Draw the latent Z matrix for fixed-rank-nomination data

Gibbs update of the latent sociomatrix Z for a fixed-rank-nomination (FRN) outcome. Each row's latent values are drawn from truncated normals whose bounds encode three rank constraints: nominated ties outrank non-nominations, higher observed ranks map to larger latents, and a non-nomination made with spare out-degree capacity must stay negative.

Usage

rZ_frn_fc(Z, EZ, rho, Y, YL, odmax, odobs)

Arguments

Z

current latent sociomatrix (square).

EZ

conditional mean matrix for Z.

rho

within-dyad correlation.

Y

square matrix of observed ranked nominations (0 = no tie, NA on the diagonal / missing).

YL

matrix whose r-th column gives, per row, the column index of the individual holding rank r (ascending preference).

odmax

scalar or per-row maximum number of nominations allowed.

odobs

per-row observed out-degree.

Value

the updated square latent matrix Z.

Details

The constraints realised are (1) Y[i,j] > Y[i,k] implies Z[i,j] > Z[i,k], (2) Y[i,j] > 0 implies Z[i,j] > 0, and (3) Y[i,j] == 0 with odobs[i] < odmax[i] implies Z[i,j] < 0.

Author

lame authors