Maximum-likelihood ability estimate

The theta maximising the 3PL log-likelihood. No finite estimate exists for an all-correct or all-wrong pattern – the likelihood is monotone and its supremum is at infinity. This returns finite = FALSE and an infinite theta rather than the edge of a search interval dressed as an estimate, which is the standard silent failure. The 3PL likelihood can also be multimodal under guessing (Samejima 1973), so a dense scan precedes local refinement.

Usage

morie_psy_mle_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, finite, information, loglik, n_local_maxima, pattern, n_items, method.

References

Lord (1980), Ch. 4; Samejima (1973), Psychometrika 38:221-233; Yen, Burket and Sykes (1991).

Examples

morie_psy_mle_theta(c(1, 1, 0, 0), b = c(-1, -0.5, 0.5, 1))$theta
#> [1] -8.326673e-17