lda: LDA and QDA

In mlesnoff/rchemo: Dimension reduction, Regression and Discrimination for Chemometrics

LDA and QDA

Description

Probabilistic (parametric) linear and quadratic discriminant analysis.

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.

Usage

lda(X, y, prior = c("unif", "prop"))

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

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	A fitted model, output of a call to the main functions.
...	Optional arguments. Not used.

Value

See the examples.

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

data(iris)

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

m <- round(.25 * N) # Test
n <- N - m          # Training
s <- sample(1:N, m)
Xtrain <- X[-s, ]
ytrain <- y[-s]
Xtest <- X[s, ]
ytest <- y[s]

prior <- "unif"
#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)

mlesnoff/rchemo documentation built on April 15, 2023, 1:25 p.m.