fconstr_pGMM: Fit constrained penalized Gaussian mixture model

In hillarykoch/CLIMB: Composite LIkelihood eMpirical Bayes

Fit constrained penalized Gaussian mixture model

Description

For a given maximum number of clusters in the data, find the optimal penalization parameter lambda and the optimal clustering. Lambda penalizes the mixing proportions. Model optimality is determined by best BIC. The constraints here are that, for any number of replicates, there are 3 components h = -1,0,1. h=0 implies no associations, while 1 and -1 imply positive and negative associations. The mean of the no association component is restricted to 0, while the positive and negative associations have mean mu and -mu. The standard deviation of the no association component is restricted to 1, while the positive and negative associations have standard deviation sigma. For two replicates where both have positive association or both have negative association, they have correlation rho. For two replicates, one with positive association and one with negative association, they have correlation -rho. Otherwise, correlation between replicates is restricted to 0.

Usage

fconstr_pGMM(x, lambda = NULL, tol=1e-06,
                itermax = 300, penaltyType = c("SCAD", "LASSO"))

Arguments

x	An n by d numeric matrix of n observations with dimension d.
lambda	Penalty parameter. If unspecified, a grid is automatically generated.
tol	Tolerance for the stopping rule for the EM algorithm. A lower tolerance will require more iterations. Defaults to 1e-06.
itermax	Maximum number of iterations of the EM algorithm to perform. Defaults to 300.
penaltyType	Character string specifying which term to use to penalize the cluster mixing proportions. Defaults to SCAD.

Details

The model is fit using the expectation-maximization algorithm. Clusters are initialized using kmeans with 3^d clusters. Initial values of mixing proportions, means, and variance (covariance) matrices for EM are computed from these clusters.

Value

k	Optimal number of clusters.
prop	Mixing proportions in each cluster.
mu	Cluster means.
sigma	Cluster variances.
rho	Correlation between replicates with association.
df	Degrees of freedom for each cluster.
cluster	Cluster labels for each of the n observations.
BIC	BIC of optimal fit.
lambda	Lambda of optimal fit.
ll	Log likelihood of the data given the optimal fit.
post_prob	Posterior probability of each observation arising from each cluster.
combos	Used internally with fconstr_pGMCM. Can be ignored by the user.

Author(s)

[e-mail]

See Also

fconstr_pGMCM

Examples

library(mvtnorm)
set.seed(234)
pal <- sample(get_pals(4), 9, replace = FALSE)

n <- 3600
prop <- c(0.4,0.05,0.1,0.05,0.1,0.05,0.1,0.05,0.1)
mu <- 4
sigma <- 1.3
rho <- 0.8
sim <- rconstr_GMCM(n, prop, mu, sigma, rho, 2)

################################################################################
# Not run:
# fit <- fconstr_pGMM(sim$data, itermax = 100)
#
# par(mfrow = c(1,2))
# plot(sim$data, col = pal[sim$cluster], main = "observed")
# plot(sim$data, col = pal[fit$cluster], main = "GMM classification")
################################################################################

hillarykoch/CLIMB documentation built on Oct. 24, 2022, 4:27 a.m.