Estimation of item parameters for the three‐parameter logistic model using the marginal likelihood of summed scores
Wen‐Hung Chen, David Thissen · British Journal of Mathematical and Statistical Psychology · 1999
While existing algorithms used in item response theory (IRT) for the estimation of three‐parameter logistic item parameters are based on response pattern frequencies, the alternative algorithm proposed here uses the summed scores. The development here of the maximum marginal summed‐score likelihood (MMSSL) algorithm contributes to the understanding of the relation of IRT with the traditional test theory, and other developments in IRT, based on summed scores. Simulated data are used to evaluate the performance of the MMSSL algorithm. The results show that estimates of the discrimination parameter obtained using the MMSSL algorithm are biased, but estimates of the threshold and lower asymptote parameters are similar to those obtained using the MML algorithm. Estimated scaled scores obtained with the MMSSL parameter estimates are approximately as accurate as those obtained using the MML estimates.