准确性与公平性视角下异常锚题对测验等值的影响
The Effect of Outlying Common Items on Test Equating: A Perspective on Accuracy and Equity
摘要: 在项目反应理论参数链接和等值过程中，锚题起着至关重要的作用。本研究在非等组锚测验设计下，采用蒙特卡洛方法，操纵异常锚题比例、区分度以及难度参数漂移程度，考查异常锚题对测验等值的影响。评估指标包括链接系数的偏差与均方根误差、等值分数的绝对偏差与加权绝对偏差以及分类准确性和一致性的绝对偏差。结果表明，在链接系数和等值分数方面，相较于传统特征曲线方法，信息量加权方法更优。此外，各方法在分类准确性和一致性方面均表现出较高可靠性。
Abstract: Common items are crucial in item response theory (IRT) linking and equating. Within a common item nonequivalent groups design, this study utilized Monte Carlo simulations to manipulate the proportion of outlying common items, the magnitude of a-parameter drift, and the magnitude of b-parameter drift, in order to examine the impact of outlying common items on test equating. Evaluation criteria included bias and root mean square error of linking constants, absolute bias of equated scores, weighted absolute bias of equated scores, and absolute bias of classification accuracy and consistency. The results for errors in linking constants and equated scores demonstrated that the information-weighted characteristic curve methods consistently outperformed traditional characteristic curve linking methods. Additionally, all IRT linking methods exhibited high fidelity in recovering classification accuracy and consistency.
文章引用：王少杰 (2026). 准确性与公平性视角下异常锚题对测验等值的影响. 心理学进展, 16(7), 213-224. https://doi.org/10.12677/ap.2026.167353

参考文献

[1] Baldwin, P. (2011). A Strategy for Developing a Common Metric in Item Response Theory When Parameter Posterior Distributions Are Known. Journal of Educational Measurement, 48, 1-11.[CrossRef] 
[2] Baldwin, P., & Clauser, B. E. (2022). Historical Perspectives on Score Comparability Issues Raised by Innovations in Testing. Journal of Educational Measurement, 59, 140-160.[CrossRef] 
[3] Barrett, M. D., & van der Linden, W. J. (2019). Estimating Linking Functions for Response Model Parameters. Journal of Educational and Behavioral Statistics, 44, 180-209.[CrossRef] 
[4] Chalmers, R. P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48, 1-29.[CrossRef] 
[5] Diao, H., & Keller, L. (2020). Investigating Repeater Effects on Small Sample Equating: Include or Exclude? Applied Measurement in Education, 33, 54-66.[CrossRef] 
[6] Fellinghauer, C., Debelak, R., & Strobl, C. (2023). What Affects the Quality of Score Transformations? Potential Issues in True-Score Equating Using the Partial Credit Model. Educational and Psychological Measurement, 83, 1249-1290.[CrossRef] [PubMed]
[7] Furter, R. T., & Dwyer, A. C. (2020). Investigating the Classification Accuracy of Rasch and Nominal Weights Mean Equating with Very Small Samples. Applied Measurement in Education, 33, 44-53.[CrossRef] 
[8] Goodman, J. T., Dallas, A. D., & Fan, F. (2020). Equating with Small and Unbalanced Samples. Applied Measurement in Education, 33, 34-43.[CrossRef] 
[9] Haebara, T. (1980). Equating Logistic Ability Scales by a Weighted Least Squares Method. Japanese Psychological Research, 22, 144-149.[CrossRef] 
[10] He, Y., & Cui, Z. (2020). Evaluating Robust Scale Transformation Methods with Multiple Outlying Common Items under IRT True Score Equating. Applied Psychological Measurement, 44, 296-310.[CrossRef] [PubMed]
[11] He, Y., Cui, Z., & Osterlind, S. J. (2015). New Robust Scale Transformation Methods in the Presence of Outlying Common Items. Applied Psychological Measurement, 39, 613-626.[CrossRef] [PubMed]
[12] He, Y., Cui, Z., Fang, Y., & Chen, H. (2013). Using a Linear Regression Method to Detect Outliers in IRT Common Item Equating. Applied Psychological Measurement, 37, 522-540.[CrossRef] 
[13] Hu, H. Q., Rogers, W. T., & Vukmirovic, Z. (2008). Investigation of Irt-Based Equating Methods in the Presence of Outlier Common Items. Applied Psychological Measurement, 32, 311-333.[CrossRef] 
[14] Kim, K. Y. (2020). Two IRT Fixed Parameter Calibration Methods for the Bifactor Model. Journal of Educational Measurement, 57, 29-50.[CrossRef] 
[15] Kim, K. Y., Lim, E., & Lee, W. (2019). A Comparison of the Relative Performance of Four IRT Models on Equating Passage-Based Tests. International Journal of Testing, 19, 248-269.[CrossRef] 
[16] Kim, S. Y., & Lee, W. (2019). Classification Consistency and Accuracy for Mixed-Format Tests. Applied Measurement in Education, 32, 97-115.[CrossRef] 
[17] Kim, S., & Kolen, M. J. (2006). Robustness to Format Effects of IRT Linking Methods for Mixed-Format Tests. Applied Measurement in Education, 19, 357-381.[CrossRef] 
[18] Kim, S., & Kolen, M. J. (2022). Scale Linking for the Testlet Item Response Theory Model. Applied Psychological Measurement, 46, 79-97.[CrossRef] [PubMed]
[19] Kolen, M. J., & Brennan, R. L. (2014). Test Equating, Scaling, and Linking: Methods and Practices. Springer.[CrossRef] 
[20] Lathrop, Q. N. (2014). R Package cacIRT: Estimation of Classification Accuracy and Consistency Under Item Response Theory. Applied Psychological Measurement, 38, 581-582.[CrossRef] 
[21] Lathrop, Q. N., & Cheng, Y. (2013). Two Approaches to Estimation of Classification Accuracy Rate under Item Response Theory. Applied Psychological Measurement, 37, 226-241.[CrossRef] 
[22] Lee, W. (2010). Classification Consistency and Accuracy for Complex Assessments Using Item Response Theory. Journal of Educational Measurement, 47, 1-17.[CrossRef] 
[23] Li, Y. (2012). Examining the Impact of Drifted Polytomous Anchor Items on Test Characteristic Curve (TCC) Linking and Irt True Score Equating. ETS Research Report Series, 2012, i-22.[CrossRef] 
[24] Liu, C., & Jurich, D. (2022). Application of Sampling Variance of Item Response Theory Parameter Estimates in Detecting Outliers in Common Item Equating. Applied Psychological Measurement, 46, 529-547.[CrossRef] [PubMed]
[25] Liu, C., & Jurich, D. (2023). Outlier Detection Using T-Test in Rasch IRT Equating under NEAT Design. Applied Psychological Measurement, 47, 34-47.[CrossRef] [PubMed]
[26] Manna, V. F., & Gu, L. (2019). Different Methods of Adjusting for Form Difficulty under the Rasch Model: Impact on Consistency of Assessment Results. ETS Research Report Series, 2019, Article ID: 12244.[CrossRef] 
[27] Michaelides, M. P. (2010). Sensitivity of Equated Aggregate Scores to the Treatment of Misbehaving Common Items. Applied Psychological Measurement, 34, 365-369.[CrossRef] 
[28] Moses, T. (2022). Linking and Comparability across Conditions of Measurement: Established Frameworks and Proposed Updates. Journal of Educational Measurement, 59, 231-250.[CrossRef] 
[29] Park, S., Kim, K. Y., & Lee, W. (2023). Estimating Classification Accuracy and Consistency Indices for Multiple Measures with the Simple Structure MIRT Model. Journal of Educational Measurement, 60, 106-125.[CrossRef] 
[30] Peabody, M. R. (2020). Some Methods and Evaluation for Linking and Equating with Small Samples. Applied Measurement in Education, 33, 3-9.[CrossRef] 
[31] R Core Team (2024). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing.
[32] Rudner, L. M. (2005). Expected Classification Accuracy. Practical Assessment Research & Evaluation, 10, 1-4.
[33] Setzer, J. C., Cheng, Y., & Liu, C. (2023). Classification Accuracy and Consistency of Compensatory Composite Test Scores. Journal of Educational Measurement, 60, 501-519.[CrossRef] 
[34] Stocking, M. L., & Lord, F. M. (1983). Developing a Common Metric in Item Response Theory. Applied Psychological Measurement, 7, 201-210.[CrossRef] 
[35] Van der Linden, W. J. (2022). What Is Actually Equated in “Test Equating”? A Didactic Note. Journal of Educational and Behavioral Statistics, 47, 353-362.[CrossRef] 
[36] van der Linden, W. J., & Barrett, M. D. (2016). Linking Item Response Model Parameters. Psychometrika, 81, 650-673.[CrossRef] [PubMed]
[37] Wang, S., Lee, W., Zhang, M., & Yuan, L. (2024). IRT Characteristic Curve Linking Methods Weighted by Information for Mixed-Format Tests. Applied Measurement in Education, 37, 377-390.[CrossRef] 
[38] Wang, S., Zhang, M., Lee, W., Huang, F., Li, Z., Li, Y. et al. (2022). Two IRT Characteristic Curve Linking Methods Weighted by Information. Journal of Educational Measurement, 59, 423-441.[CrossRef] 
[39] Wolkowitz, A. A., & Wright, K. D. (2019). Effectiveness of Equating at the Passing Score for Exams with Small Sample Sizes. Journal of Educational Measurement, 56, 361-390.[CrossRef] 
[40] Wyse, A. E., & Hao, S. (2012). An Evaluation of Item Response Theory Classification Accuracy and Consistency Indices. Applied Psychological Measurement, 36, 602-624.[CrossRef] 
[41] Yi, H. S., Kim, S., & Brennan, R. L. (2007). A Method for Estimating Classification Consistency Indices for Two Equated Forms. Applied Psychological Measurement, 31, 275-291.[CrossRef] 
[42] Zhang, Z. (2021). Asymptotic Standard Errors of Generalized Partial Credit Model True Score Equating Using Characteristic Curve Methods. Applied Psychological Measurement, 45, 331-345.[CrossRef] [PubMed]