An Iterative Scale Purification Procedure on l_z for the Detection of Aberrant Responses

References

• Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 397–472). Addison-Wesley.
   Google Scholar
• Chalmers, R. P. (2012). mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1–29. https://doi.org/10.18637/jss.v048.i06
   Web of Science ®Google Scholar
• Cizek, G. J., & Wollack, J. A. (Eds.) (2017). Handbook of quantitative methods for detecting cheating on tests. Routledge.
   Google Scholar
• de la Torre, J., & Deng, W. (2008). Improving person-fit assessment by correcting the ability estimate and its reference distribution. Journal of Educational Measurement, 45(2), 159–177. https://www.jstor.org/stable/20461887 https://doi.org/10.1111/j.1745-3984.2008.00058.x
   Web of Science ®Google Scholar
• Drasgow, F., Levine, M. V., & Williams, E. A. (1985). Appropriateness measurement with polychotomous item response models and standardized indices. British Journal of Mathematical and Statistical Psychology, 38(1), 67–86. https://doi.org/10.1111/j.2044-8317.1985.tb00817.x
   Web of Science ®Google Scholar
• Embretson, S., & Reise, S. P. (2000). Item response theory for psychologists. Lawrence Erlbaum Associates Publisher.
   Google Scholar
• French, B. F., & Maller, S. J. (2007). Iterative purification and effect size use with logistic regression for differential item functioning detection. Educational and Psychological Measurement, 67(3), 373–393. https://doi.org/10.1177/0013164406294781
   Web of Science ®Google Scholar
• Glas, C. A. W., & Dagohoy, A. V. T. (2007). A person fit test for IRT models for polytomous items. Psychometrika, 72(2), 159–180. https://doi.org/10.1007/s11336-003-1081-5
   Web of Science ®Google Scholar
• Hendrawan, I., Glas, C. W., & Meijer, R. R. (2005). The effect of person misfit on classification decisions. Applied Psychological Measurement, 29(1), 26–44. https://doi.org/10.1177/0146621604270902
   Web of Science ®Google Scholar
• Hidalgo-Montesinos, M. D., & Gómez-Benito, J. (2003). Test purification and the evaluation of differential item functioning with multinominal logistic regression. European Journal of Psychological Assessment, 19(1), 1–11. https://doi.org/10.1027/1015-5759.19.1.1
   Web of Science ®Google Scholar
• Hong, M. R., & Cheng, Y. (2019). Robust maximum marginal likelihood (RMML) estimation for item response theory models. Behavior Research Methods, 51(2), 573–588. https://doi.org/10.3758/s13428-018-1150-4
   PubMed Web of Science ®Google Scholar
• Karabatsos, G. (2003). Comparing the aberrant response detection performance of thirty-six person-fit statistics. Applied Measurement in Education, 16(4), 277–298. https://doi.org/10.1207/S15324818AME1604_2
   Web of Science ®Google Scholar
• Lautenschlager, G. I., Flaherty, V. L., & Park, D. G. (1994). IRT differential item functioning: An examination of ability scale purifications. Educational and Psychological Measurement, 54(1), 21–31. https://doi.org/10.1177/0013164494054001003
   Web of Science ®Google Scholar
• Lee, P., Stark, S., & Chernyshenko, O. S. (2014). Detecting aberrant responding on unidimensional pairwise preference tests: An application of lz based on the Zinnes-Griggs ideal point IRT model. Applied Psychological Measurement, 38(5), 391–403. https://doi.org/10.1177/0146621614526636
   Web of Science ®Google Scholar
• Levine, M. V., & Rubin, D. B. (1979). Measuring the appropriateness of multiple-choice test scores. Journal of Educational Statistics, 4(4), 269–290. https://doi.org/10.2307/1164595
   Google Scholar
• Li, M.-N. F., & Olejnik, S. (1997). The power of Rasch person-fit statistics in detecting unusual response patterns. Applied Psychological Measurement, 21(3), 215–231. https://doi.org/10.1177/01466216970213002
   Web of Science ®Google Scholar
• Magis, D., Raîche, G., & Béland, S. (2012). A didactic presentation of Snijders’s lz* index of person fit with emphasis on response model selection and ability estimation. Journal of Educational and Behavioral Statistics, 37(1), 57–81. https://doi.org/10.3102/1076998610396894
   Web of Science ®Google Scholar
• Meijer, R. R., & Sijtsma, K. (2001). Methodology review: Evaluating person fit. Applied Psychological Measurement, 25(2), 107–135. https://doi.org/10.1177/01466210122031957
   Web of Science ®Google Scholar
• Mislevy, R. J., & Bock, R. D. (1982). Biweight estimates of latent ability. Educational and Psychological Measurement, 42(3), 725–737. https://doi.org/10.1177/001316448204200
   Web of Science ®Google Scholar
• Molenaar, I. W., & Hoijtink, H. (1990). The many null distributions of person fit indices. Psychometrika, 55(1), 75–106. https://doi.org/10.1007/BF02294745
   Web of Science ®Google Scholar
• Nering, M. L. (1995). The distribution of person fit using true and estimated person parameters. Applied Psychological Measurement, 19(2), 121–129. https://doi.org/10.1177/014662169501900201
   Web of Science ®Google Scholar
• Noonan, B. W., Boss, M. W., & Gessaroli, M. E. (1992). The effect of test length and IRT model on the distribution and stability of three appropriateness indexes. Applied Psychological Measurement, 16(4), 345–352. https://doi.org/10.1177/014662169201600405
   Web of Science ®Google Scholar
• Patton, J. M., Cheng, Y., Hong, M., & Diao, Q. (2019). Detection and treatment of careless responses to improve item parameter estimation. Journal of Educational and Behavioral Statistics, 44(3), 309–341. https://doi.org/10.3102/1076998618825116
   Web of Science ®Google Scholar
• Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. University of Chicago Press.
   Google Scholar
• Reise, S. P. (1995). Scoring method and the detection of person misfit in a personality assessment context. Applied Psychological Measurement, 19(3), 213–229. https://doi.org/10.1177/014662169501900301
   Web of Science ®Google Scholar
• Reise, S. P., & Due, A. M. (1991). The influence of test characteristics on the detection of aberrant response patterns. Applied Psychological Measurement, 15(3), 217–226. https://doi.org/10.1177/014662169101500301
   Web of Science ®Google Scholar
• Rupp, A. A. (2013). A systematic review of the methodology for person fit research in item response theory: Lessons about generalizability of inferences from the design of simulation studies. Psychological Test and Assessment Modeling, 55(1), 3–38.
   Google Scholar
• Schuster, C., & Yuan, K. H. (2011). Robust estimation of latent ability in item response models. Journal of Educational and Behavioral Statistics, 36(6), 720–735. https://doi.org/10.3102/1076998610396890
   Web of Science ®Google Scholar
• Seo, D. G., & Weiss, D. J. (2013). lz person-fit index to identify misfit students with achievement test data. Educational and Psychological Measurement, 73(6), 994–1016. https://doi.org/10.1177/0013164413497015
   Web of Science ®Google Scholar
• Sinharay, S. (2016). The choice of the ability estimate with asymptotically correct standardized person‐fit statistics. The British Journal of Mathematical and Statistical Psychology, 69(2), 175–193. https://doi.org/10.1111/bmsp.12067
   PubMed Web of Science ®Google Scholar
• Sinharay, S. (2017). Detection of item preknowledge using likelihood ratio test and score test. Journal of Educational and Behavioral Statistics, 42(1), 46–68. https://doi.org/10.3102/1076998616673872
   Web of Science ®Google Scholar
• Snijders, T. A. B. (2001). Asymptotic null distribution of person fit statistics with estimated person parameter. Psychometrika, 66(3), 331–342. https://doi.org/10.1007/BF02294437
   Web of Science ®Google Scholar
• St-Onge, C., Valois, P., Abdous, B., & Germain, S. (2011). Accuracy of person-fit statistics: A Monte Carlo study of the influence of aberrance. Applied Psychological Measurement, 35(6), 419–432. https://doi.org/10.1177/0146621610391777
   Web of Science ®Google Scholar
• Tendeiro, J. N. (2021). PerFit (Version 1.4.5) [Computer software]. https://CRAN.R-project.org/package=PerFit
   Google Scholar
• van Krimpen-Stoop, E. M. L. A., & Meijer, R. R. (1999). The null distribution of person-fit statistics for conventional and adaptive tests. Applied Psychological Measurement, 23(4), 327–345. https://doi.org/10.1177/01466219922031446
   Web of Science ®Google Scholar
• Walker, A. A., Engelhard, G., Jr., Hedgpeth, M. W., & Royal, K. D. (2016). Exploring aberrant responses using person fit and person response functions. Journal of Applied Measurement, 17(2), 194–208.
   PubMedGoogle Scholar
• Wang, W.-C. (2008). Assessment of differential item functioning. Journal of Applied Measurement, 9(4), 384–408.
   Google Scholar
• Wang, W.-C., Shih, C.-L., & Sun, G.-W. (2012). The DIF-free-then-DIF strategy for the assessment of differential item functioning. Educational and Psychological Measurement, 72(4), 687–708. https://doi.org/10.1177/0013164411426157
   Web of Science ®Google Scholar
• Wang, X., Liu, Y., & Hambleton, R. K. (2017). Detecting item preknowledge using a predictive checking method. Applied Psychological Measurement, 41(4), 243–263. https://doi.org/10.1177/0146621616687285
   PubMed Web of Science ®Google Scholar