# CANCELLED - Seminar: A Modified Maximum Likelihood Estimate of Person Parameters for the Dichotomous Rasch Model

By Beyza Doganay Erdogan, Ankara University, Biostatistics Department.

A Modified Maximum Likelihood Estimate of Person Parameters for the Dichotomous Rasch Model Rasch class models are characterized by total scores of persons and items are sufficient statistics for person and item parameters, respectively. When the purpose is to measure persons by administering a conventional scale, first the item parameters are estimated by conditioning out the person sufficient statistics of the estimation equations derived from the Rasch model. Then the person parameters are estimated using the item parameters estimates as known values. Rasch class models are also used in tailored testing procedures i.e. computerized adaptive testing (CAT) which gained more attention in the last decades. In a CAT, persons are measured by different sets of items from a given item bank. This is based on the principle of selecting items to match the current person parameter estimate.When the purpose is to measure persons by a CAT, person parameters are re-estimated after each response is given to pre-calibrated items chosen from the item bank. Four person parameter estimation methods available are Maximum Likelihood Estimation (MLE), Weighted Maximum Likelihood Estimation (WLE), Maximum a Posteriori (MAP) and Expected a Posteriori (EAP). The latter two methods fall under Bayesian inference. While all of these methods can be implemented to estimate person parameters of the Rasch models in both paper-pencil versions of scales and CAT algorithm, they compete with each other in terms of accuracy and precision. We adapted an estimation method which modifies the MLE in such a way to make linear approximations for non-iterative estimation, to estimate the person parameters of the dichotomous Rasch model. This method was first proposed by Tiku as a robust parameter estimation method based on order statistics. The method first expresses the likelihood equation(s) in terms of order statistics and then linearizes the intractable terms. The resulting equations have explicit solutions, called modified maximum likelihood (MML) estimators. MML estimates are easy to compute because they are explicit functions of sample observations. They also give estimates where ordinary MLE fails to converge.

For an overview of planned future seminars at the section of Biostatistics, UCPH, see

The seminar will be held at CSS (“det gamle Kommunehospital”), Øster Farimagsgade 5, 1353 Copenhagen K, room 5.2.46. Tea will be served in the library of the section of Biostatistics half an hour before the seminar starts.