Warm's weighted likelihood ability estimate

Maximise loglik + log sqrt(I(theta)). The weight is NOT a prior: Warm (1989) chooses it so the O(1/n) BIAS of the ML estimator is removed to first order. It also makes perfect patterns finite – sqrt(I) tends to zero in both tails, so the weighted objective turns over where the raw likelihood does not, giving the existence property MAP buys with a prior, without one.

Usage

morie_psy_wle_theta(y, a = NULL, b = NULL, c = NULL, bounds = c(-6, 6))

Arguments

y

binary responses.

a, b, c

item parameters; b required.

bounds

search interval.

Value

list: theta, se, information, loglik, weight_term, bias_corrected, finite_for_perfect_patterns, vs_ml, n_items, method.

References

Warm (1989), Psychometrika 54:427-450.

Examples

morie_psy_wle_theta(rep(1, 4), b = c(-1, -0.5, 0.5, 1))$theta
#> [1] 2.520158