#' Build a Hidden Markov Model
#'
#' Function \code{build_hmm} constructs a hidden Markov model object of class \code{hmm}.
#'
#' The returned model contains some attributes such as \code{nobs} and \code{df},
#' which define the number of observations in the model and the number of estimable
#' model parameters, used in computing BIC.
#' When computing \code{nobs} for a multichannel model with \eqn{C} channels,
#' each observed value in a single channel amounts to \eqn{1/C} observation,
#' i.e. a fully observed time point for a single sequence amounts to one observation.
#' For the degrees of freedom \code{df}, zero probabilities of the initial model are
#' defined as structural zeroes.
#' @export
#' @param observations An \code{stslist} object (see \code{\link[TraMineR]{seqdef}}) containing
#' the sequences, or a list of such objects (one for each channel).
#' @param n_states A scalar giving the number of hidden states. Not used if starting values for model parameters
#' are given with \code{initial_probs}, \code{transition_probs}, or \code{emission_probs}.
#' @param transition_probs A matrix of transition probabilities.
#' @param emission_probs A matrix of emission probabilities or a list of such
#' objects (one for each channel). Emission probabilities should follow the
#' ordering of the alphabet of observations (\code{alphabet(observations)}, returned as \code{symbol_names}).
#' @param initial_probs A vector of initial state probabilities.
#' @param state_names A list of optional labels for the hidden states. If \code{NULL},
#' the state names are taken from the row names of the transition matrix. If this is
#' also \code{NULL}, numbered states are used.
#' @param channel_names A vector of optional names for the channels.
#' @param ... Additional arguments to \code{simulate_transition_probs}.
#'
#' @return Object of class \code{hmm} with the following elements:
#' \describe{
#' \item{\code{observations}}{State sequence object or a list of such objects containing the data.}
#' \item{\code{transition_probs}}{A matrix of transition probabilities.}
#' \item{\code{emission_probs}}{A matrix or a list of matrices of emission probabilities.}
#' \item{\code{initial_probs}}{A vector of initial probabilities.}
#' \item{\code{state_names}}{Names for hidden states.}
#' \item{\code{symbol_names}}{Names for observed states.}
#' \item{\code{channel_names}}{Names for channels of sequence data.}
#' \item{\code{length_of_sequences}}{(Maximum) length of sequences.}
#' \item{\code{n_sequences}}{Number of sequences.}
#' \item{\code{n_symbols}}{Number of observed states (in each channel).}
#' \item{\code{n_states}}{Number of hidden states.}
#' \item{\code{n_channels}}{Number of channels.}
#' }
#'
#' @seealso \code{\link{fit_model}} for estimating model parameters; and
#' \code{\link{plot.hmm}} for plotting \code{hmm} objects.
#' @examples
#'
#' # Single-channel data
#'
#' data("mvad", package = "TraMineR")
#'
#' mvad_alphabet <- c(
#' "employment", "FE", "HE", "joblessness", "school",
#' "training"
#' )
#' mvad_labels <- c(
#' "employment", "further education", "higher education",
#' "joblessness", "school", "training"
#' )
#' mvad_scodes <- c("EM", "FE", "HE", "JL", "SC", "TR")
#' mvad_seq <- seqdef(mvad, 17:86,
#' alphabet = mvad_alphabet, states = mvad_scodes,
#' labels = mvad_labels, xtstep = 6
#' )
#'
#' # Initializing an HMM with 4 hidden states, random starting values
#' init_hmm_mvad1 <- build_hmm(observations = mvad_seq, n_states = 4)
#'
#' # Starting values for the emission matrix
#' emiss <- matrix(NA, nrow = 4, ncol = 6)
#' emiss[1, ] <- seqstatf(mvad_seq[, 1:12])[, 2] + 1
#' emiss[2, ] <- seqstatf(mvad_seq[, 13:24])[, 2] + 1
#' emiss[3, ] <- seqstatf(mvad_seq[, 25:48])[, 2] + 1
#' emiss[4, ] <- seqstatf(mvad_seq[, 49:70])[, 2] + 1
#' emiss <- emiss / rowSums(emiss)
#'
#' # Starting values for the transition matrix
#'
#' tr <- matrix(
#' c(
#' 0.80, 0.10, 0.05, 0.05,
#' 0.05, 0.80, 0.10, 0.05,
#' 0.05, 0.05, 0.80, 0.10,
#' 0.05, 0.05, 0.10, 0.80
#' ),
#' nrow = 4, ncol = 4, byrow = TRUE
#' )
#'
#' # Starting values for initial state probabilities
#' init <- c(0.3, 0.3, 0.2, 0.2)
#'
#' # HMM with own starting values
#' init_hmm_mvad2 <- build_hmm(
#' observations = mvad_seq, transition_probs = tr,
#' emission_probs = emiss, initial_probs = init
#' )
#'
#' #########################################
#'
#'
#' # Multichannel data
#'
#' # Three-state three-channel hidden Markov model
#' # See ?hmm_biofam for a five-state version
#'
#' data("biofam3c")
#'
#' # Building sequence objects
#' marr_seq <- seqdef(biofam3c$married,
#' start = 15,
#' alphabet = c("single", "married", "divorced")
#' )
#' child_seq <- seqdef(biofam3c$children,
#' start = 15,
#' alphabet = c("childless", "children")
#' )
#' left_seq <- seqdef(biofam3c$left,
#' start = 15,
#' alphabet = c("with parents", "left home")
#' )
#'
#' # Define colors
#' attr(marr_seq, "cpal") <- c("violetred2", "darkgoldenrod2", "darkmagenta")
#' attr(child_seq, "cpal") <- c("darkseagreen1", "coral3")
#' attr(left_seq, "cpal") <- c("lightblue", "red3")
#'
#' # Left-to-right HMM with 3 hidden states and random starting values
#' set.seed(1010)
#' init_hmm_bf1 <- build_hmm(
#' observations = list(marr_seq, child_seq, left_seq),
#' n_states = 3, left_right = TRUE, diag_c = 2
#' )
#'
#'
#' # Starting values for emission matrices
#'
#' emiss_marr <- matrix(NA, nrow = 3, ncol = 3)
#' emiss_marr[1, ] <- seqstatf(marr_seq[, 1:5])[, 2] + 1
#' emiss_marr[2, ] <- seqstatf(marr_seq[, 6:10])[, 2] + 1
#' emiss_marr[3, ] <- seqstatf(marr_seq[, 11:16])[, 2] + 1
#' emiss_marr <- emiss_marr / rowSums(emiss_marr)
#'
#' emiss_child <- matrix(NA, nrow = 3, ncol = 2)
#' emiss_child[1, ] <- seqstatf(child_seq[, 1:5])[, 2] + 1
#' emiss_child[2, ] <- seqstatf(child_seq[, 6:10])[, 2] + 1
#' emiss_child[3, ] <- seqstatf(child_seq[, 11:16])[, 2] + 1
#' emiss_child <- emiss_child / rowSums(emiss_child)
#'
#' emiss_left <- matrix(NA, nrow = 3, ncol = 2)
#' emiss_left[1, ] <- seqstatf(left_seq[, 1:5])[, 2] + 1
#' emiss_left[2, ] <- seqstatf(left_seq[, 6:10])[, 2] + 1
#' emiss_left[3, ] <- seqstatf(left_seq[, 11:16])[, 2] + 1
#' emiss_left <- emiss_left / rowSums(emiss_left)
#'
#' # Starting values for transition matrix
#' trans <- matrix(
#' c(
#' 0.9, 0.07, 0.03,
#' 0, 0.9, 0.1,
#' 0, 0, 1
#' ),
#' nrow = 3, ncol = 3, byrow = TRUE
#' )
#'
#' # Starting values for initial state probabilities
#' inits <- c(0.9, 0.09, 0.01)
#'
#' # HMM with own starting values
#' init_hmm_bf2 <- build_hmm(
#' observations = list(marr_seq, child_seq, left_seq),
#' transition_probs = trans,
#' emission_probs = list(emiss_marr, emiss_child, emiss_left),
#' initial_probs = inits
#' )
#'
build_hmm <- function(observations, n_states, transition_probs, emission_probs, initial_probs,
state_names = NULL, channel_names = NULL, ...) {
multichannel <- is_multichannel(observations)
# Single channel but observations is a list
if (is.list(observations) && !inherits(observations, "stslist") && length(observations) == 1) {
observations <- observations[[1]]
multichannel <- FALSE
}
n_channels <- ifelse(multichannel, length(observations), 1L)
if (!missing(transition_probs) || !missing(initial_probs) || !missing(emission_probs)) {
if (missing(transition_probs) || missing(initial_probs) || missing(emission_probs)) {
stop(paste0("Provide either n_states or all three of 'initial_probs', ",
"'transition_probs', and 'emission_probs'."))
}
if (!is.matrix(transition_probs)) {
stop(paste("Object provided for 'transition_probs' is not a matrix."))
}
if (!is.vector(initial_probs)) {
stop(paste("Object provided for initial_probs is not a vector."))
}
if (dim(transition_probs)[1] != dim(transition_probs)[2]) {
stop("Argument 'transition_probs' must be a square matrix.")
}
n_states <- nrow(transition_probs)
if (length(initial_probs) != n_states) {
stop(paste("Length of 'initial_probs' is not equal to the number of states."))
}
if (is.null(state_names)) {
if (is.null(state_names <- rownames(transition_probs))) {
state_names <- paste("State", 1:n_states)
}
} else {
if (length(state_names) != n_states) {
stop("Length of 'state_names' is not equal to the number of hidden states.")
}
}
if (!isTRUE(all.equal(rowSums(transition_probs), rep(1, dim(transition_probs)[1]), check.attributes = FALSE))) {
stop("Transition probabilities in 'transition_probs' do not sum to one.")
}
dimnames(transition_probs) <- list(from = state_names, to = state_names)
if (is.list(emission_probs) && length(emission_probs) == 1) {
emission_probs <- emission_probs[[1]]
}
if (is.list(emission_probs)) {
if (length(observations) != length(emission_probs)) {
stop("Number of channels defined by 'emission_probs' differs from one defined by observations.")
}
for (j in 1:n_channels) {
if (!is.matrix(emission_probs[[j]])) {
stop(paste("Object provided in 'emission_probs' for channel", j, "is not a matrix."))
}
}
if (length(unique(sapply(observations, nrow))) > 1) {
stop("The number of subjects (rows) is not the same in all channels.")
}
if (length(unique(sapply(observations, ncol))) > 1) {
stop("The length of the sequences (number of columns) is not the same in all channels.")
}
n_sequences <- nrow(observations[[1]])
length_of_sequences <- ncol(observations[[1]])
symbol_names <- lapply(observations, alphabet)
n_symbols <- lengths(symbol_names)
if (any(sapply(emission_probs, nrow) != n_states)) {
stop("Number of rows in 'emission_probs' is not equal to the number of states.")
}
if (any(n_symbols != sapply(emission_probs, ncol))) {
stop("Number of columns in 'emission_probs' is not equal to the number of symbols.")
}
if (!isTRUE(all.equal(c(sapply(emission_probs, rowSums)), rep(1, n_channels * n_states), check.attributes = FALSE))) {
stop("Emission probabilities in 'emission_probs' do not sum to one.")
}
if (is.null(channel_names)) {
if (is.null(channel_names <- names(observations))) {
channel_names <- paste("Channel", 1:n_channels)
}
} else if (length(channel_names) != n_channels) {
warning("The length of argument 'channel_names' does not match the number of channels. Names were not used.")
channel_names <- paste("Channel", 1:n_channels)
}
for (i in 1:n_channels) {
dimnames(emission_probs[[i]]) <- list(state_names = state_names, symbol_names = symbol_names[[i]])
}
names(emission_probs) <- channel_names
} else {
if (!is.matrix(emission_probs)) {
stop(paste("Object provided for 'emission_probs' is not a matrix."))
}
if (is.null(channel_names)) {
channel_names <- "Observations"
}
n_sequences <- nrow(observations)
length_of_sequences <- ncol(observations)
symbol_names <- alphabet(observations)
n_symbols <- length(symbol_names)
if (n_states != dim(emission_probs)[1]) {
stop("Number of rows in 'emission_probs' is not equal to the number of states.")
}
if (n_symbols != dim(emission_probs)[2]) {
stop("Number of columns in 'emission_probs' is not equal to the number of symbols.")
}
if (!isTRUE(all.equal(rep(1, n_states), rowSums(emission_probs), check.attributes = FALSE))) {
stop("Emission probabilities in 'emission_probs' do not sum to one.")
}
dimnames(emission_probs) <- list(state_names = state_names, symbol_names = symbol_names)
}
# Simulate starting values
} else {
if (missing(n_states)) {
stop(paste("Provide either n_states or all three of initial_probs, transition_probs, and emission_probs."))
}
transition_probs <- simulate_transition_probs(n_states = n_states, n_clusters = 1, ...)
if (is.null(state_names)) {
if (is.null(state_names <- rownames(transition_probs))) {
state_names <- paste("State", 1:n_states)
}
}
dimnames(transition_probs) <- list(from = state_names, to = state_names)
initial_probs <- simulate_initial_probs(n_states = n_states, n_clusters = 1)
if (!multichannel) {
n_sequences <- nrow(observations)
length_of_sequences <- ncol(observations)
symbol_names <- alphabet(observations)
n_symbols <- length(symbol_names)
if (is.null(channel_names)) {
channel_names <- "Observations"
}
emission_probs <- simulate_emission_probs(n_states = n_states, n_symbols = n_symbols)
dimnames(emission_probs) <- list(state_names = state_names, symbol_names = symbol_names)
} else {
n_sequences <- nrow(observations[[1]])
length_of_sequences <- ncol(observations[[1]])
symbol_names <- lapply(observations, alphabet)
n_symbols <- lengths(symbol_names)
if (is.null(channel_names)) {
if (is.null(channel_names <- names(observations))) {
channel_names <- paste("Channel", 1:n_channels)
}
} else if (length(channel_names) != n_channels) {
warning("The length of argument channel_names does not match the number of channels. Names were not used.")
channel_names <- paste("Channel", 1:n_channels)
}
emission_probs <- vector("list", n_channels)
for (c in 1:n_channels) {
emission_probs[[c]] <- simulate_emission_probs(n_states = n_states, n_symbols = n_symbols[c])
dimnames(emission_probs[[c]]) <- list(state_names = state_names, symbol_names = symbol_names[[c]])
}
names(emission_probs) <- channel_names
}
}
names(initial_probs) <- state_names
if (multichannel) {
nobs <- sum(sapply(observations, function(x) {
sum(!(x == attr(observations[[1]], "nr") |
x == attr(observations[[1]], "void") |
is.na(x)))
})) / n_channels
} else {
nobs <- sum(!(observations == attr(observations, "nr") |
observations == attr(observations, "void") |
is.na(observations)))
}
model <- structure(
list(
observations = observations, transition_probs = transition_probs,
emission_probs = emission_probs, initial_probs = initial_probs,
state_names = state_names,
symbol_names = symbol_names, channel_names = channel_names,
length_of_sequences = length_of_sequences,
n_sequences = n_sequences,
n_symbols = n_symbols, n_states = n_states,
n_channels = n_channels
),
class = "hmm",
nobs = nobs,
df = sum(initial_probs > 0) - 1 + sum(transition_probs > 0) - n_states +
sum(unlist(emission_probs) > 0) - n_states * n_channels,
type = "hmm"
)
model
}
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