Manly.select {ManlyMix}

Manly transformation selection

Description

Runs forward or backward model selection procedures for finding the optimal model in terms of BIC.

Usage

Manly.select(X, model, method, tol = 1e-5, max.iter = 1000, silent = FALSE)

Arguments

X

dataset matrix (n x p)

model

list containing parameters of the initial model

method

model selection method (options 'forward' and 'backward')

tol

tolerance level

max.iter

maximum number of iterations

silent

output control

Details

Runs Manly forward and backward model selection procedures for a provided dataset. Forward and backward selection can be started from any ManlyMix object provided in 'model'. Manly transformation parameters are provided in matrix 'model$la'. If some transformations are not needed for specific components, zeros have to be specified in corresponding poisition. When all transformation parameters are set to zero, Manly mixture model degenerates to a Gaussian mixture model. Notation: n - sample size, p - dimensionality of the dataset X, K - number of mixture components.

Value

la

matrix of the estimated transformation parameters (K x p)

tau

vector of mixing proportions (length K)

Mu

matrix of the estimated mean vectors (K x p)

S

array of the estimated covariance matrices (p x p x K)

gamma

matrix of posterior probabilities (n x K)

id

estimated membership vector (length n)

ll

log likelihood value

bic

Bayesian Information Criterion

iter

number of EM iterations run

flag

convergence flag (0 - success, 1 - failure)

See Also

Manly.EM

Examples

set.seed(123)

K <- 3; p <- 4
X <- as.matrix(iris[,-5])
id.true <- rep(1:K, each = 50)

# Obtain initial memberships based on the K-means algorithm
id.km <- kmeans(X, K)$cluster

# Run the EM algorithm for a Gaussian mixture model based on K-means solution
G <- Manly.EM(X, id = id.km)
id.G <- G$id

# Run FORWARD SELECTION ('silent' is on)
F <- Manly.select(X, model = G, method = "forward", silent = TRUE)

# Run the EM algorithm for a full Manly mixture model based on Gaussian mixture solution
la <- matrix(0.1, K, p)
M <- Manly.EM(X, id = id.G, la = la)

# Run BACKWARD SELECTION ('silent' is off)
B <- Manly.select(X, model = M, method = "backward")

BICs <- c(G$bic, M$bic, F$bic, B$bic)
names(BICs) <- c("Gaussian", "Manly", "Forward", "Backward")
BICs