Estimation Procedures for the Rasch Model With an Eye Toward Longish Tests - A Review (From Robust Estimation in Latent Trait Analysis Final Report, 1980 - See NCJ-72747)

• NCJ Number: 72749
• Author(s): H Wainer; A Morgan; J Gustafsson
• Date Published: 1980
• Length: 29 pages
• Grant Number(s): 78-NI-AX-0047
• Sponsoring Agency: US Dept of Justice; Swedish National Board of Education; New York State; Swedish Council for Research in the Humanities and Social Sciences
• Corporate Author: Bureau of Social Science Research, Inc
• Sale Source: National Institute of Justice/
• Publication Type: Statistics
• Language: English
• Country: United States of America

Annotation

Two estimation procedures for the Rasch Model are reviewed, particularly with respect to new developments that make the more statistically rigorous Conditional Maximum Likelihood estimation practical for use with longish tests.

Abstract

The estimation procedures reviewed are the Unconditional Maximum Likelihood and the Conditional Maximum Likelihood methods. Until recently, only the unconditional method could be applied for longish tests (those with more than 30 to 40 items). This has changed recently with newer and more sophisticated estimation schemes, better numerical methods, and faster computers. These developments are reviewed with respect to how each can be brought to bear on the problem of the estimation of parameters of the Rasch Model for moderate to long tests (40 to 90 items). Also discussed are the approximation methods of Wright and his colleagues, the developments of Fischer and Scheiblechner, the numerical breakthrough of Gustafsson, and the work on tests of fit that Andersen and Martin-Lof have done. A principal advantage of the conditional procedure appears to be the known asymptotic properties of the estimates, which allows the use of the goodness-of-fit tests described. It is recommended that as soon as a thorough analysis of fit of the data to the model is judged important, the conditional procedure, along with the goodness-of-fit tests, should be used. Mathematical equations, notes, and 29 references are included.