Obtaining equivalent numerical results from different software packages can be challenging. Itemtrait interactions are an example. The RUMM2020 Item Fit Table shows the itemfit output for item I0104 from a RUMM2020 analysis. The Location is the Rasch item difficulty estimate with SE being its standarderror precision. The FitResid is the standardized sum of squared residuals with DF being its estimated degrees of freedom. FitResid is equivalent to the standardized OUTFIT statistic of Winsteps.
ItemTrait Interaction 
The ChiSq is the itemtrait interaction. In this example the latent trait is stratified into four class intervals each containing a traitgroup of approximately one quarter of the total person sample. Since there are 4 intervals, there are three degrees of freedom, DF, for the chisquare as indicated. The chisquare is computed from a comparison of the observed overall performance of each traitgroup on the item with its expected performance. This quantifies the size of the departure of the empirical item characteristic curve from its model values, so identifying the magnitude of the itembytrait (itembyability level) interaction for this item. Prob reports the statistical probability of observing the chisquare value (or worse) when the data fit the Rasch model. In this example, the chisquare has 3 degrees of freedom and so has an expected value of 3.0. Its observed value is 21.707, with a probability of that value of larger being observed by chance of only 0.000076. So we would reject the null hypothesis that the overall performance of the traitgroups fits the Rasch model. We are observing an itemtrait interaction for item I0104.
This itemtrait chisquare is featured in RUMM2020 documentation as an indicator of item behavior, more so than the FitResid, but there is no obviously equivalent statistic currently reported by Winsteps. This can be awkward when research teams are employing both software packages. Here is how to generate the equivalent statistic in Winsteps:
This procedure is now implemented as Winsteps Table 30.4 with $DIF=MA3.
1. Decide on the number of traitgroups. 4 here.
2. Order the persons by measure (location). Writing the personmeasure PFILE to Excel facilitates these steps.
3. Omit extreme scores. These cannot show an interaction.
4. Stratify the personability range into traitgroups of as equal numerical size as possible, keeping all persons with the same measure in the same group.
4. Number the traitgroups and put the traitgroup number into each person label.
5. Perform a DIF analysis of item by traitgroupnumber.
6. Obtain the tstatistic for each itemtrait DIF effect.
7. For each item, square and sum the tstatistics for the itemtrait groups. This is the RUMM2020 chisquare.
8. The chisquare d.f. is the count of traitgroups less one.
In our example, the Winsteps DIF Table shows each traitgroup as a Person Class. The Observations Count is the number of persons in the group. Average is their average rating. Baseline Expect is the expected value of the Observations Average. Measure is the item difficulty measure corresponding to the Baseline Expect rating on this item, Item 104. It is expected to be the same for every traitgroup. The DIF Score is the difference between the Observations Average and Baseline Expect ratings. The DIF Measure is the item difficulty that would produce the Observations Average. So that DIF Size is the difference between the Baseline Measure item difficulty and the item difficulty observed for this group, the DIF Measure. S.E. is the standard error of the DIF Size. The tstatistic is a hypothesis test that the DIF Size is due to chance alone, it is the DIF Size divided by its S.E.
The Winsteps tstatistic is approximately a unitnormal deviate. Squaring and summing the four of these for item I0104 amounts to 20.05, close to the RUMM2020 ChiSq of 21.707. Thus this procedure yields approximately the same number as the RUMM2020 ChiSq. Over 72% of the Winsteps chisquare is contributed by the 4th traitgroup, indicating that the itemtrait interaction is primarily due to the unexpectedly poor performance by the high ability group.
These statistics are sensitive to the number of itemtrait groups, so verify that an item is defective (from an itemtrait perspective) by replicating this process with different numbers of itemtrait groups.
RUMM2020 Item Fit Table  

Seq  Item  Type  Location  SE  FitResid  DF  ChiSq  DF  Prob 
104  I0104  Poly  0.246  0.137  2.852  228.56  21.707  3  0.000076 
Winsteps DIF Table  

Person Class  Observations  Baseline  DIF  Item  
Count  Average  Expect  Measure  Score  Measure  Size  S.E.  t  Number  Name  
1 2 3 4  57 55 59 60  0.53 0.62 0.68 0.47  0.40 0.55 0.62 0.70  0.25 0.25 0.25 0.25  0.12 0.07 0.05 0.23  0.27 0.04 0.02 1.24  0.52 0.29 0.24 0.99 
0.27 0.28 0.28 0.26  1.92 1.06 0.85 3.81  104 104 104 104  I0104 I0104 I0104 I0104 
John M. Linacre
RUMM2020 ItemTrait ChiSquare and Winsteps DIF Size. Linacre, J.M. … Rasch Measurement Transactions, 2007, 21:1 p. 1096
Rasch Publications  

Rasch Measurement Transactions (free, online)  Rasch Measurement research papers (free, online)  Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch  Applying the Rasch Model 2nd. Ed., Bond & Fox  Best Test Design, Wright & Stone 
Rating Scale Analysis, Wright & Masters  Introduction to Rasch Measurement, E. Smith & R. Smith  Introduction to ManyFacet Rasch Measurement, Thomas Eckes  Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.  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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