additive_reg_mstep function

the M step function of the EM algorithm

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

additive_reg_mstep(x, wt, control = list(K = 5, lambda0 = 0.01, resp.ind = 1))

Arguments

• x: the observation matrix

• wt: the state probabilities matrix (number of observations times number of states)

• control: the parameters to control the M-step function. The simillar name is chosen with that of dnorm_additive_reg, to be used in ... argument of the hhsmmfit function. Here, it contains the following items:

  • K the degrees of freedom for the B-spline, default is K=5
  • lambda0 the initial value of the smoothing parameter, default is lambda0=0.01
  • 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

list of emission (nonparametric mixture of splines) parameters:

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 = NULL,
ltr = FALSE, final.absorb = FALSE, verbose = TRUE, regress = TRUE)
initmodel = initialize_model(clus = clus ,mstep = additive_reg_mstep,
dens.emission = dnorm_additive_reg, sojourn = NULL, semi = rep(FALSE, 3),
M = max(train$N),verbose = TRUE)
fit1 = hhsmmfit(x = train, model = initmodel, mstep = additive_reg_mstep,
M = max(train$N))
plot(train$x[, 1] ~ train$x[, 2], col = train$s, pch = fit1$yhat, 
xlab = "x", ylab = "y")
text(0,30, "colors are real states",col="red")
text(0,28, "characters are predicted states")
pred <- addreg_hhsmm_predict(fit1, train$x[, 2], 5)
yhat1 <- pred[[1]]
yhat2 <- pred[[2]]
yhat3 <- pred[[3]]

lines(yhat1[order(train$x[, 2])]~sort(train$x[, 2]),col = 2)
lines(yhat2[order(train$x[, 2])]~sort(train$x[, 2]),col = 1)
lines(yhat3[order(train$x[, 2])]~sort(train$x[, 2]),col = 3)

References

Langrock, R., Adam, T., Leos-Barajas, V., Mews, S., Miller, D. L., and Papastamatiou, Y. P. (2018). Spline-based nonparametric inference in general state-switching models. Statistica Neerlandica, 72(3), 179-200.

Author(s)

Morteza Amini, morteza.amini@ut.ac.ir , Reza Salehian, reza.salehian@ut.ac.ir