PLS_glm_kfoldcv_formula: Partial least squares regression glm models with kfold cross validation

Description

This function implements kfold cross validation on complete or incomplete datasets for partial least squares regression generalized linear models (formula specification of the model).

Usage

PLS_glm_kfoldcv_formula(formula,data=NULL,nt=2,limQ2set=.0975,modele="pls", family=NULL, K=nrow(dataX), NK=1, grouplist=NULL, random=FALSE, scaleX=TRUE, scaleY=NULL, keepcoeffs=FALSE, keepfolds=FALSE, keepdataY=TRUE, keepMclassed=FALSE, tol_Xi=10^(-12),weights,subset,start=NULL,etastart,mustart,offset,method,control= list(),contrasts=NULL)

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

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

number of groups

number of times the group division is made

grouplist

to specify the members of the K groups

random

should the K groups be made randomly

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.

keepcoeffs

shall the coefficients for each model be returned

keepfolds

shall the groups' composition be returned

keepdataY

shall the observed value of the response for each one of the predicted value be returned

keepMclassed

shall the number of miss classed be returned (unavailable)

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.

Value

results_kfoldslist of NK. Each element of the list sums up the results for a group division: [object Object],[object Object],[object Object]
foldslist of NK. Each element of the list sums up the informations for a group division: [object Object],[object Object],[object Object]
dataY_kfoldslist of NK. Each element of the list sums up the results for a group division: [object Object],[object Object],[object Object]
callthe call of the function

Details

Predicts 1 group with the K-1 other groups. Leave one out cross validation is thus obtained for K==nrow(dataX). 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.

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)
bbb <- PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=10,NK=1,modele="pls")
kfolds2CVinfos_glm(bbb)

PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-gaussian",K=12)
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-gaussian",K=6,NK=2,random=TRUE,keepfolds=TRUE)$results_kfolds

#Different ways of model specifications
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-gaussian",K=6,NK=2,random=FALSE,keepfolds=TRUE)$results_kfolds
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-family",family=gaussian,K=6,NK=2,random=FALSE,keepfolds=TRUE)$results_kfolds
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-family",family=gaussian(),K=6,NK=2,random=FALSE,keepfolds=TRUE)$results_kfolds
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-family",family=gaussian(link=log),K=6,NK=2,random=FALSE,keepfolds=TRUE)$results_kfolds

bbb2 <- PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=10,modele="pls-glm-gaussian",keepcoeffs=TRUE)
bbb2 <- PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-family",family=gaussian(link=log),K=6,keepcoeffs=TRUE)

#For Jackknife computations
kfolds2coeff(bbb2)
boxplot(kfolds2coeff(bbb2)[,1])

kfolds2Chisqind(bbb2)
kfolds2Chisq(bbb2)
kfolds2CVinfos_glm(bbb2)
PLS_lm_formula(log(Y)~.,data=Cornell,10,typeVC="standard")$CVinfos
rm(list=c("bbb","bbb2"))


data(pine)
bbb <- PLS_glm_kfoldcv_formula(x11~.,data=pine,nt=10,modele="pls-glm-family",family=gaussian(log),K=10,keepcoeffs=TRUE,keepfolds=FALSE)
bbb <- PLS_glm_kfoldcv_formula(x11~.,data=pine,nt=10,modele="pls-glm-gaussian",K=10,keepcoeffs=TRUE,keepfolds=FALSE)

#For Jackknife computations
kfolds2coeff(bbb)
boxplot(kfolds2coeff(bbb)[,1])

kfolds2Chisqind(bbb)
kfolds2Chisq(bbb)
kfolds2CVinfos_glm(bbb)
PLS_lm_formula(log(x11)~.,data=pine,nt=10,typeVC="standard")$CVinfos

pineNAX21 <- pine
pineNAX21[1,2] <- NA
bbb2 <- PLS_glm_kfoldcv_formula(x11~.,data=pineNAX21,nt=10,modele="pls-glm-family",family=gaussian(log),K=10,keepcoeffs=TRUE,keepfolds=FALSE)
bbb2 <- PLS_glm_kfoldcv_formula(x11~.,data=pineNAX21,nt=10,modele="pls-glm-gaussian",K=10,keepcoeffs=TRUE,keepfolds=FALSE)

#For Jackknife computations
kfolds2coeff(bbb2)
boxplot(kfolds2coeff(bbb2)[,1])

kfolds2Chisqind(bbb2)
kfolds2Chisq(bbb2)
kfolds2CVinfos_glm(bbb2)
PLS_lm_formula(log(x11)~.,data=pineNAX21,nt=10,typeVC="standard")$CVinfos
rm(list=c("pineNAX21","bbb","bbb2"))


data(aze_compl)
bbb <- PLS_glm_kfoldcv_formula(y~.,data=aze_compl,nt=10,K=10,modele="pls",keepcoeffs=TRUE)

#For Jackknife computations
kfolds2coeff(bbb)
bbb2 <- PLS_glm_kfoldcv_formula(y~.,data=aze_compl,nt=3,K=10,modele="pls-glm-family",family=binomial(probit),keepcoeffs=TRUE)
bbb2 <- PLS_glm_kfoldcv_formula(y~.,data=aze_compl,nt=3,K=10,modele="pls-glm-logistic",keepcoeffs=TRUE)
kfolds2CVinfos_glm(bbb,MClassed=TRUE)
kfolds2CVinfos_glm(bbb2,MClassed=TRUE)
kfolds2coeff(bbb2)

kfolds2Chisqind(bbb2)
kfolds2Chisq(bbb2)
kfolds2CVinfos_glm(bbb2)
rm(list=c("bbb","bbb2"))



data(pine)
bbb <- PLS_glm_kfoldcv_formula(round(x11)~.,data=pine,nt=10,modele="pls-glm-family",family=poisson(log),K=10,keepcoeffs=TRUE,keepfolds=FALSE)
bbb <- PLS_glm_kfoldcv_formula(round(x11)~.,data=pine,nt=10,modele="pls-glm-poisson",K=10,keepcoeffs=TRUE,keepfolds=FALSE)

#For Jackknife computations
kfolds2coeff(bbb)
boxplot(kfolds2coeff(bbb)[,1])

kfolds2Chisqind(bbb)
kfolds2Chisq(bbb)
kfolds2CVinfos_glm(bbb)
PLS_lm_formula(log(x11)~.,data=pine,10,typeVC="standard")$CVinfos

pineNAX21 <- pine
pineNAX21[1,2] <- NA
bbb2 <- PLS_glm_kfoldcv_formula(round(x11)~.,data=pineNAX21,nt=10,modele="pls-glm-family",family=poisson(log),K=10,keepcoeffs=TRUE,keepfolds=FALSE)
bbb2 <- PLS_glm_kfoldcv_formula(round(x11)~.,data=pineNAX21,nt=10,modele="pls-glm-poisson",K=10,keepcoeffs=TRUE,keepfolds=FALSE)

#For Jackknife computations
kfolds2coeff(bbb2)
boxplot(kfolds2coeff(bbb2)[,1])

kfolds2Chisqind(bbb2)
kfolds2Chisq(bbb2)
kfolds2CVinfos_glm(bbb2)
PLS_lm_formula(log(x11)~.,data=pineNAX21,10,typeVC="standard")$CVinfos
rm(list=c("pineNAX21","bbb","bbb2"))



data(pine)
bbb <- PLS_glm_kfoldcv_formula(x11~.,data=pine,nt=10,modele="pls-glm-family",family=Gamma,K=10,keepcoeffs=TRUE,keepfolds=FALSE)
bbb <- PLS_glm_kfoldcv_formula(x11~.,data=pine,nt=10,modele="pls-glm-Gamma",K=10,keepcoeffs=TRUE,keepfolds=FALSE)

#For Jackknife computations
kfolds2coeff(bbb)
boxplot(kfolds2coeff(bbb)[,1])

kfolds2Chisqind(bbb)
kfolds2Chisq(bbb)
kfolds2CVinfos_glm(bbb)
PLS_lm_formula(log(x11)~.,data=pine,10,typeVC="standard")$CVinfos

pineNAX21 <- pine
pineNAX21[1,2] <- NA
bbb2 <- PLS_glm_kfoldcv_formula(x11~.,data=pineNAX21,nt=10,modele="pls-glm-family",family=Gamma(),K=10,keepcoeffs=TRUE,keepfolds=FALSE)
bbb2 <- PLS_glm_kfoldcv_formula(x11~.,data=pineNAX21,nt=10,modele="pls-glm-Gamma",K=10,keepcoeffs=TRUE,keepfolds=FALSE)

#For Jackknife computations
kfolds2coeff(bbb2)
boxplot(kfolds2coeff(bbb2)[,1])

kfolds2Chisqind(bbb2)
kfolds2Chisq(bbb2)
kfolds2CVinfos_glm(bbb2)
PLS_lm_formula(log(x11)~.,data=pineNAX21,10,typeVC="standard")$CVinfos
rm(list=c("pineNAX21","bbb","bbb2"))



data(Cornell)
bbb <- PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=10,NK=1,modele="pls")
kfolds2CVinfos_glm(bbb)

PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-inverse.gaussian",K=12)
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-family",family=inverse.gaussian,K=12)
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-inverse.gaussian",K=6,NK=2,random=TRUE,keepfolds=TRUE)$results_kfolds
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-family",family=inverse.gaussian(),K=6,NK=2,random=TRUE,keepfolds=TRUE)$results_kfolds
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-inverse.gaussian",K=6,NK=2,random=FALSE,keepfolds=TRUE)$results_kfolds
PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=3,modele="pls-glm-family",family=inverse.gaussian(link = "1/mu^2"),K=6,NK=2,random=FALSE,keepfolds=TRUE)$results_kfolds

bbb2 <- PLS_glm_kfoldcv_formula(Y~.,data=Cornell,nt=10,modele="pls-glm-inverse.gaussian",keepcoeffs=TRUE)

#For Jackknife computations
kfolds2coeff(bbb2)
boxplot(kfolds2coeff(bbb2)[,1])

kfolds2Chisqind(bbb2)
kfolds2Chisq(bbb2)
kfolds2CVinfos_glm(bbb2)
PLS_lm_formula(log(Y)~.,data=Cornell,10,typeVC="standard")$CVinfos
rm(list=c("bbb","bbb2"))


data(bordeaux)
bbb <- PLS_glm_kfoldcv_formula(Quality~.,data=bordeaux,10,modele="pls-glm-polr",K=7)
kfolds2CVinfos_glm(bbb)

bordeauxNA<-bordeaux
bordeauxNA[1,1] <- NA
bbbNA <- PLS_glm_kfoldcv_formula(Quality~Temperature+Sunshine+Heat+Rain,data=bordeauxNA,10,modele="pls-glm-polr",K=10)
kfolds2CVinfos_glm(bbbNA)
rm(list=c("bbb","bbbNA"))

bbb2 <- PLS_glm_kfoldcv_formula(Quality~.,data=bordeaux,nt=2,K=7,modele="pls-glm-polr",method="logistic")
bbb3 <- PLS_glm_kfoldcv_formula(Quality~.,data=bordeaux,nt=2,K=7,modele="pls-glm-polr",method="probit")
bbb4 <- PLS_glm_kfoldcv_formula(Quality~.,data=bordeaux,nt=2,K=7,modele="pls-glm-polr",method="cloglog")
bbb5 <- PLS_glm_kfoldcv_formula(Quality~.,data=bordeaux,nt=2,K=7,modele="pls-glm-polr",method="cauchit")

kfolds2CVinfos_glm(bbb2)
kfolds2CVinfos_glm(bbb3)
kfolds2CVinfos_glm(bbb4)
kfolds2CVinfos_glm(bbb5)
rm(list=c("bbb","bbbNA","bbb2","bbb3","bbb4","bbb5"))

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