MHZERO= adjustment to zero cells in Mantel cross-tabulation = 0

The Mantel-Haenszel and Mantel DIF statistics are based on 2x2 cross-tabulations of response frequencies for the Reference and Focal groups.

 

 

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.