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

Rasch Publications
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
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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