Geographic-rank Markov chain

A Markov chain that tracks, for each rank position, which unit occupies it over time (Rey, 2016). States are the geographic units, so the n by n matrix records how units exchange rank positions — a spatially explicit view of positional mobility.

Usage

geo_rank_markov(data, id, time, value)

Arguments

data

A data frame in long format with one row per unit and period. The panel must be balanced (every unit present in every period).

id, time, value

Character scalars naming the unit, period, and numeric value columns.

Value

An object of class sddr_markov (an n by n transition matrix over units, its counts, and ergodic distribution).

References

Rey, S. J. (2016). Space-time patterns of rank concordance: Local indicators of mobility association. Annals of the AAG, 106(4), 788-803.

See also

full_rank_markov(), markov()

Examples

set.seed(1)
df <- data.frame(
  id = rep(1:6, times = 8),
  time = rep(1:8, each = 6),
  value = rnorm(48)
)
geo_rank_markov(df, "id", "time", "value")
#> <sddr> geo-rank Markov chain
#>   units: 6 | transitions: 42 | classes: 6 | breaks: fixed
#> 
#> Transition probability matrix (rows = from, cols = to):
#>       1     2     3     4     5     6
#> 1 0.286 0.000 0.143 0.286 0.143 0.143
#> 2 0.000 0.143 0.286 0.143 0.143 0.286
#> 3 0.143 0.143 0.143 0.286 0.143 0.143
#> 4 0.143 0.571 0.000 0.000 0.286 0.000
#> 5 0.143 0.143 0.143 0.143 0.286 0.143
#> 6 0.286 0.000 0.286 0.143 0.000 0.286
#> 
#> Ergodic (steady-state) distribution:
#>     1     2     3     4     5     6 
#> 0.167 0.167 0.167 0.167 0.167 0.167