Construct Problems with Descriptive IRT

Items and constructs are in constant tension. Each item is intended to probe an underlying construct, but each item also has idiosyncrasies. Only when items are coerced into a sufficient level of cooperation does a stable construct emerge. The process of coercion includes painstaking item writing, item selection, investigation of misfit statistics and careful consideration of the integrity of the evolving construct as it becomes defined by an emerging item hierarchy.

In its celebration of item idiosyncrasies, IRT abandons the construct. At NCME 1996, Darrell Bock presented a Table of 2-PL (two-parameter logistic model) parameters for 100 spelling items. The 2-PL model parameterizes, as "item discrimination", differential performance on items by high and low performing examinees. Since differential item performance disrupts construct stability, variation in "item discrimination" is identified as misfit in a Rasch analysis.

2PL ogives: spelling items

Allowing each item its own life muddles the construct. ICCs for 5 words from Bock's 100 spelling items are shown in the Figure. Bock reports that these words show good fit to his 2PL model. But the item hierarchy for low performers at -2 contradicts that for high performers at +2. For middle performers at 0, tontine and incredulity are equally easy to spell. But for low performers at -2, tontine was easier to spell than incredulity, while for high performers, tontine was harder to spell than incredulity. Since a clear construct is required in order to know what measures mean, descriptive IRT is not measurement.

Construct problems with descriptive IRT. Wright BD, Bock RD. … Rasch Measurement Transactions, 1996, 10:1 p.481

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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