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#' Build a Mixture Hidden Markov Model
#'
#' Function \code{build_mhmm} constructs a mixture hidden Markov model object of class \code{mhmm}.
#'
#' 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 numerical vector giving the number of hidden states in each submodel
#' (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 list of matrices of transition
#' probabilities for the submodel of each cluster.
#' @param emission_probs A list which contains matrices of emission probabilities or
#' a list of such objects (one for each channel) for the submodel of each cluster.
#' Note that the matrices must have dimensions \eqn{m x s} where \eqn{m} is the number of
#' hidden states and \eqn{s} is the number of unique symbols (observed states) in the
#' data. Emission probabilities should follow the ordering of the alphabet of
#' observations (\code{alphabet(observations)}, returned as \code{symbol_names}).
#' @param initial_probs A list which contains vectors of initial state
#' probabilities for the submodel of each cluster.
#' @param formula Optional formula of class \code{\link{formula}} for the
#' mixture probabilities. Left side omitted.
#' @param data A data frame containing the variables used in the formula.
#' Ignored if no formula is provided.
#' @param coefficients An optional \eqn{k x l} matrix of regression coefficients for
#' time-constant covariates for mixture probabilities, where \eqn{l} is the number
#' of clusters and \eqn{k} is the number of covariates. A logit-link is used for
#' mixture probabilities. The first column is set to zero.
#' @param cluster_names A vector of optional names for the clusters.
#' @param state_names A list of optional labels for the hidden states. If \code{NULL},
#' the state names are taken as row names of transition matrices. 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{mhmm} with following elements:
#' \describe{
#' \item{\code{observations}}{State sequence object or a list of such 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{coefficients}}{A matrix of parameter coefficients for covariates (covariates in rows, clusters in columns).}
#' \item{\code{X}}{Covariate values for each subject.}
#' \item{\code{cluster_names}}{Names for clusters.}
#' \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.}
#' \item{\code{n_covariates}}{Number of covariates.}
#' \item{\code{n_clusters}}{Number of clusters.}
#' }
#' @seealso \code{\link{fit_model}} for fitting mixture Hidden Markov models;
#' \code{\link{summary.mhmm}} for a summary of a MHMM; \code{\link{separate_mhmm}} for
#' reorganizing a MHMM into a list of separate hidden Markov models; and
#' \code{\link{plot.mhmm}} for plotting \code{mhmm} objects.
#'
#' @references Helske S. and Helske J. (2019). Mixture Hidden Markov Models for Sequence Data: The seqHMM Package in R,
#' Journal of Statistical Software, 88(3), 1-32. doi:10.18637/jss.v088.i03
#'
#' @examples
#'
#' 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")
#' )
#'
#' ## Choosing colors
#' attr(marr_seq, "cpal") <- c("#AB82FF", "#E6AB02", "#E7298A")
#' attr(child_seq, "cpal") <- c("#66C2A5", "#FC8D62")
#' attr(left_seq, "cpal") <- c("#A6CEE3", "#E31A1C")
#'
#' ## MHMM with random starting values, no covariates
#' set.seed(468)
#' init_mhmm_bf1 <- build_mhmm(
#' observations = list(marr_seq, child_seq, left_seq),
#' n_states = c(4, 4, 6),
#' channel_names = c("Marriage", "Parenthood", "Residence")
#' )
#'
#'
#' ## Starting values for emission probabilities
#'
#' # Cluster 1
#' B1_marr <- matrix(
#' c(
#' 0.8, 0.1, 0.1, # High probability for single
#' 0.8, 0.1, 0.1,
#' 0.3, 0.6, 0.1, # High probability for married
#' 0.3, 0.3, 0.4
#' ), # High probability for divorced
#' nrow = 4, ncol = 3, byrow = TRUE
#' )
#'
#' B1_child <- matrix(
#' c(
#' 0.9, 0.1, # High probability for childless
#' 0.9, 0.1,
#' 0.9, 0.1,
#' 0.9, 0.1
#' ),
#' nrow = 4, ncol = 2, byrow = TRUE
#' )
#'
#' B1_left <- matrix(
#' c(
#' 0.9, 0.1, # High probability for living with parents
#' 0.1, 0.9, # High probability for having left home
#' 0.1, 0.9,
#' 0.1, 0.9
#' ),
#' nrow = 4, ncol = 2, byrow = TRUE
#' )
#'
#' # Cluster 2
#'
#' B2_marr <- matrix(
#' c(
#' 0.8, 0.1, 0.1, # High probability for single
#' 0.8, 0.1, 0.1,
#' 0.1, 0.8, 0.1, # High probability for married
#' 0.7, 0.2, 0.1
#' ),
#' nrow = 4, ncol = 3, byrow = TRUE
#' )
#'
#' B2_child <- matrix(
#' c(
#' 0.9, 0.1, # High probability for childless
#' 0.9, 0.1,
#' 0.9, 0.1,
#' 0.1, 0.9
#' ),
#' nrow = 4, ncol = 2, byrow = TRUE
#' )
#'
#' B2_left <- matrix(
#' c(
#' 0.9, 0.1, # High probability for living with parents
#' 0.1, 0.9,
#' 0.1, 0.9,
#' 0.1, 0.9
#' ),
#' nrow = 4, ncol = 2, byrow = TRUE
#' )
#'
#' # Cluster 3
#' B3_marr <- matrix(
#' c(
#' 0.8, 0.1, 0.1, # High probability for single
#' 0.8, 0.1, 0.1,
#' 0.8, 0.1, 0.1,
#' 0.1, 0.8, 0.1, # High probability for married
#' 0.3, 0.4, 0.3,
#' 0.1, 0.1, 0.8
#' ), # High probability for divorced
#' nrow = 6, ncol = 3, byrow = TRUE
#' )
#'
#' B3_child <- matrix(
#' c(
#' 0.9, 0.1, # High probability for childless
#' 0.9, 0.1,
#' 0.5, 0.5,
#' 0.5, 0.5,
#' 0.5, 0.5,
#' 0.1, 0.9
#' ),
#' nrow = 6, ncol = 2, byrow = TRUE
#' )
#'
#'
#' B3_left <- matrix(
#' c(
#' 0.9, 0.1, # High probability for living with parents
#' 0.1, 0.9,
#' 0.5, 0.5,
#' 0.5, 0.5,
#' 0.1, 0.9,
#' 0.1, 0.9
#' ),
#' nrow = 6, ncol = 2, byrow = TRUE
#' )
#'
#' # Starting values for transition matrices
#' A1 <- matrix(
#' c(
#' 0.80, 0.16, 0.03, 0.01,
#' 0, 0.90, 0.07, 0.03,
#' 0, 0, 0.90, 0.10,
#' 0, 0, 0, 1
#' ),
#' nrow = 4, ncol = 4, byrow = TRUE
#' )
#'
#' A2 <- matrix(
#' c(
#' 0.80, 0.10, 0.05, 0.03, 0.01, 0.01,
#' 0, 0.70, 0.10, 0.10, 0.05, 0.05,
#' 0, 0, 0.85, 0.01, 0.10, 0.04,
#' 0, 0, 0, 0.90, 0.05, 0.05,
#' 0, 0, 0, 0, 0.90, 0.10,
#' 0, 0, 0, 0, 0, 1
#' ),
#' nrow = 6, ncol = 6, byrow = TRUE
#' )
#'
#' # Starting values for initial state probabilities
#' initial_probs1 <- c(0.9, 0.07, 0.02, 0.01)
#' initial_probs2 <- c(0.9, 0.04, 0.03, 0.01, 0.01, 0.01)
#'
#' # Birth cohort
#' biofam3c$covariates$cohort <- cut(biofam3c$covariates$birthyr, c(1908, 1935, 1945, 1957))
#' biofam3c$covariates$cohort <- factor(
#' biofam3c$covariates$cohort,
#' labels = c("1909-1935", "1936-1945", "1946-1957")
#' )
#'
#' ## MHMM with own starting values and covariates
#' init_mhmm_bf2 <- build_mhmm(
#' observations = list(marr_seq, child_seq, left_seq),
#' initial_probs = list(initial_probs1, initial_probs1, initial_probs2),
#' transition_probs = list(A1, A1, A2),
#' emission_probs = list(
#' list(B1_marr, B1_child, B1_left),
#' list(B2_marr, B2_child, B2_left),
#' list(B3_marr, B3_child, B3_left)
#' ),
#' formula = ~ sex + cohort, data = biofam3c$covariates,
#' cluster_names = c("Cluster 1", "Cluster 2", "Cluster 3"),
#' channel_names = c("Marriage", "Parenthood", "Residence"),
#' state_names = list(
#' paste("State", 1:4), paste("State", 1:4),
#' paste("State", 1:6)
#' )
#' )
#'
build_mhmm <- function(observations,
n_states,
transition_probs,
emission_probs,
initial_probs,
formula = NULL,
data = NULL,
coefficients = NULL,
cluster_names = NULL,
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 any initial values are given, ignore n_states and use these
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.list(transition_probs)) {
n_clusters <- length(transition_probs)
} else {
stop("'Transition_probs' is not a list.")
}
if (!is.list(emission_probs)) {
stop("'Emission_probs' is not a list.")
}
if (!is.list(initial_probs)) {
stop("'initial_probs' is not a list.")
}
if (length(emission_probs) != n_clusters || length(initial_probs) != n_clusters) {
stop("Unequal list lengths of 'transition_probs', 'emission_probs' and 'initial_probs'.")
}
if (is.null(cluster_names)) {
cluster_names <- paste("Cluster", 1:n_clusters)
} else if (length(cluster_names) != n_clusters) {
warning("The length of argument cluster_names does not match the number of clusters. Names were not used.")
cluster_names <- paste("Cluster", 1:n_clusters)
}
for (i in 1:n_clusters) {
if (!is.matrix(transition_probs[[i]])) {
stop(paste("Object provided in 'transition_probs' for cluster", i, "is not a matrix."))
}
if (!is.vector(initial_probs[[i]])) {
stop(paste("Object provided in 'initial_probs' for cluster", i, "is not a vector."))
}
}
# States
n_states <- unlist(lapply(transition_probs, nrow))
if (any(rep(n_states, each = 2) != unlist(lapply(transition_probs, dim)))) {
stop("Transition matrices must be square matrices.")
}
if (any(n_states != lengths(initial_probs))) {
stop("Lengths of `initial_probs` does not match with the number of states.")
}
if (is.null(state_names)) {
state_names <- vector("list", n_clusters)
for (m in 1:n_clusters) {
if (is.null(state_names[[m]] <- rownames(transition_probs[[m]]))) {
state_names[[m]] <- paste("State", 1:n_states[m])
}
}
} else {
for (m in 1:n_clusters) {
if (length(state_names[[m]]) != n_states[m]) {
stop(paste0("Length of 'state_names' for cluster ", m, " is not equal to the number of hidden states."))
}
}
}
names(state_names) <- cluster_names
for (i in 1:n_clusters) {
if (!isTRUE(all.equal(rowSums(transition_probs[[i]]),
rep(1, n_states[i]),
check.attributes = FALSE
))) {
stop(paste("Row sums of the transition probabilities in cluster", i, "do not sum to one."))
}
if (!isTRUE(all.equal(sum(initial_probs[[i]]), 1, check.attributes = FALSE))) {
stop(paste("Initial state probabilities in cluster", i, "do not sum to one."))
}
}
for (i in 1:n_clusters) {
dimnames(transition_probs[[i]]) <- list(from = state_names[[i]], to = state_names[[i]])
# Single channel but emission_probs is list of lists
if (is.list(emission_probs[[i]]) && !multichannel) {
emission_probs[[i]] <- emission_probs[[i]][[1]]
}
}
for (i in 1:n_clusters) {
if (!multichannel) {
if (!is.matrix(emission_probs[[i]])) {
stop(paste("Object provided in 'emission_probs' for cluster", i, "is not a matrix."))
}
} else {
for (j in 1:n_channels) {
if (!is.matrix(emission_probs[[i]][[j]])) {
stop(paste("Object provided in 'emission_probs' for cluster", i, "and channel", j, "is not a matrix."))
}
}
}
}
if (multichannel) {
if (any(sapply(emission_probs, length) != n_channels)) {
stop("Unequal number of channels per clusters based on 'emission_probs'.")
}
n_sequences <- nrow(observations[[1]])
length_of_sequences <- ncol(observations[[1]])
symbol_names <- lapply(observations, alphabet)
n_symbols <- lengths(symbol_names)
for (i in 1:n_clusters) {
if (length(initial_probs[[i]]) != n_states[i]) {
stop(paste("Length of initial_probs of cluster", i, "is not equal to the number of states."))
}
if (any(lapply(emission_probs[[i]], nrow) != n_states[i])) {
stop(paste("Number of rows in emission_probs of cluster", i, "is not equal to the number of states."))
}
if (any(n_symbols != sapply(emission_probs[[i]], ncol))) {
stop(paste("Number of columns in emission_probs of cluster", i, "is not equal to the number of symbols."))
}
if (!isTRUE(all.equal(c(sapply(emission_probs[[i]], rowSums)),
rep(1, n_channels * n_states[i]),
check.attributes = FALSE
))) {
stop(paste("Emission probabilities in emission_probs of cluster", i, "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 (j in 1:n_channels) {
dimnames(emission_probs[[i]][[j]]) <- list(state_names = state_names[[i]], symbol_names = symbol_names[[j]])
}
names(emission_probs[[i]]) <- channel_names
names(initial_probs[[i]]) <- state_names[[i]]
}
} else {
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)
for (i in 1:n_clusters) {
if (n_states[i] != dim(emission_probs[[i]])[1]) {
stop("Number of rows in 'emission_probs' is not equal to the number of states.")
}
if (n_symbols != dim(emission_probs[[i]])[2]) {
stop("Number of columns in 'emission_probs' is not equal to the number of symbols.")
}
if (!isTRUE(all.equal(rep(1, n_states[i]), rowSums(emission_probs[[i]]), check.attributes = FALSE))) {
stop("Emission probabilities in 'emission_probs' do not sum to one.")
}
dimnames(emission_probs[[i]]) <- list(state_names = state_names[[i]], symbol_names = symbol_names)
names(initial_probs[[i]]) <- state_names[[i]]
}
}
# 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."))
}
n_clusters <- length(n_states)
if (identical(n_clusters, 1L)) {
stop("Argument 'n_states' is of length 1, leading to ordinary HMM. Please use 'build_hmm' instead.")
}
if (is.null(cluster_names)) {
cluster_names <- paste("Cluster", 1:n_clusters)
} else if (length(cluster_names) != n_clusters) {
warning("The length of argument cluster_names does not match the length of n_clusters. Names were not used.")
cluster_names <- paste("Cluster", 1:n_clusters)
}
transition_probs <- simulate_transition_probs(n_states = n_states, n_clusters = n_clusters, ...)
if (is.null(state_names)) {
state_names <- vector("list", n_clusters)
for (m in 1:n_clusters) {
state_names[[m]] <- paste("State", 1:n_states[m])
}
} else {
for (m in 1:n_clusters) {
if (length(state_names[[m]]) != n_states[m]) {
stop(paste0("Length of state_names for cluster ", m, " is not equal to the number of hidden states."))
}
}
}
for (k in 1:n_clusters) {
dimnames(transition_probs[[k]]) <- list(from = state_names[[k]], to = state_names[[k]])
}
initial_probs <- simulate_initial_probs(n_states = n_states, n_clusters = n_clusters)
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 <- vector("list", n_clusters)
for (k in 1:n_clusters) {
emission_probs[[k]] <- simulate_emission_probs(n_states = n_states[k], n_symbols = n_symbols)
dimnames(emission_probs[[k]]) <- list(state_names = state_names[[k]], symbol_names = symbol_names)
names(initial_probs[[k]]) <- state_names[[k]]
}
} 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_clusters)
for (k in 1:n_clusters) {
emission_probs[[k]] <- vector("list", n_channels)
for (c in 1:n_channels) {
emission_probs[[k]][[c]] <- simulate_emission_probs(n_states = n_states[k], n_symbols = n_symbols[c])
dimnames(emission_probs[[k]][[c]]) <- list(state_names = state_names[[k]], symbol_names = symbol_names[[c]])
}
names(emission_probs[[k]]) <- channel_names
names(initial_probs[[k]]) <- state_names[[k]]
}
}
}
if (is.null(formula)) {
formula <- stats::formula(~ 1)
X <- model.matrix(formula, data = data.frame(y = rep(1, n_sequences)))
n_covariates <- 1L
} else {
if (inherits(formula, "formula")) {
if (is.null(data)) {
stop("Argument 'data' is missing, but 'formula' was provided.")
}
X <- model.matrix(formula, data)
if (nrow(X) != n_sequences) {
if (length(all.vars(formula)) > 0 && sum(!complete.cases(data[all.vars(formula)])) > 0) {
stop(
paste0(
"Missing cases are not allowed in covariates. Use e.g. the ",
"'complete.cases' function to detect them, then fix, impute, or remove."
)
)
} else {
stop(
paste0(
"Number of subjects in data for covariates does not match the ",
"number of subjects in the sequence data."
)
)
}
}
n_covariates <- ncol(X)
} else {
stop("Object given for argument formula is not of class formula.")
}
}
if (is.null(coefficients)) {
coefficients <- matrix(0, n_covariates, n_clusters)
} else {
if (ncol(coefficients) != n_clusters | nrow(coefficients) != n_covariates) {
stop("Wrong dimensions of coefficients.")
}
coefficients[, 1] <- 0
}
rownames(coefficients) <- colnames(X)
colnames(coefficients) <- cluster_names
names(transition_probs) <- names(emission_probs) <- names(initial_probs) <- cluster_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,
coefficients = coefficients, X = X, cluster_names = cluster_names, state_names = state_names,
symbol_names = symbol_names, channel_names = channel_names,
length_of_sequences = length_of_sequences,
n_sequences = n_sequences, n_clusters = n_clusters,
n_symbols = n_symbols, n_states = n_states,
n_channels = n_channels,
n_covariates = n_covariates, formula = formula
),
class = "mhmm",
nobs = nobs,
df = sum(unlist(initial_probs) > 0) - n_clusters + sum(unlist(transition_probs) > 0) - sum(n_states) +
sum(unlist(emission_probs) > 0) - sum(n_states) * n_channels + n_covariates * (n_clusters - 1),
type = "mhmm"
)
model
}
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