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## Use an ECM algorithm (in the sense of Meng and Rubin, Biometrika 1993)
## to search for a local maximum of the likelihood surface for a
## univariate finite mixture of normals with possible equality
## constraints on the stdev parameters.
## It is assumed here that there are three components and the three normal means
## are equal to alpha, alpha-delta, and alpha+delta for unknown parameters
## alpha and delta.
## In other words, this function implements the specific model described in
## Thomas et al (2009), Extensions of Reliability Theory.
## It is a modified version of normalmixEM.
tauequivnormalmixEM <-
function (x, lambda = NULL, mu = NULL, sigma = NULL, k = 3,
mean.constr = NULL, sd.constr = NULL, gparam = NULL,
epsilon = 1e-08, maxit = 10000, maxrestarts=20,
verb = FALSE, fast=FALSE, ECM = TRUE,
arbmean = TRUE, arbvar = TRUE) {
M <- A <- NULL
if (is.null(mean.constr)) {
# In this case, we will be fitting a 3-component mixture model with means
# constrained to be alpha, alpha-delta, and alpha+delta for
# parameters alpha and delta.
k <- 3
if (length(mu) != 3) mu <- NULL
if (length(sigma) != 3) sigma <- NULL
M <- matrix(c(1, 1, 1, 0, -1, 1), 3, 2)
# We will also constain the reciprocals of the variances to be
# gamma_1+gamma_2, gamma_1, and gamma_1 for positive
# parameters gamma_1 and gamma_2.
A <- matrix(c(1, 1, 1, 1, 0, 0), 3, 2)
}
normalmixMMlc(x,
lambda = lambda,
mu = mu,
sigma = sigma,
k = k,
mean.constr = mean.constr,
mean.lincstr = M,
var.lincstr = A,
gparam = gparam,
epsilon = epsilon,
maxit = maxit,
maxrestarts = maxrestarts,
verb = verb)
}
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