Build a Mixture Hidden Markov Model
Function build_mhmm constructs a mixture hidden Markov model object of class mhmm.
build_mhmm(observations, n_states, transition_probs, emission_probs, initial_probs, formula, data, coefficients, cluster_names = NULL, state_names = NULL, channel_names = NULL, ...)
observations |
An |
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
|
transition_probs |
A list of matrices of transition probabilities for the submodel of each cluster. |
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 m x s where m is the number of
hidden states and s is the number of unique symbols (observed states) in the
data. Emission probabilities should follow the ordering of the alphabet of
observations ( |
initial_probs |
A list which contains vectors of initial state probabilities for the submodel of each cluster. |
formula |
Covariates as an object of class |
data |
An optional data frame, list or environment containing the variables
in the model. If not found in data, the variables are taken from
|
coefficients |
An optional k x l matrix of regression coefficients for time-constant covariates for mixture probabilities, where l is the number of clusters and k is the number of covariates. A logit-link is used for mixture probabilities. The first column is set to zero. |
cluster_names |
A vector of optional names for the clusters. |
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 mhmm with following elements:
observationsState sequence object or a list of such 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.
coefficientsA matrix of parameter coefficients for covariates (covariates in rows, clusters in columns).
XCovariate values for each subject.
cluster_namesNames for clusters.
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.
n_covariatesNumber of covariates.
n_clustersNumber of clusters.
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
fit_model for fitting mixture Hidden Markov models;
summary.mhmm for a summary of a MHMM; separate_mhmm for
reorganizing a MHMM into a list of separate hidden Markov models; and
plot.mhmm for plotting mhmm objects.
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)))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.