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 sample 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 and 10 if any of:

 

 

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.