"The objective of person-fit measurement is to detect item-score patterns that are improbable given an IRT model or given the other patterns in a sample." (Meijer & Sitsma, 2001)
This sounds correct to the conventional statistician, but W. E. Deming's response to this line of reasoning was: "Of course we don't wish to violate specifications, but we must do better" (Neave, 1990, p.169).
Here are ways we can do better:
(i) Person-fit measurement must not only identify patterns that are improbable, but also ones that are too probable! The Rasch model predicts uncertainty. Too much certainty can indicate a constraint on the responses, perhaps the hidden imputation of "wrong" to not-reached items, or a response set on an attitude survey. Since the substantive length of a logit depends on the randomness in the data, constraints on the data artificially reduce the randomness. This makes the differences between items and persons appear greater when expressed in logits. If the constraints are limited to a subset of persons or items, then the measurement system is distorted accordingly.
(ii) Person-measurement fit statistics must flag misleading or ambiguous measures. Simply because a response string is improbable does not mean that it is misleading, and vice-versa. Meijer & Sitsma (2001) criticize residual-based fit statistics, such as OUTFIT and INFIT, because they "do not reflect the probability of ordering of the score patterns" (p.130). This is true, but is it relevant? What is needed is an indication of how much misfit disturbs the estimated measures, not the likelihood of any particular response pattern.
Meijer & Sitsma (2001) end their section "Improving Measurement Practice" with this sound advice:
"Smith (1985) mentioned four actions that could be taken when an item-score pattern is classified as misfitting:
(1) report several [ability] estimates (rather than just one) for an examinee based on subtests that are in agreement with the model,
(2) modify the item-score pattern (e.g., eliminate the unreached items at the end) and re-estimate [ability],
(3) do not report the [ability] estimate and retest the examinee, or
(4) decide that the error is small enough for the impact on [ability] to be [negligible]. ...
Which of these actions is taken depends on the context in which testing takes place. The usefulness of a person-fit statistic thus also depends heavily on the application for which it is intended."
Meijer R.R., & Sijtsma K. (2001) Methodology review: evaluating person fit. Applied Psychological Measurement 25(2), 107-135
Neave H.R. (1990) The Deming Dimension. Knoxville TN: SPC Press.
Smith R.M. (1985) A comparison of Rasch person analysis and robust estimators. Educational and Psychological Measurement, 16, 149-157.
Person Fit Statistic - What is Their Purpose? Meijer R.R., Sitsma K. Rasch Measurement Transactions, 2001, 15:2 p. 823
|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
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|March 21, 2019, Thur.||13th annual meeting of the UK Rasch user group, Cambridge, UK, http://www.cambridgeassessment.org.uk/events/uk-rasch-user-group-2019|
|April 4 - 8, 2019, Thur.-Mon.||NCME annual meeting, Toronto, Canada,https://ncme.connectedcommunity.org/meetings/annual|
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|April 12, 2019, Fri.||On-line course: Understanding Rasch Measurement Theory - Master's Level (G. Masters), https://www.acer.org/au/professional-learning/postgraduate/rasch|
|May 24 - June 21, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|May 22 - 30, 2019, Wed.-Thu.||Measuring and scale construction (with the Rasch Model), University of Manchester, England, https://www.cmist.manchester.ac.uk/study/short/intermediate/measurement-with-the-rasch-model/|
|June 4 - 7, 2019, Tue.-Fri.||In-Person Italian Rasch Analysis Workshop based on RUMM (Fabio La Porta and Serena Caselli; entirely in Italian). Prof David Andrich from Western Australia University will be hosted by the workshop. For enquiries and registration email to email@example.com|
|June 17-19, 2019, Mon.-Wed.||In-person workshop, Melbourne, Australia: Applying the Rasch Model in the Human Sciences: Introduction to Rasch measurement (Trevor Bond, Winsteps), Announcement|
|June 20-21, 2019, Thurs.-Fri.||In-person workshop, Melbourne, Australia: Applying the Rasch Model in the Human Sciences: Advanced Rasch measurement with Facets (Trevor Bond, Facets), Announcement|
|June 28 - July 26, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|July 2-5, 2019, Tue.-Fri.||2019 International Measurement Confederation (IMEKO) Joint Symposium, St. Petersburg, Russia,https://imeko19-spb.org|
|July 11-12 & 15-19, 2019, Thu.-Fri.||A Course in Rasch Measurement Theory (D.Andrich), University of Western Australia, Perth, Australia, flyer - http://www.education.uwa.edu.au/ppl/courses|
|Aug 5 - 10, 2019, Mon.-Sat.||6th International Summer School "Applied Psychometrics in Psychology and Education", Institute of Education at HSE University Moscow, Russia.https://ioe.hse.ru/en/announcements/248134963.html|
|Aug. 9 - Sept. 6, 2019, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Aug. 14 - 16, 2019. Wed.-Fri.||An Introduction to Rasch Measurement: Theory and Applications (workshop led by Richard M. Smith) https://www.hkr.se/pmhealth2019rs|
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|Oct. 11 - Nov. 8, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Nov. 3 - Nov. 4, 2019, Sun.-Mon.||International Outcome Measurement Conference, Chicago, IL,http://jampress.org/iomc2019.htm|
|Jan. 24 - Feb. 21, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
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