A Comparison of the Person Response Function and the lz Person-Fit Statistic

Michael L. Nering · Rob R. Meijer

60 citations0/0 files storedApplied Psychological Measurement

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Psychometric Methodologies and Testing Psychological Testing and Assessment Educational Assessment and Pedagogy

Abstract

In the past several decades, there has been an increasing interest in the development of statistics used to identify examinees who respond to test items in a manner that is divergent from the underlying test model. One statistic that has received a great deal of attention is the lz index (Drasgow, Levine, & Williams, 1985). Trabin & Weiss (1983) developed a slightly different approach for identifying model-divergent response patterns, based on the discrepancy between observed and expected person response functions (PRFs). Here, the PRF method was compared theoretically and empirically to 1z. Although the results suggest that the performance of lz was, in most conditions studied, superior to the PRF method, the PRF method was useful in investigating why a response vector was model divergent. The PRF method can be used along with lz to identify different types of model divergent response patterns.

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References

1982Rating scale analysis 1984Item Response Theory: Principles and Applications 1985Item Response Theory 1985Appropriateness measurement with polychotomous item response models and standardized indices 1983Item response theory : application to psychological measurement 1983New horizons in testing : latent trait test theory and computerized adaptive testing 1979Measuring the Appropriateness of Multiple-Choice Test Scores 1984Caution Indices based on Item Response Theory

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2000Using Multilevel Logistic Regression to Evaluate Person-Fit in IRT Models 2001The Person Response Function as a Tool in Person-Fit Research 2011A Didactic Presentation of Snijders’s l z * Index of Person Fit With Emphasis on Response Model Selection and Ability Estimation 2000Detecting Person Misfit in Adaptive Testing Using Statistical Process Control Techniques 2019Detection and Treatment of Careless Responses to Improve Item Parameter Estimation 2004

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