Build a Hidden Markov Model
Function build_hmm constructs a hidden Markov model object of class hmm.
build_hmm(observations, n_states, transition_probs, emission_probs, initial_probs, state_names = NULL, channel_names = NULL, ...)
observations |
An |
n_states |
A scalar giving the number of hidden states (not used if starting values for model parameters
are given with |
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 ( |
initial_probs |
A vector of initial state probabilities. |
state_names |
A list of optional labels for the hidden states. If |
channel_names |
A vector of optional names for the channels. |
... |
Additional arguments to |
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.
Object of class hmm with the following elements:
observationsState sequence object or a list of such objects containing the data.
transition_probsA matrix of transition probabilities.
emission_probsA matrix or a list of matrices of emission probabilities.
initial_probsA vector of initial probabilities.
state_namesNames for hidden states.
symbol_namesNames for observed states.
channel_namesNames for channels of sequence data.
length_of_sequences(Maximum) length of sequences.
n_sequencesNumber of sequences.
n_symbolsNumber of observed states (in each channel).
n_statesNumber of hidden states.
n_channelsNumber of channels.
# 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.