Monte Carlo estimation of the conditional Rasch model

In order to obtain conditional maximum likelihood estimates, the conditioning constants are needed. Geyer and Thompson (1992) proposed a Markov chain Monte Carlo method that can be used to approximate these constants when they are difficult to calculate exactly. In the present paper, their method is applied to the conditional estimation of person parameters in the Rasch model. The results obtained with the Monte Carlo method can be very accurate, but in that case the method is rather slow. However, for only slightly less precise results the Monte Carlo method can be faster than the exact calculations. For the estimation of the ability parameters in a 5 item test taken by 1000 persons the Monte Carlo method took about half the time needed for the exact calculations; and still the difference between two corresponding estimates was less than 1 percent of the associated standard error in all cases.