﻿ Quality-control misfit selection criteria

# Quality-control misfit selection criteria

Rasch measurement does not make any presumptions about the underlying distribution of the parameters. Maximum likelihood estimation expects "errors" in the observations to be more or less normally distributed around their expected values. Since all observations are integral values, this expectation can be met only asymptotically as the number of persons and items becomes infinite. The information-weighted fit statistic, "infit", and the outlier-sensitive fit statistic, "outfit", are described in BTD and RSA. Possible values, and hence interpretation, of these statistics is influenced by the observed distribution the person and item statistics. This is particularly true of their t standardized values which are designed to follow standard normal (0,1) distributions. The local significance of these statistics is best interpreted in terms of their means and standard deviations reported in Table 3.1. Start investigating the misfit causing the most extreme values of these statistics, and stop your investigation when the observed responses become coherent with your intentions.

The fit statistics reported will not exactly match those printed in BTD or RSA, or those produced by another program. This is because the reported values of these statistics are the result of a continuing process of development in statistical theory and practice. Neither "correct" fit statistics nor "correct" values exist, but see the Appendices for guidance.

Report measure in Tables 6 (FITP=) and Table 10 (FITI=) if any of:

 Statistic Less than Greater than t standardized INFIT -(FITP or FITI) FITP or FITI t standardized OUTFIT -(FITP or FITI) FITP or FITI mean-square INFIT 1 - (FITP or FITI)/10 1 + (FITP or FITI)/10 mean-square OUTFIT 1 - (FITP or FITI)/10 1 + (FITP or FITI)/10 point-biserial correlation negative

To include every person, specify FITP=0. For every item, FITI=0.

For Table 7, the diagnosis of misfitting persons, persons with a t standardized fit greater than FITP= are reported. Selection is based on the OUTFIT statistic, unless you set OUTFIT=N in which case the INFIT statistic is used.

For Table 11, the diagnosis of misfitting items, items with a t standardized fit greater than FITI= are reported. Selection is based on the OUTFIT statistic, unless you set OUTFIT=N in which case the INFIT statistic is used.

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Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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