Simulation-based cutoffs for conditional item fit in Rasch models: iterations, multiplicity correction, and decision stability

<p>Simulation-based cutoff values for conditional item fit can be estimated by parametric bootstrappingand reported as an interval of a chosen width. Johansson (2025) recommended thisover rule-of-thumb critical values and gave iteration guidance based on detection rates andconditioned on sample size, without an account of the error rate that the interval width controls.This paper re-examines iterations and width against the familywise error rate (FWER),and compares FWER and false discovery rate control. Seven simulation studies vary item countand the targeting of misfitting items, with both dichotomous and polytomous conditions.The interval width is shown to be the error rate parameter of the procedure, setting theFWER jointly with the number of items. Bootstrap p-values with a Westfall-Young FWERcorrection target that error rate directly, detect more misfit than a width-matched interval,and are calibrated from 400 iterations, with fewer false positives than Benjamini-Hochberg.Outfit was consistently less powerful than infit, confirming earlier dichotomous findings andextending them to polytomous items.Updated recommendations include flagging items on the Westfall-Young FWER correctedp-value, using at least 400 iterations and 1000 to 2000 for a final analysis, and reporting theinterval as a descriptive band at width .95. The described methods are available in the Rpackage easyRasch2 and the jamovi module easyRasch2jmv.</p>