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ERIC Number: ED555725
Record Type: Non-Journal
Publication Date: 2013-Sep
Pages: 34
Abstractor: As Provided
Reference Count: 32
ISBN: N/A
ISSN: N/A
Estimation of a Ramsay-Curve Item Response Theory Model by the Metropolis-Hastings Robbins-Monro Algorithm. CRESST Report 834
Monroe, Scott; Cai, Li
National Center for Research on Evaluation, Standards, and Student Testing (CRESST)
In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however, does not produce the parameter covariance matrix as an automatic byproduct upon convergence. In turn, researchers are limited in when they can employ RC-IRT, as the covariance matrix is needed for many statistical inference procedures. The present research remedies this problem by estimating the RC-IRT model parameters by the Metropolis-Hastings Robbins-Monro (MH-RM, Cai, 2010) algorithm. An attractive feature of MH-RM is that the structure of the algorithm makes estimation of the covariance matrix convenient. Additionally, MH-RM is ideally suited for multidimensional IRT, whereas EM is limited by the "curse of dimensionality." Based on the current research, when RC-IRT or similar semi-nonparametric IRT models are eventually generalized to include multiple latent dimensions, MH-RM would appear to be the logical choice for estimation. Complete Data Log-Likelihood and Derivatives for the Ramsay Curve is appended.
National Center for Research on Evaluation, Standards, and Student Testing (CRESST). 300 Charles E Young Drive N, GSE&IS Building 3rd Floor, Mailbox 951522, Los Angeles, CA 90095-1522. Tel: 310-206-1532; Fax: 310-825-3883; Web site: http://www.cresst.org
Publication Type: Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: Institute of Education Sciences (ED); National Institute on Drug Abuse (DHHS/PHS)
Authoring Institution: National Center for Research on Evaluation, Standards, and Student Testing
IES Funded: Yes
Grant or Contract Numbers: R305B080016; R305D100039; R01DA026943; R01DA030466