Open AccessMarginal maximum likelihood estimation of item response theory (IRT) equating coefficients for the common‐examinee design
Author(s) -
Ogasawara Haruhiko
Publication year - 2001
Publication title -
japanese psychological research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.392
H-Index - 30
eISSN - 1468-5884
pISSN - 0021-5368
DOI - 10.1111/1468-5884.00162
Subject(s) - equating , mathematics , item response theory , statistics , standard deviation , estimation , standard error , maximum likelihood , distribution (mathematics) , econometrics , psychometrics , mathematical analysis , rasch model , management , economics
A method of estimating item response theory (IRT) equating coefficients by the common‐examinee design with the assumption of the two‐parameter logistic model is provided. The method uses the marginal maximum likelihood estimation, in which individual ability parameters in a common‐examinee group are numerically integrated out. The abilities of the common examinees are assumed to follow a normal distribution but with an unknown mean and standard deviation on one of the two tests to be equated. The distribution parameters are jointly estimated with the equating coefficients. Further, the asymptotic standard errors of the estimates of the equating coefficients and the parameters for the ability distribution are given. Numerical examples are provided to show the accuracy of the method.