Theta rank-mobility statistic

The Theta statistic (Rey, 2004) measures how much of the overall rank movement in a system is within-regime exchange. For each period-to-period transition it is the sum over regimes of the absolute net within-regime rank change, divided by the total absolute rank change. Values near zero indicate that rank movement is dominated by within-regime shuffling that nets out; larger values indicate coherent regime-level movement.

Usage

theta(y, regime)

Arguments

y

A numeric matrix of values, units in rows and time periods in columns (at least two columns).

regime

A vector of length nrow(y) assigning each unit to a regime.

Value

An object of class sddr_theta: a list with theta (one value per period-to-period transition), the per-period total absolute rank change, and the column rank matrix ranks.

References

Rey, S. J. (2004). Spatial dependence in the evolution of regional income distributions. In Spatial Econometrics and Spatial Statistics, 194-213.

See also

tau()

Examples

set.seed(1)
y <- matrix(rnorm(40), nrow = 10)    # 10 units, 4 periods
regime <- rep(c("a", "b"), each = 5)
theta(y, regime)
#> <sddr> Theta rank-mobility statistic
#>   2 regimes | 3 period transitions
#>   theta by transition:
#> [1] 0.1429 0.6364 0.3750