A Comparison of Two Procedures for Computing IRT Equating Coefficients

Frank B. Baker · Ali Al‐Karni

105 citations0/0 files storedJournal of Educational Measurement

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Educational Technology and Assessment

Abstract

In order to equate tests under Item Response Theory (IRT), one must obtain the slope and intercept coefficients of the appropriate linear transformation. This article compares two methods for computing such equating coefficients–Loyd and Hoover (1980) and Stocking and Lord (1983). The former is based upon summary statistics of the test calibrations; the latter is based upon matching test characteristic curves by minimizing a quadratic loss function. Three types of equating situations: horizontal, vertical, and that inherent in IRT parameter recovery studies–were investigated. The results showed that the two computing procedures generally yielded similar equating coefficients in all three situations. In addition, two sets of SAT data were equated via the two procedures, and little difference in the obtained results was observed. Overall, the results suggest that the Loyd and Hoover procedure usually yields acceptable equating coefficients. The Stocking and Lord procedure improves upon the Loyd and Hoover values and appears to be less sensitive to atypical test characteristics. When the user has reason to suspect that the test calibrations may be associated with data sets that are typically troublesome to calibrate, the Stocking and Lord procedure is to be preferred.

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References

2012Applications of Item Response Theory To Practical Testing Problems 1983Developing a Common Metric in Item Response Theory 1984Estimating Latent Distributions 1980EQUATING LOGISTIC ABILITY SCALES BY A WEIGHTED LEAST SQUARES METHOD 1980VERTICAL EQUATING USING THE RASCH MODEL 1977ITEM CHARACTERISTIC CURVE SOLUTIONS TO THREE INTRACTABLE TESTING PROBLEMS1

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1993A Study of Criteria Used in Equating 1994The Effect of Speededness on Parameter Estimation in Item Response Theory 2006A Comparative Study of IRT Fixed Parameter Calibration Methods 2002Recovery of Item Parameters in the Nominal Response Model: A Comparison of Marginal Maximum Likelihood Estimation and Markov Chain Monte Carlo Estimation 1996Practical issues in Large-Scale Computerized Adaptive Testing 1992Effects of Linking Methods on Detection of DIF 1992Equating Tests Under the Graded Response Model 1999Item Parameter Recovery for the Nominal Response Model

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