Using Functional Clustering to Diagnose Person Misfit

References

• Abraham, C., Cornillon, P. A., Matzner-Lober, E., & Molinari, N. (2003). Unsupervised curve clustering using B-splines. Scandinavian Journal of Statistics, 30(3), 581–595. https://doi.org/10.1111/1467-9469.00350
   Web of Science ®Google Scholar
• Artner, R. (2016). A simulation study of person-fit in the Rasch model. Psychological Test and Assessment Modeling, 58(3), 531–563.
   Google Scholar
• Baker, F. B., & Kim, S. (2004). Item response theory: Parameter estimation techniques. Second Edition, Revised and expanded. Marcel Dekker.
   Google Scholar
• Bouveyron, C. (2021). funFEM: Clustering in the Discriminative Functional Subspace (Version 1.2) [R package]. https://CRAN.R-project.org/package=funFEM
   Google Scholar
• Bouveyron, C., Côme, E., & Jacques, J. (2015). The discriminative functional mixture model for a comparative analysis of bike sharing systems. The Annals of Applied Statistics, 9(4), 1726–1760. https://doi.org/10.1214/15-AOAS861
   Web of Science ®Google Scholar
• Cuevas, A. (2014). A partial overview of the theory of statistics with Functional Data. Journal of Statistical Planning and Inference, 147, 1–23. https://doi.org/10.1016/j.jspi.2013.04.002
   Web of Science ®Google Scholar
• Doval, E., & Delicado, P. (2020). Identifying and classifying aberrant response patterns through functional data analysis. Journal of Educational and Behavioral Statistics, 45(6), 719–749. https://doi.org/10.3102/1076998620911941
   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. E., & Reise, S. P. (2000). Item response theory for psychologists. Lawrence Erlbaum Associates, Publishers.
   Google Scholar
• Engelhard, G. (2013). Invariant measurement: Using Rasch models in the social, behavioral, and health sciences. Routledge.
   Google Scholar
• Engelhard, G., & Wang, J. (2021). Rasch models for solving measurement problems: Invariant measurement in the social sciences. Sage Publications.
   Google Scholar
• Ferrando, P. J. (2015). Assessing person fit in typical-response measures. In S. P. Reise & D. A. Revicki (Eds.), Handbook of item response theory modeling: Applications to typical performance assessment. Routledge.
   Google Scholar
• Glas, C. A. W., & Khalid, N. (2019). Person fit. In W. J. van der Linden (Ed.), Handbook of item response theory: Applications (Vol. 3, pp. 107–126). Chapman & Hall/CRC.
   Google Scholar
• Jacques, J., & Preda, C. (2014). Functional data clustering: A survey. Advances in Data Analysis and Classification, 8(3), 231–255. https://doi.org/10.1007/s11634-013-0158-y
   Web of Science ®Google Scholar
• James, G. M., & Sugar, C. A. (2003). Clustering for sparsely sampled functional data. Journal of the American Statistical Association, 98(462), 397–408. https://doi.org/10.1198/016214503000189
   Web of Science ®Google Scholar
• James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning: With applications in R. Springer.
   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
• Kokoszka, P., & Reimherr, M. (2017). Introduction to functional data analysis. CRC Press.
   Google Scholar
• Levitin, D. J., Nuzzo, R. L., Vines, B. W., & Ramsay, J. O. (2007). Introduction to functional data analysis. Canadian Psychology / Psychologie Canadienne, 48(3), 135–155. https://doi.org/10.1037/cp2007014
   Web of Science ®Google Scholar
• Lumsden, J. (1977). Person reliability. Applied Psychological Measurement, 1(4), 477–482. https://doi.org/10.1177/014662167700100403
   Google Scholar
• Mair, P., Hatzinger, R., Maier, M. J. (2021). eRm: Extended Rasch Modeling (Version 1.0-2) [R package]. https://cran.r-project.org/package=eRm
   Google Scholar
• R Core Team. (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/.
   Google Scholar
• Ramsay, J. O., & Silverman, B. W. (2005). Functional data analysis (2nd ed.). Springer Science + Business Media.
   Google Scholar
• Ramsay, J. O., Graves, S., Hooker, G. (2021). FDA: Functional Data Analysis (Version 5.5.1) [R package]. https://CRAN.R-project.org/package=fda
   Google Scholar
• Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests. University of Chicago Press.
   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
• Sijtsma, K. (1986). A coefficient of deviance of response patterns. Journal Kwantitatieve Methoden: Nieuwsbrief Voor Toegepaste Statistiek En Operationele Research, 7(22), 131–145.
   Google Scholar
• Tarpey, T., & Kinateder, K. K. (2003). Clustering functional data. Journal of Classification, 20(1), 93–114. https://doi.org/10.1007/s00357-003-0007-3
   Web of Science ®Google Scholar
• Tendeiro, J. N., Meijer, R. R., & Niessen, A. S. M. (2016). PerFit: An R package for person-fit analysis in IRT. Journal of Statistical Software, 74(5), 1–27. https://doi.org/10.18637/jss.v074.i05
   Web of Science ®Google Scholar
• Turner, K. T., & Engelhard Jr, G. (in press). Functional data analysis and person response Functions. Measurement: Interdisciplinary Research & Perspectives.
   Web of Science ®Google Scholar
• Ullah, S., & Finch, C. F. (2013). Applications of functional data analysis: A systematic review. BMC Medical Research Methodology, 13(1), 1–12. https://doi.org/10.1186/1471-2288-13-43
   PubMedGoogle Scholar
• Walker, A. A., Engelhard, G., Royal, K., & Hedgpeth, M. (2016). Exploring aberrant responses using person fit and person response functions. Journal of Applied Measurement, 17(2), 1–15.
   PubMedGoogle Scholar
• Walker, A. A., Jennings, J. K., & Engelhard, G. (2018). Using person response functions to investigate areas of person misfit related to item characteristics. Educational Assessment, 23(1), 47–68. https://doi.org/10.1080/10627197.2017.1415143
   Web of Science ®Google Scholar
• Wang, J. L., Chiou, J. M., & Müller, H. G. (2015). Review of functional data analysis. arXiv preprint arXiv1507.05135.
   Google Scholar
• Wright, B. D., & Stone, M. H. (1979). Best test design. Mesa Press.
   Google Scholar
• Wright, B. D., Linacre, J. M., Gustafson, J. E., & Martin-Löf, P. (1994). Reasonable mean-square fit values. Rasch Measurement Transactions, 8, 370. Rasch Measurement Transactions, 8(3), 370.
   Google Scholar