Good Measures from Bad Data

In many assessments, there are examinees who misbehave, and items that are poorly constructed. Nevertheless, everyone must be measured, and every item must be included except those that are obviously, blatantly faulty.

Blatantly faulty items are those that we can show to a content expert (who knows nothing about statistics) and say: "Do you see this ... (typographical error, ambiguity, scoring problem, irrelevant content, ... ). This item is obviously wrong or off-topic!"

Items with conspicuous DIF are more awkward to handle, and depend on the policy of the testing agency. It is easiest to treat them as blatantly faulty and omit them, but they can be split into separate items for separate DIF groups.

But what about random guessing, doubtful items and other problematic data? A three-stage estimation process provides a solution:

i) Analyze all the data. Identify problems.

ii) Reanalyze all the data, but with items and persons with misfit problems deleted and obviously errant or off-target responses omitted. This is the "good" dataset. Save the estimates of the item difficulties and Rasch-Andrich thresholds (for polytomies).

iii) Analyze all the data. Delete only obviously, blatantly faulty items. Anchor (fix) the "good" items at their "good" difficulties, and the polytomies at their "good" thresholds. Output the final set of person measures and item difficulties.

The measure for each person is now estimated in the frame-of-reference of the "good" data with the minimum of distortion of that measure by irrelevant (to that person) "bad" data.

Timed Tests

If we have a timed test, and score all incorrect answers and all item-not-reached answers as "0", then the final items have few correct answers, "1", even if the very last item is the conceptually easiest item on the test.

To get around this problem we do the three-stage analysis. In the second stage, we use only data from examinees who have definitely reached an item (right or wrong). All unreached responses are coded "not administered" (e.g., M for missing) and excluded from the analysis. This analysis gives us the best estimates of the difficulties of the items. We save these "good" item difficulties.

In the third stage, we score all the data 0-1, but use the "good" item difficulties, so that the measures of students who responded to most of the items are not distorted by the performances of students who responded to fewer items.

John M. Linacre

Good Measures from Bad Data, J.M. Linacre ... Rasch Measurement Transactions, 2011, 24:4, 1313

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Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
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Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
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Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

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