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Global, local, and graphical person-fit analysis using person-response functions
Wilco H M Emons1, Klaas Sijtsma, Rob R Meijer
1Department of Methodology and Statistics, Tilburg University, Tilburg, Netherlands. w.h.m.emons@uvt.nl
Psychological Methods
|April 7, 2005
Summary
This study introduces a new method for person-fit analysis using nonparametric item response theory. It helps identify and understand unusual response patterns beyond simple fit/misfit decisions.
Area of Science:
- Psychometrics
- Educational Measurement
- Statistical Modeling
Background:
- Person-fit statistics assess response vector likelihood against item response theory (IRT) models.
- Binary fit/misfit information is often insufficient for diagnosing response anomalies.
Purpose of the Study:
- To propose a comprehensive methodology for person-fit analysis within nonparametric IRT.
- To extend beyond binary decisions to diagnose causes of misfitting response vectors.
Main Methods:
- Utilizes H. Van der Flier's (1982) global person-fit statistic U3 for initial fit/misfit decisions.
- Employs kernel smoothing (J. O. Ramsay, 1991) to estimate person-response functions for misfitting cases.
- Introduces a new local person-fit statistic (W. H. M. Emons, 2003) to evaluate unexpected trends in estimated functions.
Main Results:
- The proposed methodology provides a more nuanced approach to person-fit analysis.
- Demonstrates practical application through an empirical data example.
- Effectively identifies and evaluates unusual response patterns in test data.
Conclusions:
- The comprehensive methodology enhances the diagnostic capabilities of person-fit analysis.
- Offers a valuable tool for researchers and practitioners in educational and psychological measurement.
- Facilitates deeper understanding of individual response behavior in testing contexts.