Full-rank Markov chain

A Markov chain over ranks rather than discretised classes: each unit's rank within the cross-section (1 = highest value, n = lowest) becomes its state, and the n by n matrix records how ranks transition from one period to the next (Rey, 2014). Unlike markov() no binning is needed — the full rank ordering is retained.

Usage

full_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 rank transition matrix, its counts, and ergodic distribution).

References

Rey, S. J. (2014). Fast algorithms for a space-time concordance measure. Computational Statistics, 29(3-4), 799-811.

See also

markov(), geo_rank_markov()

Examples

set.seed(1)
df <- data.frame(
  id = rep(1:6, times = 8),
  time = rep(1:8, each = 6),
  value = rnorm(48)
)
full_rank_markov(df, "id", "time", "value")
#> <sddr> full-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 0.143 0.143 0.286
#> 2 0.429 0.000 0.000 0.000 0.143 0.429
#> 3 0.143 0.286 0.143 0.143 0.143 0.143
#> 4 0.000 0.143 0.429 0.286 0.143 0.000
#> 5 0.143 0.286 0.000 0.000 0.429 0.143
#> 6 0.000 0.286 0.286 0.429 0.000 0.000
#> 
#> Ergodic (steady-state) distribution:
#>     1     2     3     4     5     6 
#> 0.167 0.167 0.167 0.167 0.167 0.167