rchemo (version 0.1-3)

lda: LDA and QDA

Description

Probabilistic (parametric) linear and quadratic discriminant analysis.

Usage

lda(X, y, prior = c("unif", "prop"))
qda(X, y, prior = c("unif", "prop"))
  
# S3 method for Lda
predict(object, X, ...)  
# S3 method for Qda
predict(object, X, ...)

Value

For lda and qda:

ct

centers (column-wise means) for classes of observations.

W

unbiased within covariance matrices for classes of observations.

wprior

prior probabilities of the classes.

lev

y levels.

ni

number of observations by level of y.

For predict.Lda and predict.Qda:

pred

predicted classes of observations.

ds

Prediction of the normal probability density.

posterior

posterior probabilities of the classes.

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.

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.

Details

For each observation to predict, the posterior probability to belong to a given class is estimated using the Bayes' formula, assuming priors (proportional or uniform) and a multivariate Normal distribution for the dependent variables \(X\). The prediction is the class with the highest posterior probability.

LDA assumes homogeneous \(X-\)covariance matrices for the classes while QDA assumes different covariance matrices. The functions use dmnorm for estimating the multivariate Normal densities.

References

Saporta, G., 2011. Probabilités analyse des données et statistique. Editions Technip, Paris, France.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

## EXAMPLE 1

data(iris)

X <- iris[, 1:4]
y <- iris[, 5]
N <- nrow(X)

nTest <- round(.25 * N)
nTraining <- N - nTest
s <- sample(1:N, nTest)
Xtrain <- X[-s, ]
ytrain <- y[-s]
Xtest <- X[s, ]
ytest <- y[s]

prior <- "unif"

fm <- lda(Xtrain, ytrain, prior = prior)
res <- predict(fm, Xtest)
names(res)

headm(res$pred)
headm(res$ds)
headm(res$posterior)

err(res$pred, ytest)

## EXAMPLE 2

data(iris)

X <- iris[, 1:4]
y <- iris[, 5]
N <- nrow(X)

nTest <- round(.25 * N)
nTraining <- N - nTest
s <- sample(1:N, nTest)
Xtrain <- X[-s, ]
ytrain <- y[-s]
Xtest <- X[s, ]
ytest <- y[s]

prior <- "prop"

fm <- lda(Xtrain, ytrain, prior = prior)
res <- predict(fm, Xtest)
names(res)

headm(res$pred)
headm(res$ds)
headm(res$posterior)

err(res$pred, ytest)