Open AccessESTIMATING ABILITY WITH THREE ITEM RESPONSE MODELS WHEN THE MODELS ARE WRONG AND THEIR PARAMETERS ARE INACCURATE
Author(s) -
Jones Douglas H.,
Wainer Howard,
Kaplan Bruce
Publication year - 1984
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2330-8516.1984.tb00066.x
Subject(s) - estimator , bayesian probability , statistics , mathematics , constant (computer programming) , econometrics , estimation theory , prior probability , sampling (signal processing) , maximum likelihood , item response theory , computer science , psychometrics , filter (signal processing) , computer vision , programming language
We investigate the accuracy of the maximum likelihood estimator of ability for the one‐ two‐ and three‐parameter logistic models. This is accomplished by fitting of those models to generated item characteristic curves derived from the Armed Services Vocational Aptitude Battery. The mathematical details as to how this is accomplished and our results are included. Among these results is the finding that the 3‐PL model is the least biased, but that for lower abilities it has both the highest M.S.E. and is the most fragile with respect to sampling fluctuations of the parameter estimates. It is recommended that the current practice of utilizing some method of restricting the variability of parameters continue to be employed (i.e., Bayesian priors, robust estimation, fixing some parameters to be constant).