Stable estimates of item calibration are important and the results should be consistent using different software programs for research to progress satisfactorily. Items tend to greater consistency although produced by person responses (Fisher, 2010). The database of 3,121 persons and 26 items for the KCT-R (Stone, 2002) produced a test separation value of 38.22 corresponding to a test reliability of 0.99. The person separation value was 2.54 corresponding to a person reliability of 0.87. A sample of 260 persons ages 5 - 60 produced a test-retest coefficient of 0.96.
Two programs for producing estimations - Winsteps (Linacre, 2002) and RUMM (Andrich, D., et al., 2000) - were utilized. A well-defined variable and wide item/ability logit range made the KCT-R data useful for this comparison. Newer releases provide additional enhancements, but the basic estimation algorithms remain constant.
Figure 1 is a plot of item calibration estimations using Winsteps and RUMM2010. This figure accents the differences. The Winsteps estimates were lower than the estimates using RUMM2010 for items 1 - 12, and slightly higher for items 13 - 26. A difference of about 0.8 logits was observed for the two easiest items of the test. These differences decreased to item 12. They reversed thereafter with the difference continuing to about 0.3 for the most difficult items.
Figure 2 identifies the stability in the estimations. The lowest four calibration estimates show the largest deviations that diminish towards 0.0 and then increase with the highest two calibration estimates showing the greatest difference. In spite of the noted differences between the two software programs, the item calibration estimates are highly correlated. The wide-range of the calibration estimates contributes to a high r2 of 0.99, but with Winsteps estimates slightly more extreme than RUMM2010 estimates. Stability exists between the two estimations processes with the differences well within any meaningful difference. Nevertheless, a slight difference exists in the estimation process.
American Institutes for Research
Collaborative for Research on Outcomes and Metrics
Aurora University, Aurora, IL
Andrich, D., Lyne, A., Sheridan, B., & Luo, G. (2000). RUMM 2010: Rasch Unidimensional Measurement Models. Australia: Rumm Laboratory Try Ltd.
Fisher, W. P., Jr. (2010, 30 September). Distinguishing between consistency and error in reliability coefficients: Improving the estimation and interpretation of information on measurement precision. Social Science Research Network. Retrieved from http://ssrn.com/abstract=1685556.
Linacre, J. M. (2003). Winsteps. Beaverton Oregon: Winsteps.com.
Figure 1. A plot of item calibration estimates using Winsteps and RUMM2010. Points on the solid line are RUMM estimates. Points on the dashed line are Winsteps estimates. The y-axis is "Difficulty in Logits"
Figure 2. A cross-plot of the KCT-R items calibration estimates using Winsteps (y-axis) and RUMM2010 (x-axis) .
Comparing Item Calibration Estimates using Winsteps and RUMM2010, Futoshi Yumoto & Mark Stone ... Rasch Measurement Transactions, 2011, 25:3, 1329
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