The Mantel-Haenszel and Mantel DIF statistics are based on 2x2 cross-tabulations of response frequencies for the Reference and Focal groups.
|
Low Category
|
High Category
|
Focal Group
|
FL
|
FH
|
Reference Group
|
RL
|
RH
|
If all 4 cells of the cross-tab are non-zero, then the computation proceeds.
If FL+RL = 0 and/or FH+RH=0 then the computation is skipped.
Otherwise FL = maximum of FL + MHZERO and similarly for the other 4 cells, and the computation proceeds.
The default is MHZERO = 0, no adjustment.
SAS uses MHZERO = 0.5
Example: with Exam1.txt
MHZERO=0
----------------------------------------------------------------------------------------------
| KID KID DIF JOINT Rasch-Welch Mantel-Haenszel Size Active TAP |
| CLASS CLASS CONTRAST S.E. t d.f. Prob. Chi-squ Prob. CUMLOR Slices Number Name |
|--------------------------------------------------------------------------------------------|
| F M 1.23 2.11 .58 21 .5677 .0000 1.000 5 4 1-3-4 |
| F M 1.92 2.06 .93 20 .3626 5 5 2-1-4 |
| F M -1.22 1.28 -.95 31 .3484 .6901 .4061 5 6 3-4-1 |
| F M -2.20 1.46 -1.51 31 .1414 1.0057 .3159 5 7 1-4-3-2 |
| F M -1.86 1.09 -1.71 31 .0982 .6901 .4061 5 8 1-4-2-3 |
MHZERO=0.5
----------------------------------------------------------------------------------------------
| KID KID DIF JOINT Rasch-Welch Mantel-Haenszel Size Active TAP |
| CLASS CLASS CONTRAST S.E. t d.f. Prob. Chi-squ Prob. CUMLOR Slices Number Name |
|--------------------------------------------------------------------------------------------|
| F M 1.23 2.11 .58 21 .5677 .2222 .6374 1.39 10 4 1-3-4 |
| F M 1.92 2.06 .93 20 .3626 .6000 .4386 -.69 10 5 2-1-4 |
| F M -1.22 1.28 -.95 31 .3484 .0360 .8496 -1.30 10 6 3-4-1 |
| F M -2.20 1.46 -1.51 31 .1414 .4792 .4888 -2.23 10 7 1-4-3-2 |
| F M -1.86 1.09 -1.71 31 .0982 .0360 .8496 -1.30 10 8 1-4-2-3 |
Notice that CUMLOR, the cumulative log-odds ratio, the size of the DIF according to Mantel-Haenszel/Mantel, cannot be computed for these data with MHZERO=0, and generally approximates the Rasch DIF CONTRAST when MHZERO=0.5
If Rasch and Mantel-Haenszel/Mantel disagree, then there is probably not enough data to draw strong conclusions.
