mixlm_mstep: the M step function of the EM algorithm

In hhsmm: Hidden Hybrid Markov/Semi-Markov Model Fitting

the M step function of the EM algorithm

Description

The M step function of the EM algorithm for the mixture of Gaussian linear (Markov-switching) regressions as the emission distribution using the responses and covariates matrices and the estimated weight vectors

Usage

mixlm_mstep(x, wt1, wt2, resp.ind = 1)

Arguments

x	the observation matrix including responses and covariates
wt1	the state probabilities matrix (number of observations times number of states)
wt2	the mixture components probabilities list (of length nstate) of matrices (number of observations times number of mixture components)
resp.ind	a vector of the column numbers of x which contain response variables. The default is 1, which means that the first column of x is the univariate response variable

Value

list of emission (mixture of Gaussian linear regression models) parameters: (intercept, coefficients, csigma (conditional covariance) and mix.p)

Author(s)

Morteza Amini, [e-mail]

References

Kim, C. J., Piger, J. and Startz, R. (2008). Estimation of Markov regime-switching regression models with endogenous switching. Journal of Econometrics, 143(2), 263-273.

Examples

J <- 3
initial <- c(1, 0, 0)
semi <- rep(FALSE, 3)
P <- matrix(c(0.5, 0.2, 0.3, 0.2, 0.5, 0.3, 0.1, 0.4, 0.5), nrow = J, 
byrow = TRUE)
par <- list(intercept = list(3, list(-10, -1), 14),
coefficient = list(-1, list(1, 5), -7),
csigma = list(1.2, list(2.3, 3.4), 1.1),
mix.p = list(1, c(0.4, 0.6), 1))
model <- hhsmmspec(init = initial, transition = P, parms.emis = par,
dens.emis = dmixlm, semi = semi)
train <- simulate(model, nsim = c(20, 30, 42, 50), seed = 1234, 
remission = rmixlm, covar = list(mean = 0, cov = 1))
clus = initial_cluster(train = train, nstate = 3, nmix = c(1, 2, 1),
ltr = FALSE, final.absorb = FALSE, verbose = TRUE, regress = TRUE)
initmodel = initialize_model(clus = clus ,mstep = mixlm_mstep,
dens.emission = dmixlm, sojourn = NULL, semi = rep(FALSE, 3),
M = max(train$N),verbose = TRUE)
fit1 = hhsmmfit(x = train, model = initmodel, mstep = mixlm_mstep,
M = max(train$N))
plot(train$x[, 1] ~ train$x[, 2], col = train$s, pch = 16, 
xlab = "x", ylab = "y")
abline(fit1$model$parms.emission$intercept[[1]],
fit1$model$parms.emission$coefficient[[1]], col = 1)
abline(fit1$model$parms.emission$intercept[[2]][[1]],
fit1$model$parms.emission$coefficient[[2]][[1]], col = 2)
abline(fit1$model$parms.emission$intercept[[2]][[2]],
fit1$model$parms.emission$coefficient[[2]][[2]], col = 2)
abline(fit1$model$parms.emission$intercept[[3]],
fit1$model$parms.emission$coefficient[[3]], col = 3)

hhsmm documentation built on Aug. 8, 2023, 9:06 a.m.