|Title||Optimal design for item calibration in computerized adaptive testing|
|Publication Type||Journal Article|
|Year of Publication||1999|
|Journal||Dissertation Abstracts International: Section B: the Sciences & Engineering|
|Keywords||computerized adaptive testing|
Item Response Theory is the psychometric model used for standardized tests such as the Graduate Record Examination. A test-taker's response to an item is modelled as a binary response with success probability depending on parameters for both the test-taker and the item. Two popular models are the two-parameter logistic (2PL) model and the three-parameter logistic (3PL) model. For the 2PL model, the logit of the probability of a correct response equals ai(theta j-bi), where ai and bi are item parameters, while thetaj is the test-taker's parameter, known as "proficiency." The 3PL model adds a nonzero left asymptote to model random response behavior by low theta test-takers. Assigning scores to students requires accurate estimation of theta s, while accurate estimation of theta s requires accurate estimation of the item parameters. The operational implementation of Item Response Theory, particularly following the advent of computerized adaptive testing, generally involves handling these two estimation problems separately. This dissertation addresses the optimal design for item parameter estimation. Most current designs calibrate items with a sample drawn from the overall test-taking population. For 2PL models a sequential design based on the D-optimality criterion has been proposed, while no 3PL design is in the literature. In this dissertation, we design the calibration with the ultimate use of the items in mind, namely to estimate test-takers' proficiency parameters. For both the 2PL and 3PL models, this criterion leads to a locally L-optimal design criterion, named the Minimal Information Loss criterion. In turn, this criterion and the General Equivalence Theorem give a two point design for the 2PL model and a three point design for the 3PL model. A sequential implementation of this optimal design is presented. For the 2PL model, this design is almost 55% more efficient than the simple random sample approach, and 12% more efficient than the locally D-optimal design. For the 3PL model, the proposed design is 34% more efficient than the simple random sample approach. (PsycINFO Database Record (c) 2003 APA, all rights reserved).