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Markov Stability Analysis

Source: R/markov.R
markov_stability.Rd

Computes per-state stability metrics from a transition network: persistence (self-loop probability), stationary distribution, mean recurrence time, sojourn time, and mean accessibility to/from other states.

Usage

markov_stability(x, normalize = TRUE)

# S3 method for class 'net_markov_stability'
plot(
  x,
  metrics = c("persistence", "stationary_prob", "return_time", "sojourn_time",
    "avg_time_to_others", "avg_time_from_others"),
  combined = TRUE,
  ...
)

Arguments

x

A netobject, cograph_network, tna object, row-stochastic numeric transition matrix, or a wide sequence data.frame (rows = actors, columns = time-steps).

normalize

Logical. Normalize rows to sum to 1? Default TRUE.

metrics

Character vector. Which metrics to plot. Options: "persistence", "stationary_prob", "return_time", "sojourn_time", "avg_time_to_others", "avg_time_from_others". Default: all six.

combined

When TRUE (default), all selected metrics are shown in one ggplot via facet_wrap(~ metric). When FALSE, returns a named list of single-panel ggplots, one per metric, so each can be printed, saved, or re-laid-out independently.

...

Ignored.

Value

An object of class "net_markov_stability" with:

stability

Data frame with one row per state and columns: state, persistence (\(P_{ii}\)), stationary_prob (\(\pi_i\)), return_time (\(1/\pi_i\)), sojourn_time (\(1/(1-P_{ii})\)), avg_time_to_others (mean MFPT leaving state \(i\)), avg_time_from_others (mean MFPT arriving at state \(i\)).

mpt

The underlying net_mpt object.

Details

Sojourn time is the expected consecutive time steps spent in a state before leaving: \(1/(1-P_{ii})\). States with persistence = 1 have sojourn_time = Inf.

avg_time_to_others: mean passage time from this state to all others; reflects how "sticky" or "isolated" the state is.

avg_time_from_others: mean passage time from all other states to this one; reflects accessibility (attractor strength).

See also

passage_time

Examples

net <- build_network(as.data.frame(trajectories), method = "relative")
ms  <- markov_stability(net)
print(ms)
#> Markov Stability Analysis
#> 
#>       state persistence stationary_prob return_time sojourn_time
#>      Active      0.6976          0.3719        2.69         3.31
#>     Average      0.6099          0.4431        2.26         2.56
#>  Disengaged      0.4831          0.1850        5.41         1.93
#>  avg_time_to_others avg_time_from_others
#>                6.99                 5.84
#>                6.74                 3.20
#>                4.47                 9.16
# \donttest{
plot(ms)

# }