Simulate Markov chains

Usage

simulate_markov(
  n,
  transition,
  chain_length,
  initial = NULL,
  states = NULL,
  trim_state = NULL,
  id = "id",
  period = "period",
  state = "state",
  seed = NULL,
  batch = NULL
)

Arguments

n: Number of chains.
transition: Square transition matrix, or a tidy transition table with from, to, and probability columns. Every row of the implied matrix must sum to one.
chain_length: Chain length.
initial: Starting-state probabilities or a single fixed start state. When NULL, every chain starts in the first state.
states: Optional state labels.
trim_state: Optional terminal state. The first occurrence is kept and all later observations of that chain are removed.
id, period, state: Output variable names.
seed: Optional random seed.
batch: Optional single positive whole number. When given, the simulator runs batch times and returns a plain list of batch results, each exactly what the same call without batch returns. With a seed, every dataset gets its own seed drawn from seed, so the whole batch is reproducible; without one the datasets are consecutive draws from the session's random-number stream. The default NULL returns a single result.

Value

A long-form simulab_sim base data.frame with columns id, period, and state (renamed by those arguments), one row per chain position. as.data.frame(x, what = ) also returns transitions (from, to, probability), initial_probabilities (state, probability), and wide (one row per chain, columns id, S1, S2, ...).

Examples

transition <- matrix(c(0.7, 0.3, 0.4, 0.6), nrow = 2, byrow = TRUE)

result <- simulate_markov(
  n = 50, transition = transition, chain_length = 20,
  states = c("A", "B"), seed = 1
)
head(result)
#> <simulab_sim:markov> 6 rows x 3 columns
#>   id period state
#> 1  1      1     A
#> 2  1      2     A
#> 3  1      3     A
#> 4  1      4     B
#> 5  1      5     B
#> 6  1      6     A
#> 
#> Truth (transitions):
#>   from to probability
#> 1    A  A         0.7
#> 2    B  A         0.4
#> 3    A  B         0.3
#> 4    B  B         0.6
#> 
#> Other tables: initial_probabilities, wide. Read one with as.data.frame(x, what = "initial_probabilities").
summarize_transitions(result, normalize = TRUE)
#>   from to count probability
#> 1    A  A   392   0.6938053
#> 2    A  B   173   0.3061947
#> 3    B  A   149   0.3870130
#> 4    B  B   236   0.6129870

# Transitions may also be given as a tidy from/to/probability table.
tidy_transitions <- data.frame(
  from = c("A", "A", "B", "B"),
  to = c("A", "B", "A", "B"),
  probability = c(0.7, 0.3, 0.4, 0.6)
)
head(simulate_markov(
  n = 50, transition = tidy_transitions, chain_length = 20, seed = 1
))
#> <simulab_sim:markov> 6 rows x 3 columns
#>   id period state
#> 1  1      1     A
#> 2  1      2     A
#> 3  1      3     A
#> 4  1      4     B
#> 5  1      5     B
#> 6  1      6     A
#> 
#> Truth (transitions):
#>   from to probability
#> 1    A  A         0.7
#> 2    B  A         0.4
#> 3    A  B         0.3
#> 4    B  B         0.6
#> 
#> Other tables: initial_probabilities, wide. Read one with as.data.frame(x, what = "initial_probabilities").