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.