plsRglm: Partial least squares Regression generalized linear models

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

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

Usage

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
plsRglm(x, ...)
## Default S3 method:
plsRglmmodel(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,
sparse=FALSE,sparseStop=TRUE,naive=FALSE,verbose=TRUE)
## S3 method for class 'formula'
plsRglmmodel(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,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

x

a formula or a response (training) dataset

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 det(pp'*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
[email protected]
http://www-irma.u-strasbg.fr/~fbertran/

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

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
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"))

fbertran/plsRglm documentation built on May 16, 2019, 9:16 a.m.