# R/additive-reg-mstep.R In hhsmm: Hidden Hybrid Markov/Semi-Markov Model Fitting

#### Documented in additive_reg_mstep

#' 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
#'
#' @author Morteza Amini, \email{morteza.amini@@ut.ac.ir},
#' Reza Salehian,  \email{reza.salehian@@ut.ac.ir}
#'
#' @param x the observation matrix
#' @param wt the state probabilities matrix (number of observations
#' times number of states)
#' @param control the parameters to control the M-step function.
#' The simillar name is chosen with that of \code{\link{dnorm_additive_reg}},
#' to be used in \code{...} argument of the \code{\link{hhsmmfit}} function.
#' Here, it contains the following items:
#' \itemize{
#' \item \code{K} the degrees of freedom for the B-spline, default is \code{K=5}
#' \item \code{lambda0} the initial value of the smoothing parameter, default is \code{lambda0=0.01}
#' \item \code{resp.ind} a vector of the column numbers of \code{x} which contain response variables.
#' The default is 1, which means that the first column of \code{x} is the univariate
#' response variable
#'}
#'
#' @return list of emission (nonparametric mixture of splines) parameters:
# \code{coef}, \code{intercept} and \code{sigma}
#'
#' @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$x[, 2]),col = 3) #' #' @references #' Langrock, R., Adam, T., Leos-Barajas, V., #' Mews, S., Miller, D. L., and Papastamatiou, Y. P. (2018). #' Spline-based nonparametric inference in general state-switching models. #' Statistica Neerlandica, 72(3), 179-200. #' #' @importFrom magic adiag #' @importFrom splines2 bSpline #' #' @export additive_reg_mstep <- function(x, wt, control = list(K = 5, lambda0 = 0.01, resp.ind = 1)) { defcon <- list(K = 5, lambda0 = 0.01, resp.ind = 1) control <- modifyList(defcon, control) K <- control$K
lambda0 <- control$lambda0 resp.ind <- control$resp.ind
nstate = ncol(wt)
wt <- wt / rowSums(wt)
n = nrow(x)
y = as.matrix(x[, resp.ind])
x = as.matrix(x[1:nrow(y), - resp.ind])
dx = ncol(x)
dy = ncol(y)
basis = lapply(1:dx, function(i) bSpline(x[,i], df = K,
Boundary.knots = c(min(x[, i]) - 0.01,
max(x[, i]) + 0.01)))
z <- Reduce(cbind, basis)
z <- cbind(1, z)
emission = list(coef = list(), intercept = list(),
sigma =  list())
D2 = diff(diag(K),differences = 2)
D2 = t(D2) %*% D2
lambda = array(lambda0, dim = c(nstate, dx, dy))
for (j in 1:nstate) {
emission$sigma[[j]] = cov(y) S = list() for (i in 1:dy) { S[[i]] = adiag(0) for (k in 1:dx) { S[[i]] = adiag(S[[i]], lambda[j, k, i] * D2) } } W = diag(wt[, j]) coef = sapply(1:dy, function(i) ginv(t(z) %*% W %*% z + S[[i]]) %*% t(z) %*% W %*% y[,i]) emission$intercept[[j]] = coef[1,]
emission$coef[[j]] = array(coef[-1,], dim = c(K, dx, dy)) residuals = y - sapply(1:dy, function(p) emission$intercept[[j]][p] + rowSums(sapply(1:dx, function(i)
basis[[i]] %*% emission$coef[[j]][, i, p]))) swt = wt[, j]/sum(wt[,j]) residuals = sapply(1:n, function(i) sqrt(swt[i]) * residuals[i,]) residuals = matrix(residuals, n, dy, byrow=TRUE) emission$sigma[[j]] = t(residuals) %*% (residuals)/(1-sum(swt^2))
for(i in 1:dx){
F = n * ginv(t(basis[[i]]) %*% basis[[i]])
for(p in 1:dy){
lambda[j, i, p] = 2 /
((t(emission$coef[[j]][, i, p]) %*% D2 %*% emission$coef[[j]][, i, p])/
emission$sigma[[j]][p, p] + sum(diag(F %*% D2) / n)) } } S = list() for(i in 1:dy) { S[[i]] = adiag(0) for (k in 1:dx) { S[[i]] = adiag(S[[i]], lambda[j, k, i] * D2) } } coef = sapply(1:dy, function(i) ginv(t(z) %*% W %*% z + S[[i]]) %*% t(z) %*% W %*% y[,i]) emission$intercept[[j]] = coef[1,]
emission$coef[[j]] = array(coef[-1,], dim = c(K, dx, dy)) residuals = y - sapply(1:dy, function(p) emission$intercept[[j]][p] + rowSums(sapply(1:dx, function(i)
basis[[i]] %*% emission$coef[[j]][, i, p]))) residuals = sapply(1:n, function(i) sqrt(swt[i]) * residuals[i,]) residuals = matrix(residuals, n, dy, byrow=TRUE) emission$sigma[[j]] = t(residuals) %*% (residuals)/(1-sum(swt^2))
}# for j
emission
}# end of function


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hhsmm documentation built on May 29, 2024, 6:08 a.m.