Richard Smith (1982, 2009) proposes group-level fit statistics. These statistics "more or less consistently across CLASSes". Lack of consistency may indicate "more or less likely" (conventional DIF or DPF) or some other interaction across CLASSes or inside of CLASSes.

 

For each item, the persons are segmented into CLASSes using DIF=

 

Table 30.4 - Between-group fit statistic for person CLASSes:

"This fit statistic is based on the difference between an item's observed score on a subset of persons and the score on that subset as predicted by the item's overall difficulty estimate."

 

Table 30.5 - Within-group outfit statistic for a person CLASS for an item:

The outfit mean-square statistic for the item computed only across persons in the person CLASS.

 

Table 30.5 - Within-group infit statistic for an item CLASS for a person:

The infit mean-square statistic for the item computed only across persons in the person CLASS.

 

For each person, the items are segmented into CLASSes using DPF=

 

Table 31.4 - Between-group fit statistic for item CLASSes:

"This fit statistic is based on the difference between a person's observed score on a subset of items and the score on that subset as predicted by the person's overall ability estimate."

 

Table 31.5 - Within-group outfit statistic for an item CLASS for a person:

The outfit mean-square statistic for the person computed only across items in the item CLASS.

 

Table 31.5 - Within-group infit statistic for an item CLASS for a person:

The infit mean-square statistic for the person computed only across items in the item CLASS.

 

Smith RM, Hedges LV. Comparison of Likelihood Ratio χ² and Pearsonian χ² Tests of Fit in the Rasch Model.

Education Research and Perspectives, 1982; 9(1):44-54

 

Smith RM, Plackner C. The family approach to assessing fit in Rasch measurement. Journal of Applied Measurement. 2009;10(4):424-37