,modele="pls-glm-gaussian")$Coeffs,PLS_glm_formula_family_gaussian=PLS_glm_formula(Y~.,data=Cornell,10,modele="pls-glm-family",family=gaussian())$Coeffs)

mod <- PLS_glm_formula(Y~.,data=Cornell,10,pvals.expli =TRUE)
mod2 <- PLS_glm_formula(Y~.,data=Cornell,10,sparse=TRUE)
mod3 <- PLS_glm_formula(Y~.,data=Cornell,10,sparse=TRUE,sparseStop=FALSE)


## User specified links can be used.
## Example of user-specified link, a logit model for p^days
## See Shaffer, T.  2004. Auk 121(2): 526-540 and ?family.
logexp <- function(days = 1)
{
    linkfun <- function(mu) qlogis(mu^(1/days))
    linkinv <- function(eta) plogis(eta)^days
    mu.eta <- function(eta) days * plogis(eta)^(days-1) *
      .Call("logit_mu_eta", eta, PACKAGE = "stats")
    valideta <- function(eta) TRUE
    link <- paste("logexp(", days, ")", sep="")
    structure(list(linkfun = linkfun, linkinv = linkinv,
                   mu.eta = mu.eta, valideta = valideta, name = link),
              class = "link-glm")
}
binomial(logexp(3))

data(aze_compl)
modpls <- PLS_glm_formula(y~.,data=aze_compl,nt=10,modele="pls-glm-family",family=binomial(link=logexp(3)),MClassed=TRUE,pvals.expli=TRUE)
modpls$InfCrit
rm(list=c("modpls","logexp","aze_compl"))


data(pine)
PLS_glm_formula(log(x11)~.,data=pine,1)$Std.Coeffs
PLS_glm_formula(log(x11)~.,data=pine,1)$Coeffs
PLS_glm_formula(log(x11)~.,data=pine,4)$Std.Coeffs
PLS_glm_formula(log(x11)~.,data=pine,4)$Coeffs
PLS_glm_formula(log(x11)~.,data=pine,4)$PredictY[1,]
PLS_glm_formula(log(x11)~.,data=pine,4,dataPredictY=pine[1,-11])$PredictY[1,]
PLS_glm_formula(log(x11)~.,data=pine,4,dataPredictY=pine[1,-11])$ValsPredictY[1]

pineNAX21 <- pine
pineNAX21[1,2] <- NA
str(PLS_glm_formula(log(x11)~.,data=pineNAX21,2))
PLS_glm_formula(log(x11)~.,data=pineNAX21,4)$Std.Coeffs
PLS_glm_formula(log(x11)~.,data=pineNAX21,4)$YChapeau[1,]
PLS_glm_formula(log(x11)~.,data=pine,4)$YChapeau[1,]
PLS_glm_formula(log(x11)~.,data=pineNAX21,4)$CoeffC
PLS_glm_formula(log(x11)~.,data=pineNAX21,4,EstimXNA=TRUE)$XChapeau
PLS_glm_formula(log(x11)~.,data=pineNAX21,4,EstimXNA=TRUE)$XChapeauNA

# compare pls-glm-gaussian with classic plsR
cbind(PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls")$Std.Coeffs,PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls-glm-gaussian")$Std.Coeffs)

# without missing data
cbind(log(pine$x11),PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls")$YChapeau,PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls-glm-gaussian")$YChapeau)
cbind(log(pine$x11),PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls")$YChapeau,PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls-glm-gaussian")$YChapeau)

# with missing data
cbind((log(pine$x11)),PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls")$YChapeau,PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls-glm-gaussian")$YChapeau)
cbind((log(pine$x11)),PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls")$ValsPredictY,PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls-glm-gaussian")$ValsPredictY)


# compare pls-glm-gaussian with log link with classic plsR on the log
cbind(PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls")$Std.Coeffs,PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls-glm-gaussian")$Std.Coeffs,PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls-glm-family",family=gaussian(link="identity"))$Std.Coeffs,PLS_glm_formula(x11~.,data=pine,4,modele="pls-glm-family",family=gaussian(link=log))$Std.Coeffs)

# without missing data
cbind(log(pine$x11),PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls")$YChapeau,PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls-glm-gaussian")$YChapeau,PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls-glm-family",family=gaussian(link="identity"))$YChapeau,log(PLS_glm_formula(x11~.,data=pineNAX21,4,modele="pls-glm-family",family=gaussian(link=log))$YChapeau))

# with missing data
cbind(log(pine$x11),PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls")$YChapeau,PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls-glm-gaussian")$YChapeau,PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls-glm-family",family=gaussian(link="identity"))$YChapeau,log(PLS_glm_formula(x11~.,data=pineNAX21,4,modele="pls-glm-family",family=gaussian(link=log))$YChapeau))
cbind(log(pine$x11),PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls")$ValsPredictY,PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls-glm-gaussian")$ValsPredictY,PLS_glm_formula(log(x11)~.,data=pineNAX21,4,modele="pls-glm-family",family=gaussian(link="identity"))$ValsPredictY,log(PLS_glm_formula(x11~.,data=pineNAX21,4,modele="pls-glm-family",family=gaussian(link=log))$ValsPredictY))


#other links
data.frame(pls=PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls")$Std.Coeffs,identity=PLS_glm_formula(log(x11)~.,data=pine,4,modele="pls-glm-family",family=gaussian(link="identity"))$Std.Coeffs,log=PLS_glm_formula(x11~.,data=pine,4,modele="pls-glm-family",family=gaussian(link=log))$Std.Coeffs,inverse=PLS_glm_formula(x11~.,data=pine,4,modele="pls-glm-family",family=gaussian(link=inverse))$Std.Coeffs)



data(fowlkes)
modpls <- PLS_glm_formula(Y~.,data=fowlkes,4,modele="pls-glm-logistic",pvals.expli=TRUE)
modpls$pvalstep
rm(list=c("modpls"))


data(aze_compl)
PLS_glm_formula(y~.,data=aze_compl,nt=10,modele="pls",MClassed=TRUE)$InfCrit
modpls <- PLS_glm_formula(y~.,data=aze_compl,nt=10,modele="pls-glm-logistic",MClassed=TRUE,pvals.expli=TRUE)
modpls$InfCrit
modpls$valpvalstep
modpls$Coeffsmodel_vals
modpls2 <- PLS_glm_formula(y~.,data=aze_compl,nt=10,modele="pls-glm-family",family=binomial(link=logit),MClassed=TRUE,pvals.expli=TRUE)
modpls3 <- PLS_glm_formula(y~.,data=aze_compl,nt=10,modele="pls-glm-family",family=binomial(link=probit),MClassed=TRUE,pvals.expli=TRUE)
modpls4 <- PLS_glm_formula(y~.,data=aze_compl,nt=10,modele="pls-glm-family",family=binomial(link=cauchit),MClassed=TRUE,pvals.expli=TRUE)
#fails modpls5 <- PLS_glm_formula(y~.,data=aze_compl,nt=10,modele="pls-glm-family",family=binomial(link=log),MClassed=TRUE,pvals.expli=TRUE)
modpls6 <- PLS_glm_formula(y~.,data=aze_compl,nt=10,modele="pls-glm-family",family=binomial(link=cloglog),MClassed=TRUE,pvals.expli=TRUE)
data.frame(logit=modpls2$Std.Coeffs,probit=modpls3$Std.Coeffs,cauchit=modpls4$Std.Coeffs,log=NA,cloglog=modpls6$Std.Coeffs)

plot(PLS_glm_formula(y~.,data=aze_compl,4,modele="pls-glm-logistic")$FinalModel)
PLS_glm_formula(y~.,data=aze_compl[-c(99,72),],4,modele="pls-glm-logistic",pvals.expli=TRUE)$pvalstep
plot(PLS_glm_formula(y~.,data=aze_compl[-c(99,72),],4,modele="pls-glm-logistic",pvals.expli=TRUE)$FinalModel)

modpls7 <- PLS_glm(yaze_compl,Xaze_compl,nt=10,modele="pls-glm-logistic",MClassed=TRUE,sparse=TRUE)
modpls8 <- PLS_glm(yaze_compl,Xaze_compl,nt=10,modele="pls-glm-logistic",MClassed=TRUE,sparse=TRUE,sparseStop=FALSE)
modpls7$InfCrit
modpls7$valpvalstep
modpls7$Coeffs

modpls$InfCrit
modpls7$InfCrit
colSums(modpls$pvalstep)
colSums(modpls7$pvalstep)
rm(list=c("modpls"))


data(bordeaux)
modpls <- PLS_glm_formula(Quality~.,data=bordeaux,10,modele="pls-glm-polr")
modpls <- PLS_glm_formula(Quality~Temperature+Sunshine+Heat+Rain,data=bordeaux,10,modele="pls-glm-polr")
modpls$Coeffsmodel_vals
modpls$InfCrit

bordeauxNA<-bordeaux
bordeauxNA[1,1] <- NA
modplsNA <- PLS_glm_formula(Quality~Temperature+Sunshine+Heat+Rain,data=bordeauxNA,10,modele="pls-glm-polr")
modplsNA$Coeffsmodel_vals
modplsNA$InfCrit
rm(list=c("bordeauxNA"))

modpls2 <- PLS_glm_formula(Quality~.,data=bordeaux,10,modele="pls-glm-polr",method="logistic")
modpls3 <- PLS_glm_formula(Quality~.,data=bordeaux,10,modele="pls-glm-polr",method="probit")
modpls4 <- PLS_glm_formula(Quality~.,data=bordeaux,10,modele="pls-glm-polr",method="cloglog")
modpls5 <- PLS_glm_formula(Quality~.,data=bordeaux,2,modele="pls-glm-polr",method="cauchit")

cbind(modpls2$Coeffs,modpls3$Coeffs,modpls4$Coeffs,modpls5$Coeffs)
rbind(modpls2$InfCrit[,"Chi2_Pearson_Y"],modpls3$InfCrit[,"Chi2_Pearson_Y"],modpls4$InfCrit[,"Chi2_Pearson_Y"],c(modpls5$InfCrit[,"Chi2_Pearson_Y"],NA,NA))

modpls6 <- PLS_glm(ybordeaux,Xbordeaux,10,modele="pls-glm-polr",pvals.expli=TRUE)
modpls6$Coeffsmodel_vals
modpls6$InfCrit
modpls6$valpvalstep
modpls6$Coeffs

modpls7 <- PLS_glm(ybordeaux,Xbordeaux,10,modele="pls-glm-polr",alpha.pvals.expli=.15,sparse=TRUE)
modpls8 <- PLS_glm(ybordeaux,Xbordeaux,10,modele="pls-glm-polr",alpha.pvals.expli=.15,sparse=TRUE,sparseStop=FALSE)
modpls7$Coeffsmodel_vals
modpls7$InfCrit
modpls7$valpvalstep
modpls7$Coeffs

modpls6$InfCrit
modpls7$InfCrit
colSums(modpls6$pvalstep)
colSums(modpls7$pvalstep)
rm(list=c("modpls","modplsNA","modpls2","modpls3","modpls4","modpls5","modpls6","modpls7"))


# Test of other families and links on the same datasets.
data(pine)
modpls <- PLS_glm_formula(x11~.,data=pine,10,modele="pls")
modpls$computed_nt
modpls$InfCrit
modpls2 <- PLS_glm_formula(x11~.,data=pine,10,modele="pls-glm-Gamma")
modpls2$InfCrit
modpls2a <- PLS_glm_formula(x11~.,data=pine,10,modele="pls-glm-family",family=Gamma(link=inverse))
modpls2a$InfCrit
modpls2b <- PLS_glm_formula(x11+1~.,data=pine,10,modele="pls-glm-family",family=Gamma(link=identity))
modpls2b$InfCrit
modpls2c <- PLS_glm_formula(x11~.,data=pine,10,modele="pls-glm-family",family=Gamma(link=log))
modpls2c$InfCrit


modpls3 <- PLS_glm_formula(x11~.,data=pine,10,modele="pls-glm-gaussian")
modpls3$InfCrit
modpls3a <- PLS_glm_formula(x11~.,data=pine,10,modele="pls-glm-family",family=gaussian(link=identity))
modpls3a$InfCrit
modpls3b <- PLS_glm_formula(x11~.,data=pine,10,modele="pls-glm-family",family=gaussian(link=log))
modpls3b$InfCrit
modpls3c <- PLS_glm_formula(x11~.,data=pine,10,modele="pls-glm-family",family=gaussian(link=inverse))
modpls3c$InfCrit


modpls4 <- PLS_glm_formula(round(x11)~.,data=pine,10,modele="pls-glm-poisson")
modpls4$InfCrit
modpls4a <- PLS_glm_formula(round(x11)~.,data=pine,10,modele="pls-glm-family",family=poisson(link=log))
modpls4a$InfCrit
modpls4b <- PLS_glm_formula(round(x11)+1~.,data=pine,10,modele="pls-glm-family",family=poisson(link=identity))
modpls4b$InfCrit
modpls4c <- PLS_glm_formula(round(x11)+1~.,data=pine,10,modele="pls-glm-family",family=poisson(link=sqrt))
modpls4c$InfCrit
rm(list=c("pine","modpls","modpls2","modpls3","modpls4","modpls2a","modpls3a","modpls4a","modpls2b","modpls3b","modpls4b","modpls2c","modpls3c","modpls4c"))

data(Cornell)
modpls <- PLS_glm_formula(Y~.,data=Cornell,10,modele="pls-glm-inverse.gaussian")
modpls$InfCrit
modplsa <- PLS_glm_formula(Y~.,data=Cornell,10,modele="pls-glm-family",family=inverse.gaussian(link=1/mu^2))
modplsa$InfCrit
modplsb <- PLS_glm_formula(Y~.,data=Cornell,10,modele="pls-glm-family",family=inverse.gaussian(link=inverse))
modplsb$InfCrit
modplsc <- PLS_glm_formula(Y~.,data=Cornell,10,modele="pls-glm-family",family=inverse.gaussian(link=identity))
modplsc$InfCrit
modplsd <- PLS_glm_formula(Y~.,data=Cornell,10,modele="pls-glm-family",family=inverse.gaussian(link=log))
modplsd$InfCrit
rm(list=c("modpls","modplsa","modplsb","modplsc","modplsd"))


dimX <- 6
Astar <- 4
dataAstar4 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ysimbin1 <- dicho(dataAstar4)[,1]
Xsimbin1 <- dicho(dataAstar4)[,2:(dimX+1)]
modplsglm <- PLS_glm_formula(ysimbin1~Xsimbin1,nt=10,modele="pls-glm-logistic")
modplsglm$computed_nt
modplsglm$InfCrit
rm(list=c("dimX","Astar","dataAstar4","ysimbin1","Xsimbin1","modplsglm"))


dimX <- 24
Astar <- 2
dataAstar2 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ysimbin1 <- dicho(dataAstar2)[,1]
Xsimbin1 <- dicho(dataAstar2)[,2:(dimX+1)]
modplsglm <- PLS_glm_formula(ysimbin1~Xsimbin1,nt=10,modele="pls-glm-logistic")
modplsglm$computed_nt
modplsglm$InfCrit
rm(list=c("dimX","Astar","dataAstar2","ysimbin1","Xsimbin1","modplsglm"))


dimX <- 24
Astar <- 3
dataAstar3 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ysimbin1 <- dicho(dataAstar3)[,1]
Xsimbin1 <- dicho(dataAstar3)[,2:(dimX+1)]
modplsglm <- PLS_glm_formula(ysimbin1~Xsimbin1,nt=10,modele="pls-glm-logistic")
modplsglm$computed_nt
modplsglm$InfCrit
rm(list=c("dimX","Astar","dataAstar3","ysimbin1","Xsimbin1","modplsglm"))


dimX <- 24
Astar <- 4
dataAstar4 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ysimbin1 <- dicho(dataAstar4)[,1]
Xsimbin1 <- dicho(dataAstar4)[,2:(dimX+1)]
modplsglm <- PLS_glm_formula(ysimbin1~Xsimbin1,nt=10,modele="pls-glm-logistic")
modplsglm$computed_nt
modplsglm$InfCrit
rm(list=c("dimX","Astar","dataAstar4","ysimbin1","Xsimbin1","modplsglm"))


dimX <- 24
Astar <- 5
dataAstar5 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ysimbin1 <- dicho(dataAstar5)[,1]
Xsimbin1 <- dicho(dataAstar5)[,2:(dimX+1)]
modplsglm <- PLS_glm_formula(ysimbin1~Xsimbin1,nt=10,modele="pls-glm-logistic")
modplsglm$computed_nt
modplsglm$InfCrit
rm(list=c("dimX","Astar","dataAstar5","ysimbin1","Xsimbin1","modplsglm"))


dimX <- 24
Astar <- 6
dataAstar6 <- t(replicate(250,simul_data_UniYX(dimX,Astar)))
ysimbin1 <- dicho(dataAstar6)[,1]
Xsimbin1 <- dicho(dataAstar6)[,2:(dimX+1)]
modplsglm <- PLS_glm_formula(ysimbin1~Xsimbin1,nt=10,modele="pls-glm-logistic")
modplsglm$computed_nt
modplsglm$InfCrit
rm(list=c("dimX","Astar","dataAstar6","ysimbin1","Xsimbin1","modplsglm"))

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