Heteroskedastic IRT scales given ideal points (Lauderdale 2010)

Per-legislator noise scales for the probit ideal-point model P(yea) = pnorm((beta_j x_i - alpha_j) / psi_i); a large psi_i marks an unpredictable voter. Ideal points and item parameters are taken as given; each psi_i is fitted by one-dimensional ML and the vector is normalised to geometric mean 1 for identification. Mirrors morie.fn.hsirt (with fixed items).

Usage

morie_heteroskedastic_scales(votes, ideal_points, alpha, beta)

Arguments

votes

Binary vote matrix (NA = missing).

ideal_points

Fixed ideal points, one per row of votes.

alpha, beta

Fixed item parameters (one per column).

Value

List with psi, loglik, n, q.

References

Lauderdale BE (2010). Unpredictable voters in ideal point estimation. Political Analysis 18(2), 151-171.

Examples

votes <- rbind(c(1, 1, 0), c(0, 1, 1), c(1, 0, 0), c(0, 0, 1))   # four legislators, three roll calls
morie_heteroskedastic_scales(votes, ideal_points = c(-1, 0.5, -0.5, 1),
  alpha = c(0, 0.2, -0.1), beta = c(1, 0.8, 1.2))
#> $psi
#> [1] 3.9655166 0.2954364 0.2152469 3.9655127
#> 
#> $loglik
#> [1] -12.52594
#> 
#> $n
#> [1] 4
#> 
#> $q
#> [1] 3
#>