Monte Carlo estimation of the conditional Rasch model

Wies Akkermans

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Abstract

In order to obtain conditional maximum likelihood estimates, the so-called conditioning estimates have to be calculated. In this paper a method is examined that does not calculate these constants exactly, but approximates them using Monte Carlo Markov Chains. As an example, the method is applied to the conditional estimation of both item and person parameters in the Rasch model. The key idea for this approach was developed by C. J. Geyer and E. A. Thompson (1992), who showed that, in the exponential family, a quantity that is proportional to the conditioning constant can be expressed as an expectation with respect to a certain distribution. Simulating from this distribution, an estimate of the proportional quantity can be obtained as the observed sample mean. Inserting this estimate into the conditional likelihood then allows one to maximize the approximate likelihood, as the proportionality constant does not depend on the parameters to be estimated.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages35
Publication statusPublished - 1994

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.94-09

Keywords

  • Statistical Distributions
  • Monte Carlo Methods
  • Maximum Likelihood Statistics
  • Markov Processes
  • Estimation (Mathematics)
  • METIS-140150
  • IR-104214
  • Foreign Countries

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