dmixlm function

pdf of the mixture of Gaussian linear (Markov-switching) models for hhsmm

The probability density function of a mixture Gaussian linear (Markov-switching) models for a specified observation vector, a specified state and a specified model's parameters

dmixlm(x, j, model, resp.ind = 1)

Arguments

• x: the observation matrix including responses and covariates
• j: a specified state between 1 to nstate
• model: a hhsmmspec model
• 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

Returns

the probability density function value

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)

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.

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir