ERIC Number: ED333029
Record Type: RIE
Publication Date: 1991-Apr
Reference Count: N/A
Non-Linear Transformation of IRT Scale To Account for the Effect of Non-Normal Ability Distribution of the Item Parameter Estimation.
Yamamoto, Kentaro; Muraki, Eiji
The extent to which properties of the ability scale and the form of the latent trait distribution influence the estimated item parameters of item response theory (IRT) was investigated using real and simulated data. Simulated data included 5,000 ability values randomly drawn from the standard normal distribution. Real data included the results for a random sample of 2,000 examinees on the age 13 mathematics trend assessments of the 1986 and 1988 National Assessments of Educational Progress. Results suggest that the prior distribution in marginal maximum likelihood estimation should be as close to reality as possible. Because of the lack of knowledge of the real ability distribution, it may be necessary to simultaneously estimate the multinomial ability distribution with the item parameters. When used with real data, this method is often unstable and sensitive to the initial values. A two-step procedure is recommended. First, converged model parameters are found using the normal prior distribution. Second, with these converged values as initial values, the multinomial ability distribution is estimated. Implications for IRT are discussed. Three tables and 10 graphs supplement the discussion. (SLD)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Ability Estimates; Item Parameters; National Assessment of Educational Progress; Nonnormal Distributions
Note: Paper presented at the Annual Meeting of the American Educational Research Association (Chicago, IL, April 3-7, 1991).