mhmm_biofam {seqHMM}

Mixture hidden Markov model for the biofam data

Description

A mixture hidden Markov model (MHMM) fitted for the biofam data.

Format

A mixture hidden Markov model of class mhmm: three clusters with left-to-right models including 4, 4, and 6 hidden states. Two covariates, sex and cohort, explaining the cluster membership.

Details

The model was created with the following code:

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")

## 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 <- factor(cut(biofam3c$covariates$birthyr,
    c(1908, 1935, 1945, 1957)), labels = c("1909-1935", "1936-1945", "1946-1957"))

# Build mixture HMM
init_mhmm_bf <- 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,
  channel_names = c("Marriage", "Parenthood", "Residence"))

# Fitting the model
mhmm_biofam <- fit_model(init_mhmm_bf)$model

See Also

Examples of building and fitting MHMMs in build_mhmm and fit_model; and biofam for the original data and biofam3c for the three-channel version used in this model.

Examples

data("mhmm_biofam")

# use conditional_se = FALSE for more accurate standard errors
# (these are considerebly slower to compute)
summary(mhmm_biofam$model)

if (interactive()) {
  # Plotting the model for each cluster (change with Enter)
  plot(mhmm_biofam)
}