Articlehybrid2020

Item fit statistics for Rasch analysis: can we trust them?

95 citations0/0 files storedJournal of Statistical Distributions and Applications

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Psychometric Methodologies and Testing Statistical Distribution Estimation and Applications Statistical Methods and Bayesian Inference

Abstract

Abstract Aim To compare fit statistics for the Rasch model based on estimates of unconditional or conditional response probabilities. Background Using person estimates to calculate fit statistics can lead to problems because the person estimates are biased. Conditional response probabilities given the total person score could be used instead. Methods Data sets are simulated which fit the Rasch model. Type I error rates are calculated and the distributions of the fit statistics are compared with the assumed normal or chi-square distribution. Parametric bootstrap is used to further study the distributions of the fit statistics. Results Type I error rates for unconditional chi-square statistics are larger than expected even for moderate sample sizes. The conditional chi-square statistics maintain the significance level. Unconditional outfit and infit statistics have asymmetric distributions with means slighly below 1. Conditional outfit and infit statistics have reduced Type I error rates. Conclusions Conditional residuals should be used. If only unconditional residuals are available parametric bootstrapping is recommended to calculate validp-values. Bootstrapping is also necessary for conditional outfit statistics. For conditional infit statistics the adjusted rule-of-thumb critical values look useful.

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References

1961Probabilistic Models for Some Intelligence and Attainment Tests 2003Applying the Rasch Model: Fundamental Measurement in the Human Sciences 2015Applying the Rasch Model 2000Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models 2007Extended Rasch Modeling: TheeRmPackage for the Application of IRT Models inR 1998Using item mean squares to evaluate fit to the Rasch model.2000A critique of Rasch residual fit statistics.1991The Distributional Properties of Rasch Item Fit Statistics

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