cmb.search: Optimal conditioning order search

Description

Runs forward, backward, or stepwise variable selection procedure for obtaining the parsimonious conditional mixture models when all conditional orders are considered. Alternatively, runs the optimal order search algorithm, and parsimonious conditional mixture modeling for the obtained order.

Usage

cmb.search(x, l, K, method = "stepwise", all.perms  = TRUE, id0 = NULL,  n.em = 200,
em.iter = 5, EM.iter = 200, nk.min = NULL, max.spur = 5, tol = 1e-06, silent = FALSE, 
Parallel = TRUE, n.cores = 4)

Value

The list models is returned when all.perms = TRUE.

best.model

membership assignments and estimated parameters of mixture model with the optimal contioning order.

data: the input dataset
model: estimated regression models for each cluster (K x p)
id: vector of estimated membership (length n)
loglik: estimated log likelihood
BIC: Bayesian Information Criterion
Pi: vector of estimated mixing proportions (length K)
tau: matrix of estimated posterior probabilities (n x K)
beta: matrix of estimated regression parameters (K x (p + p(p-1)l/2) )
s2: matrix of estimated variances (K x p)
order: applied conditioning order (length p)
n_pars: number of parameters

models

membership assignments and model parameters of mixture models with all conditioning orders.

model: list of estimated regression models for all clusters (K x p x p!)

id

p! vectors of estimated memberships (n x p!)

loglik

estimated log likelihood values (length p!)

BIC

Bayesian Information Criterion values (length p!)

Pi

p! vectors of estimated mixing proportions (K x p!)

tau

p! matrices of estimated posterior probabilities (K x p!)

beta

p! matrices of estimated regression parameters (K x (p + p(p-1)l/2) x p! )

s2

p! matrices of estimated variances (K x p x p!)

order

appled conditioning orders (p! x p )

n_pars

number of parameters in p! models (length p!)

Arguments

x: dataset matrix (n x p)
l: order of polynomial regression model
K: number of clusters
method: variable selection method (options 'stepwise', 'forward', 'backward' and 'none')
all.perms: conditioning order search algorithm (TRUE: full search; FALSE proposed search algorithm)
id0: initial group membership (length n)
n.em: number of short EM in emEM procedure
em.iter: maximum number of short EM iterations in emEM
EM.iter: maximum number of EM iterations
nk.min: spurious output control
max.spur: number of trials
tol: tolerance level
silent: output control
Parallel: Parallel computing
n.cores: number of cores in parallel computing

Details

Functions 'cmb.search' and 'cmb.em' have common arguments except 'all.perm'. With all.perms = TRUE, a full search is applied to data, that is running parsimonious conditional mixture modeling for all orders and recognizing the optimal order based on the BIC. Then two lists are returned: best.model stores the results for the conditional mixture model with the optimal order, and models has results for all orders. With the option all.perms = FALSE, the optimal conditional order search algorithm is applied, and then only the list best.model is returned.

Examples

Run this code

set.seed(1)
K = 3
l <- 2
x <- as.matrix(iris[,-5])

# \donttest{
obj <- cmb.search(x = x, l, K, method = "stepwise", all.perms = FALSE,
Parallel = FALSE, silent = FALSE)
obj$best.model$BIC
# }