TitleComparison of Pretest Item Calibration Methods in a Computerized Adaptive Test (CAT)
Publication TypeConference Paper
Year of Publication2017
AuthorsMeng, H, Han, C
Conference NameIACAT 2017 Conference
Date Published08/2017
PublisherNiigata Seiryo University
Conference LocationNiigata, Japan
KeywordsCAT, Pretest Item Calibration

Calibration methods for pretest items in a computerized adaptive test (CAT) are not a new area of research inquiry. After decades of research on CAT, the fixed item parameter calibration (FIPC) method has been widely accepted and used by practitioners to address two CAT calibration issues: (a) a restricted ability range each item is exposed to, and (b) a sparse response data matrix. In FIPC, the parameters of the operational items are fixed at their original values, and multiple expectation maximization (EM) cycles are used to estimate parameters of the pretest items with prior ability distribution being updated multiple times (Ban, Hanson, Wang, Yi, & Harris, 2001; Kang & Peterson, 2009; Pommerich & Segall, 2003).

Another calibration method is the fixed person parameter calibration (FPPC) method proposed by Stocking (1988) as “Method A.” Under this approach, candidates’ ability estimates are fixed in the calibration of pretest items and they define the scale on which the parameter estimates are reported. The logic of FPPC is suitable for CAT applications because the person parameters are estimated based on operational items and available for pretest item calibration. In Stocking (1988), the FPPC was evaluated using the LOGIST computer program developed by Wood, Wingersky, and Lord (1976). He reported that “Method A” produced larger root mean square errors (RMSEs) in the middle ability range than “Method B,” which required the use of anchor items (administered non-adaptively) and linking steps to attempt to correct for the potential scale drift due to the use of imperfect ability estimates.

Since then, new commercial software tools such as BILOG-MG and flexMIRT (Cai, 2013) have been developed to handle the FPPC method with different implementations (e.g., the MH-RM algorithm with flexMIRT). The performance of the FPPC method with those new software tools, however, has rarely been researched in the literature.

In our study, we evaluated the performance of two pretest item calibration methods using flexMIRT, the new software tool. The FIPC and FPPC are compared under various CAT settings. Each simulated exam contains 75% operational items and 25% pretest items, and real item parameters are used to generate the CAT data. This study also addresses the lack of guidelines in existing CAT item calibration literature regarding population ability shift and exam length (more accurate theta estimates are expected in longer exams). Thus, this study also investigates the following four factors and their impact on parameter estimation accuracy, including: (1) candidate population changes (3 ability distributions); (2) exam length (20: 15 OP + 5 PT, 40: 30 OP + 10 PT, and 60: 45 OP + 15 PT); (3) data model fit (3PL and 3PL with fixed C), and (4) pretest item calibration sample sizes (300, 500, and 1000). This study’s findings will fill the gap in this area of research and thus provide new information on which practitioners can base their decisions when selecting a pretest calibration method for their exams.


Ban, J. C., Hanson, B. A., Wang, T., Yi, Q., & Harris, D. J. (2001). A comparative study of online pretest item—Calibration/scaling methods in computerized adaptive testing. Journal of Educational Measurement, 38(3), 191–212.

Cai, L. (2013). flexMIRT® Flexible Multilevel Multidimensional Item Analysis and Test Scoring (Version 2) [Computer software]. Chapel Hill, NC: Vector Psychometric Group.

Kang, T., & Petersen, N. S. (2009). Linking item parameters to a base scale (Research Report No. 2009– 2). Iowa City, IA: ACT.

Pommerich, M., & Segall, D.O. (2003, April). Calibrating CAT pools and online pretest items using marginal maximum likelihood methods. Paper presented at the annual meeting of the National Council on Measurement in Education, Chicago, IL.

Stocking, M. L. (1988). Scale drift in online calibration (Research Report No. 88–28). Princeton, NJ: Educational Testing Service.

Wood, R. L., Wingersky, M. S., & Lord, F. M. (1976). LOGIST: A computer program for estimating examinee ability and item characteristic curve parameters (RM76-6) [Computer program]. Princeton, NJ: Educational Testing Service.

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