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Publication type: Article in scientific journal
Type of review: Peer review (publication)
Title: Item fit statistics for Rasch analysis : can we trust them?
Authors: Müller, Marianne
et. al: No
DOI: 10.1186/s40488-020-00108-7
Published in: Journal of Statistical Distributions and Applications
Volume(Issue): 7
Issue: 5
Issue Date: 28-Aug-2020
Publisher / Ed. Institution: Springer
ISSN: 2195-5832
Language: English
Subjects: Rasch model; Chi-square test statistics; Outfit and infit statistics; Conditional probability
Subject (DDC): 510: Mathematics
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 valid p-values. Bootstrapping is also necessary for conditional outfit statistics. For conditional infit statistics the adjusted rule-of-thumb critical values look useful.
Fulltext version: Published version
License (according to publishing contract): CC BY 4.0: Attribution 4.0 International
Departement: School of Engineering
Organisational Unit: Institute of Data Analysis and Process Design (IDP)
Appears in collections:Publikationen School of Engineering

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