Markov Stability Analysis

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'
print(x, ...)

# S3 method for class 'net_markov_stability_group'
print(x, ...)

# S3 method for class 'net_markov_stability'
summary(object, ...)

# 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). For the print() and plot() methods: an object of class net_markov_stability or net_markov_stability_group.
normalize: Logical. Normalize rows to sum to 1? Default TRUE.
...: Ignored. In plot.net_markov_stability(), print.net_markov_stability() and summary.net_markov_stability(): Ignored. In print.net_markov_stability_group(): Forwarded to print.net_markov_stability for each element.
object: For the summary() method: an object of class net_markov_stability.
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.

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.

For a netobject_group the result is a "net_markov_stability_group": a named list holding one such object per group.

In print.net_markov_stability(): x, invisibly.

In print.net_markov_stability_group(): x invisibly.

In plot.net_markov_stability(): plot.net_markov_stability returns a faceted ggplot object when combined = TRUE, and (invisibly) a named list of single-metric ggplots, one per entry of metrics, when combined = FALSE.

In summary.net_markov_stability(): the per-state stability table (the $stability data frame: one row per state with state, persistence, stationary_prob, return_time, sojourn_time, avg_time_to_others, avg_time_from_others), after printing the attractor and the most persistent state.

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).

References

Kemeny, J.G. and Snell, J.L. (1976). Finite Markov Chains. Springer-Verlag.

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)

# }