build_hmm: Build a Hidden Markov Model

Description

Function build_hmm constructs a hidden Markov model object of class hmm.

Usage

build_hmm(
  observations,
  n_states,
  transition_probs,
  emission_probs,
  initial_probs,
  state_names = NULL,
  channel_names = NULL,
  ...
)

Value

Object of class hmm with the following elements:

observations: State sequence object or a list of such objects containing the data.
transition_probs: A matrix of transition probabilities.
emission_probs: A matrix or a list of matrices of emission probabilities.
initial_probs: A vector of initial probabilities.
state_names: Names for hidden states.
symbol_names: Names for observed states.
channel_names: Names for channels of sequence data.
length_of_sequences: (Maximum) length of sequences.
n_sequences: Number of sequences.
n_symbols: Number of observed states (in each channel).
n_states: Number of hidden states.
n_channels: Number of channels.

Arguments

observations: An stslist object (see seqdef) containing the sequences, or a list of such objects (one for each channel).
n_states: A scalar giving the number of hidden states. Not used if starting values for model parameters are given with initial_probs, transition_probs, or emission_probs.
transition_probs: A matrix of transition probabilities.
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 (alphabet(observations), returned as symbol_names).
initial_probs: A vector of initial state probabilities.
state_names: A list of optional labels for the hidden states. If NULL, the state names are taken from the row names of the transition matrix. If this is also NULL, numbered states are used.
channel_names: A vector of optional names for the channels.
...: Additional arguments to simulate_transition_probs.

Details

The returned model contains some attributes such as nobs and df, which define the number of observations in the model and the number of estimable model parameters, used in computing BIC. When computing nobs for a multichannel model with \(C\) channels, each observed value in a single channel amounts to \(1/C\) observation, i.e. a fully observed time point for a single sequence amounts to one observation. For the degrees of freedom df, zero probabilities of the initial model are defined as structural zeroes.

Examples

Run this code


# 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
)