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I need to run a logistic regression with a binary response variable and a categorical explanatory variable.

My explanatory variable has 3 levels:

  • Forest
  • Plantation1
  • Plantation2

I would like to find a way to test the significance of all 3 possible contrasts:

  • Plantation1 vs. Forest
  • Plantation2 vs. Forest
  • Plantation1 vs. Plantation2

I have coded my categorical variable as 2 dummy variables (Plantation1 and Plantation2), using Forest as the "reference" group, which allows me to test the first 2 contrasts. If I recode the dummy variables using Plantation1 as the "reference" group, I can run the regression again and test the 1st and 3rd contrasts, giving me all the information I need.

Is this approach statistically "wrong"? If so, why?

UPDATE: Thanks to fg nu's answer, I have found a function in R that does multiple comparisons for main effects: the glht function in the multcomp package.

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You don't say what platform you are using. Stata makes this very easy to do using the margins, pwcompare command.

For example,

webuse nhanes2
logistic highbp sex##agegrp##c.bmi
margins agegrp, pwcompare

gives you the output,

. margins agegrp, pwcompare

Pairwise comparisons of predictive margins
Model VCE    : OIM

Expression   : Pr(highbp), predict()

--------------------------------------------------------------
             |            Delta-method         Unadjusted
             |   Contrast   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
      agegrp |
     2 vs 1  |   .0182344   .0069751      .0045635    .0319054
     3 vs 1  |     .08395   .0097271      .0648852    .1030148
     4 vs 1  |   .1443977   .0111944       .122457    .1663383
     5 vs 1  |   .1517272   .0082323      .1355922    .1678622
     6 vs 1  |   .1443064   .0126661      .1194813    .1691314
     3 vs 2  |   .0657156    .010205      .0457141    .0857171
     4 vs 2  |   .1261632   .0116121      .1034039    .1489225
     5 vs 2  |   .1334928   .0087919       .116261    .1507245
     6 vs 2  |   .1260719   .0130367      .1005205    .1516234
     4 vs 3  |   .0604477   .0134464      .0340932    .0868021
     5 vs 3  |   .0677772   .0111023       .046017    .0895374
     6 vs 3  |   .0603564   .0146942      .0315562    .0891565
     5 vs 4  |   .0073296    .012408     -.0169898    .0316489
     6 vs 4  |  -.0000913   .0157041     -.0308707    .0306882
     6 vs 5  |  -.0074208   .0137504     -.0343712    .0195295
--------------------------------------------------------------

which gives you the pairwise comparisons of the average predicted probability of high BP within each of the age groups defined by the agegrp variable.

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  • $\begingroup$ Thanks for the response. I'm using R. If Stata has a nice command for all pairwise contrasts, does this mean it is perfectly acceptable from a statistical point of view? I'm trying to understand if I will be inflating alpha or causing some other problem if I do this. $\endgroup$ – KTwildginger Nov 10 '12 at 20:32
  • $\begingroup$ @KTwildginger I am assuming you are worried about multiple comparison issues. I am going to say I don't know. Although, I am pretty sure you can get at all the contrasts using an appropriate Wald test and hence using one application of the Delta method, so multiple comparison issues should not apply. $\endgroup$ – tchakravarty Nov 12 '12 at 13:46

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