[R] R equivalent of SAS Cochran-Mantel-Haenszel tests?

Michael Friendly friendly at yorku.ca
Mon Feb 9 17:37:38 CET 2009

Dear Vito,

Yes, these tests are *similar* in spirit to loglinear models using 
either row/col/both scores for the association.
But I'm still looking for something equivalent to give the same results 
as SAS with CMH for
non-parametric tests.  One advantage of the CMH tests is that for 
stratified tables, a largish sample
size is not required in the individual strata, only the total n.

The computations are described in:

vito muggeo wrote:
> Dear Michael,
> It sounds as a linear-by-linear loglinear model (and its variants) 
> which uses scores for one or more variables in the table.. (see 
> Agresti, 1990, Categorical Data Analysis. I do remember the pages and 
> I have not the book here..)
> If this is the case, you can use standard call to glm(.., 
> family=poisson) with score variables in the linear predictor. For 
> instance for a two-way table with ordered variables the 
> linear-by-linear model is,
> glm(freq~factor(x)+factor(y)+I(score.x*score.y), family=poisson)
> The CMH test, probably, is the score test of the parameter of 
> I(score.x*score.y)..
> best,
> vito
> Michael Friendly ha scritto:
>> In SAS, for a two-way (or 3-way, stratified) table, the CMH option in 
>> SAS PROC FREQ gives
>> 3 tests that take ordinality of the factors into account, for both 
>> variables, just the column variable
>> or neither.   Is there an equivalent in R?
>> The mantelhaen.test in stats gives something quite different (a test 
>> of conditional independence for
>> *nominal* factors in a 3-way table).
>> e.g. I'd like to reproduce:
>> *-- CMH tests;
>> proc freq data=sexfun order=data;
>>  weight count;
>>  tables husband * wife / cmh chisq nocol norow;
>>  run;
>>                              The FREQ Procedure
>>                     Summary Statistics for Husband by Wife
>>          Cochran-Mantel-Haenszel Statistics (Based on Table Scores)
>>        Statistic    Alternative Hypothesis    DF       Value      Prob
>>            1        Nonzero Correlation        1     10.0142    0.0016
>>            2        Row Mean Scores Differ     3     12.5681    0.0057
>>            3        General Association        9     16.7689    0.0525

Michael Friendly     Email: friendly AT yorku DOT ca 
Professor, Psychology Dept.
York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele Street    http://www.math.yorku.ca/SCS/friendly.html
Toronto, ONT  M3J 1P3 CANADA

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