JSM 2004 - Toronto

Abstract #300346

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Activity Number: 187
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract - #300346
Title: Bayesian Multivariate Item Response Theory Model and Its Software BMIRT
Author(s): Lihua Yao*+
Companies: CTB McGraw-Hill
Address: 20 Ryan Ranch Rd., Monterey, CA, 93940,
Keywords: item response theory ; Bayesian ; MCMC ; multidimension ; multigroup
Abstract:

We propose a multivariate item response theory model for educational testing data (MIRT). This model is a generalization of the standard item response theory model. We use a Bayesian approach and MCMC for parameter estimation of this model. The estimation procedure is implemented in a computer program called BMIRT (Bayesian Multivariate Item Response Theory model). BMIRT has several important properties. First, the guessing parameters are estimated based on the data, not fixed in an ad hoc manner prior to fitting the model as in some existing software such as TESTFACT, and MICROFACT. Second, by combining different content areas for concurrent calibration, BMIRT provides more accurate objective scores. Third, BMIRT can determine the dimension loadings of the test items that are in different categories but are correlated, and as a result, more accurate parameter estimation and score reporting. Finally, with BMIRT, multigroup tests can be put on the same scale so that guidance and methods to measure longitudinal growth at the student level can be provided. We use real and simulated data sets to illustrate the applications of the model and BMIRT.

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