Exposure (interaction) index — ExposureIndex • rmorie

xPy_kl = sum_i (x_ik / X_k)(x_il / t_i) (exact: without replacement), and with a distance matrix Morgan's distance-decay interaction with kernel K_ij = t_j exp(-beta d_ij) / sum_j t_j exp(-beta d_ij).

Usage

ExposureIndex(x, exact = FALSE, distance = NULL, beta = 1)

Arguments

x: Units x groups count matrix.
exact: Sample without replacement.
distance: Optional distance matrix.
beta: Decay rate.

Value

list(xPy, DPxy).

References

Massey, D. S. and Denton, N. A. (1988). The dimensions of residential segregation. Social Forces 67, 281-315. Morgan, B. S. (1983). An alternate approach to the development of a distance-based measure of racial segregation. American Journal of Sociology 88, 1237-1249.

Examples

ExposureIndex(rbind(c(5, 5), c(5, 5)))$xPy
#>      [,1] [,2]
#> [1,]  0.5  0.5
#> [2,]  0.5  0.5