Obtaining a Common Scale for Item Response Theory Item Parameters Using Separate Versus Concurrent Estimation in the Common-Item Equating Design

Abstract

Item response theory item parameters can be estimated using data from a common-item equating design either separately for each form or concurrently across forms. This paper reports the results of a simulation study of separate versus concurrent item parameter estimation. Using simulated data from a test with 60 dichotomous items, four factors were considered: (a) estimation program (MULTILOG versus BILOG-MG), (b) sample size per form (3,000 versus 1,000), (c) number of common items (20 versus 10), and (d) equivalent versus nonequivalent groups taking the two forms (no mean difference versus a mean difference of 1 SD). In addition, four methods of item parameter scaling were used in the separate estimation condition: two item characteristic curve methods (Stocking-Lord and Haebara) and two moment methods (Mean/Mean and Mean/Sigma). Concurrent estimation generally resulted in lower error than separate estimation, although not universally so. The results suggest that one factor accounting for the lower error when using concurrent estimation may be that the parameter estimates for the common item parameters are based on larger samples. It is argued that the results of this study, together with other research on this topic, are not sufficient to recommend completely avoiding separate estimation in favor of concurrent estimation.

References

ACT, Inc. (1997). ACT Assessment technical manual. Iowa City, IA: Author.

Béguin, A. A. , Hanson, B. A. , & Glas, C.A.W. (2000, April). Effect of multidimensionality on separate and concurrent estimation in IRT equating. Paper presented at the Annual Meeting of the National Council on Measurement in Education, New Orleans, LA. Available from http://www.b-a-h.com/papers/paper0002.html

Haebara, T. (1980). Equating logistic ability scales by a weighted least squares method. Japanese Psychological Research, 22, 144-149.

Kim, S. , & Cohen, A. S. (1998). A comparison of linking and concurrent calibration under item response theory. Applied Psychological Measurement, 22, 131-143.

Kolen, M. J. , & Brennan, R. L. (1995). Test equating methods and practices. New York: Springer-Verlag.

Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.

Mislevy, R. J. , & Bock, R. D. (1990). BILOG 3 (2nd ed.) [Computer program]. Mooresville, IN: Scientific Software International.

Petersen, N. S. , Cook, L. L. , & Stocking, M. L. (1983). IRT versus conventional equating methods: A comparative study of scale stability. Journal of Educational Statistics, 8, 137-156.

Stocking, M. L. , & Lord, F. M. (1983). Developing a common metric in item response theory. Applied Psychological Measurement, 7, 201-210.

10.

Thissen, D. (1991). Multilog user’s guide: Multiple, categorical item analysis and test scoring using item response theory [Computer program]. Chicago: Scientific Software International.

11.

Wingersky, M. S. , Barton, M. A. , & Lord, R. M. (1982). LOGIST user’s guide. Princeton, NJ: Educational Testing Service.

12.

Wingersky, M. S. , Cook, L. L. , & Eignor, D. R. (1987). Specifying the characteristics of linking items used for item response theory item calibration [Computer program]. ETS Research Report 87-24. Princeton, NJ: Educational Testing Service.

13.

Zimowski, M. F. , Muraki, E. , Mislevy, R. J. , & Bock, R. D. (1996). BILOG-MG: Multiple-group IRT analysis and test maintenance for binary items [Computer program]. Chicago: Scientific Software International.