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An improved CML estimation procedure for the Rasch model with item response data
Author(s) -
Sheng Xiaoming,
Carrière K. C.
Publication year - 2002
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1026
Subject(s) - rasch model , estimator , item response theory , polytomous rasch model , computer science , ordinal data , statistics , conditional independence , independence (probability theory) , goodness of fit , local independence , econometrics , mathematics , psychometrics
Ordinal response data are commonly observed in health and medical investigations that include several items. The primary goal in the modelling of item response data is to find a unique measurement of the person's abilities and of the item difficulties that satisfies the properties of the fundamental measurement. One such analytic method in item response theory is the Rasch measurement, which is a way to convert ordinal observations into linear measures. Current estimation strategies assume the independence of the Rasch model parameters. In this paper, based on the conditional maximum likelihood, we implemented a simultaneous estimation method that can compare the Rasch parameters more efficiently. We also obtained the asymptotic properties of these estimators and developed the conditional likelihood ratio test for the goodness‐of‐fit of the model. Simulation studies were used to demonstrate the improved performance of our estimators as compared to that of currently used conditional method known as the CON procedure. We conclude that our estimation method outperforms CON in both model fit and the precision of the Rasch estimators. Copyright © 2002 John Wiley & Sons, Ltd.