Weighted Maximum-a-Posteriori Estimation in Tests Composed of Dichotomous and Polytomous Items

For mixed-type tests composed of dichotomous and polytomous items, polytomous items often yield more information than dichotomous items. To reflect the difference between the two types of items and to improve the precision of ability estimation, an adaptive weighted maximum-a-posteriori (WMAP) estimation is proposed. To evaluate the performance of WMAP, a Monte Carlo simulation comparison is presented with maximum likelihood estimation, maximum-a-posteriori estimation, and Jeffreys modal estimation. Simulation results show that the proposed method is much less biased than any of the other estimators, with relatively smaller standard errors and root mean square errors.