mgsim.cv {plsgenomics} | R Documentation

## Determination of the ridge regularization parameter and the bandwidth to be used for classification with GSIM for categorical data

### Description

The function `mgsim.cv` determines the best ridge regularization parameter and bandwidth to be used for classification with MGSIM as described in Lambert-Lacroix and Peyre (2005).

### Usage

    mgsim.cv(Ytrain,Xtrain,LambdaRange,hRange,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.
`LambdaRange` | the vector of positive real value from which the best ridge regularization parameter has to be chosen by cross-validation.
`hRange` | the vector of strictly positive real value from which the best bandwidth has to be chosen by cross-validation.
`NbIterMax` | a positive integer. `NbIterMax` is the maximal number of iterations in the Newton-Rapson parts.

### Details

The cross-validation procedure described in Lambert-Lacroix and Peyre (2005) is used to determine the best ridge regularization parameter and bandwidth to be used for classification with GSIM for categorical data (for binary data see `gsim` and `gsim.cv`). At each cross-validation run, `Xtrain` is split into a pseudo training set (ntrain-1 samples) and a pseudo test set (1 sample) and the classification error rate is determined for each value of ridge regularization parameter and bandwidth. Finally, the function `mgsim.cv` returns the values of the ridge regularization parameter and bandwidth for which the mean classification error rate is minimal.

### Value

A list with the following components:

`Lambda` | the optimal regularization parameter.
`h` | the optimal bandwidth parameter.

### Author(s)

Sophie Lambert-Lacroix (http://www-lmc.imag.fr/lmc-sms/Sophie.Lambert) and Julie Peyre (http://www-lmc.imag.fr/lmc-sms/Julie.Peyre/).

### References

S. Lambert-Lacroix and Julie Peyre (2005). Local likelyhood regression in generalized linear single-index models with applications to microarray data, TR0563 IAP Statistics network (http://www.stat.ucl.ac.be/IAP/).

### See Also

`mgsim`, `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))

    # Determine optimum h and lambda
    hl <- mgsim.cv(Ytrain=SRBCT$Y[IndexLearn],Xtrain=SRBCT$X[IndexLearn,],LambdaRange=c(0.1),hRange=c(7,20))

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

[Package plsgenomics version 1.2 Index]