plsrda {rchemo}

PLSDA models

Description

Discrimination (DA) based on PLS.

The training variable y (univariate class membership) is firstly transformed to a dummy table containing nclas columns, where nclas is the number of classes present in y. Each column is a dummy variable (0/1). Then, a PLS2 is implemented on the X-data and the dummy table, returning latent variables (LVs) that are used as dependent variables in a DA model.

- plsrda: Usual "PLSDA". A linear regression model predicts the Y-dummy table from the PLS2 LVs. This corresponds to the PLSR2 of the X-data and the Y-dummy table. For a given observation, the final prediction is the class corresponding to the dummy variable for which the prediction is the highest.

- plslda and plsqda: Probabilistic LDA and QDA are run over the PLS2 LVs, respectively.

Usage

plsrda(X, y, weights = NULL, nlv)

plslda(X, y, weights = NULL, nlv, prior = c("unif", "prop"))

plsqda(X, y, weights = NULL, nlv, prior = c("unif", "prop"))

## S3 method for class 'Plsrda'
predict(object, X, ..., nlv = NULL) 

## S3 method for class 'Plsprobda'
predict(object, X, ..., nlv = NULL) 

Arguments

X

For the main functions: Training X-data (n, p). — For the auxiliary functions: New X-data (m, p) to consider.

y

Training class membership (n). Note: If y is a factor, it is replaced by a character vector.

weights

Weights (n) to apply to the training observations for the PLS2. Internally, weights are "normalized" to sum to 1. Default to NULL (weights are set to 1 / n).

nlv

The number(s) of LVs to calculate.

prior

The prior probabilities of the classes. Possible values are "unif" (default; probabilities are set equal for all the classes) or "prop" (probabilities are set equal to the observed proportions of the classes in y).

object

For the auxiliary functions: A fitted model, output of a call to the main functions.

...

For the auxiliary functions: Optional arguments. Not used.

Value

For plsrda, plslda, plsqda:

fm

list with the model: (T): X-scores matrix; (P): X-loading matrix;(R): The PLS projection matrix (p,nlv); (W): X-loading weights matrix ;(C): The Y-loading weights matrix; (TT): the X-score normalization factor; (xmeans): the centering vector of X (p,1); (ymeans): the centering vector of Y (q,1); (weights): vector of observation weights; (U): intermediate output.

lev

classes

ni

number of observations in each class

For predict.Plsrda, predict.Plsprobda:

pred

predicted class for each observation

posterior

calculated probability of belonging to a class for each observation

Note

The first example concerns PLSDA, and the second one concerns PLS LDA. fm are PLS1 models, and zfm are PLS2 models.

Examples

## EXAMPLE OF PLSDA

n <- 50 ; p <- 8
Xtrain <- matrix(rnorm(n * p), ncol = p)
ytrain <- sample(c(1, 4, 10), size = n, replace = TRUE)

Xtest <- Xtrain[1:5, ] ; ytest <- ytrain[1:5]

nlv <- 5
fm <- plsrda(Xtrain, ytrain, nlv = nlv)
names(fm)

predict(fm, Xtest)
predict(fm, Xtest, nlv = 0:2)$pred

pred <- predict(fm, Xtest)$pred
err(pred, ytest)

zfm <- fm$fm
transform(zfm, Xtest)
transform(zfm, Xtest, nlv = 1)
summary(zfm, Xtrain)
coef(zfm)
coef(zfm, nlv = 0)
coef(zfm, nlv = 2)

## EXAMPLE OF PLS LDA

n <- 50 ; p <- 8
Xtrain <- matrix(rnorm(n * p), ncol = p)
ytrain <- sample(c(1, 4, 10), size = n, replace = TRUE)
Xtest <- Xtrain[1:5, ] ; ytest <- ytrain[1:5]

nlv <- 5
fm <- plslda(Xtrain, ytrain, nlv = nlv)
predict(fm, Xtest)
predict(fm, Xtest, nlv = 1:2)$pred

zfm <- fm[[1]][[1]]
class(zfm)
names(zfm)
summary(zfm, Xtrain)
transform(zfm, Xtest[1:2, ])
coef(zfm)