mgsim {plsgenomics}

GSIM for categorical data

Description

The function mgsim performs prediction using Lambert-Lacroix and Peyre's MGSIM algorithm.

Usage

mgsim(Ytrain,Xtrain,Lambda,h,Xtest=NULL,NbIterMax=50)

Arguments

Xtrain

a (ntrain x p) data matrix of predictors. Xtrain must be a matrix. Each row corresponds to an observation and each column to a predictor variable.

Ytrain

a ntrain vector of responses. Ytrain must be a vector. Ytrain is a {1,...,c+1}-valued vector and contains the response variable for each observation. c+1 is the number of classes.

Xtest

a (ntest x p) matrix containing the predictors for the test data set. Xtest may also be a vector of length p (corresponding to only one test observation). If Xtest is not equal to NULL, then the prediction step is made for these new predictor variables.

Lambda

a positive real value. Lambda is the ridge regularization parameter.

h

a strictly positive real value. h is the bandwidth for GSIM step A.

NbIterMax

a positive integer. NbIterMax is the maximal number of iterations in the Newton-Rapson parts.

Details

The columns of the data matrices Xtrain and Xtest may not be standardized, since standardizing is performed by the function mgsim as a preliminary step before the algorithm is run.

The procedure described in Lambert-Lacroix and Peyre (2005) is used to estimate the c projection directions and the coefficients of the parametric fit obtained after projecting predictor variables onto the estimated directions. When Xtest is not equal to NULL, the procedure predicts the labels for these new predictor variables.

Value

A list with the following components:

Ytest

the ntest vector containing the predicted labels for the observations from Xtest.

beta

the (p x c) matrix containing the c estimated projection directions.

Coefficients

the (2 x c) matrix containing the coefficients of the parametric fit obtained after projecting predictor variables onto these estimated directions.

DeletedCol

the vector containing the column number of Xtrain when the variance of the corresponding predictor variable is null. Otherwise DeletedCol=NULL

Cvg

the 0-1 value indicating convergence of the algorithm (1 for convergence, 0 otherwise).

Author(s)

Sophie Lambert-Lacroix (http://membres-timc.imag.fr/Sophie.Lambert/) and Julie Peyre (https://membres-ljk.imag.fr/Julie.Peyre/).

References

S. Lambert-Lacroix, J. Peyre . (2006) Local likelyhood regression in generalized linear single-index models with applications to microarrays data. Computational Statistics and Data Analysis, vol 51, n 3, 2091-2113.

See Also

mgsim.cv, gsim, gsim.cv.

Examples

# load plsgenomics library
library(plsgenomics)

# load SRBCT data
data(SRBCT)
IndexLearn <- c(sample(which(SRBCT$Y==1),10),sample(which(SRBCT$Y==2),4),
			sample(which(SRBCT$Y==3),7),sample(which(SRBCT$Y==4),9))

# perform prediction by MGSIM
res <- mgsim(Ytrain=SRBCT$Y[IndexLearn],Xtrain=SRBCT$X[IndexLearn,],Lambda=0.001,h=19,
			Xtest=SRBCT$X[-IndexLearn,])
res$Cvg
sum(res$Ytest!=SRBCT$Y[-IndexLearn])

# prediction for another sample
Xnew <- SRBCT$X[83,]
# projection of Xnew onto the c estimated direction
Xproj <- Xnew %*% res$beta
# Compute the linear predictor for each classes expect class 1
eta <- diag(cbind(rep(1,3),t(Xproj)) %*% res$Coefficients)
Ypred <- which.max(c(0,eta))
Ypred
SRBCT$Y[83]