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ERIC Number: ED520259
Record Type: Non-Journal
Publication Date: 2010
Pages: 231
Abstractor: As Provided
ISBN: ISBN-978-1-1240-6900-5
Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory
Brossman, Bradley Grant
ProQuest LLC, Ph.D. Dissertation, The University of Iowa
The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the Multidimensional Item Response Theory (MIRT) framework. Currently, MIRT scale linking procedures exist to place item parameter estimates and ability estimates on the same scale after separate calibrations are conducted. These procedures account for indeterminacies in (1) translation, (2) dilation, (3) rotation, and (4) correlation. However, no procedures currently exist to equate number correct scores after parameter estimates are placed on the same scale. This research sought to fill this void in the current psychometric literature. Three equating procedures--two observed score procedures and one true score procedure--were created and described in detail. One observed score procedure was presented as a direct extension of unidimensional IRT observed score equating, and is referred to as the "Full MIRT Observed Score Equating Procedure." The true score procedure and the second observed score procedure incorporated the statistical definition of the "direction of best measurement" in an attempt to equate exams using unidimensional IRT (UIRT) equating principles. These procedures are referred to as the "Unidimensional Approximation of MIRT True Score Equating Procedure" and the "Unidimensional Approximation of MIRT Observed Score Equating Procedure," respectively. Three exams within the Iowa Test of Educational Development (ITED) Form A and Form B batteries were used to conduct UIRT observed score and true score equating, MIRT observed score and true score equating, and equipercentile equating. The equipercentile equating procedure was conducted for the purpose of comparison since this procedure does not explicitly violate the IRT assumption of unidimensionality. Results indicated that the MIRT equating procedures performed more similarly to the equipercentile equating procedure than the UIRT equating procedures, presumably due to the violation of the unidimensionality assumption under the UIRT equating procedures. Future studies are expected to address how the MIRT procedures perform under varying levels of multidimensionality (weak, moderate, strong), varying frameworks of dimensionality (simple structure vs. complex structure), and number of dimensions, among other conditions. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A