Transition matrix between states

The moves of people between states (regions, institutions, security levels) from their sequence of records: the counts and probabilities of each move between consecutive records of the same person, the stationary distribution of the chain (where the population would settle if the probabilities held), the share of moves that stay in their state, and the Theil index of the moves between states (0 when they spread evenly over the pairs of states, higher when a few pairs carry them).

Usage

trnmat(state, id, time = NULL)

Arguments

state

The state of each record: labels.

id

The person (or sequence) of each record: labels. Give paste(id, year) to keep the moves within a year.

time

NULL (the order of the rows) or the time of each record: numbers; ties keep the order of the rows.

Value

An object of class trnmat, a list: count and prob, the matrices of moves from (rows) and to (columns); pi, the stationary distribution (NA when a state is never left or it is not unique); and summ (moves, stay, theil).

References

Kemeny, J. G. and Snell, J. L. (1960). Finite Markov Chains. Van Nostrand.

Theil, H. (1967). Economics and Information Theory. North-Holland.

Examples

r <- trnmat(c("N", "N", "E", "N", "W", "W", "E", "E"),
            c(1, 1, 1, 2, 2, 2, 3, 3), time = c(1, 2, 3, 1, 2, 3, 1, 2))
r$prob
#>           E         N         W
#> E 1.0000000 0.0000000 0.0000000
#> N 0.3333333 0.3333333 0.3333333
#> W 0.0000000 0.0000000 1.0000000
r$pi
#>  E  N  W 
#> NA NA NA