Estimating treatment effects for each interacting variable level and testing for equal treatment effects across these levels in one command

[Maxime Bercholz]

Dear Statalisters,

Like the title says, I am trying to (1) estimate treatment effects at each level of a variable I interact with the treatment variable, and (2) test whether these treatment effects are equal across these levels, in one command. This is in the context of a binary outcome, so by treatment effect I mean the effect of the treatment on the probability of success. For example, if I'm interacting a treatment variable (three levels) with education (three levels), I'd like to estimate the treatment effects conditional on each education level and test for equal treatment effects across education levels.

I can do it in two commands (see below for a bare-bone example), but I'm wondering if there is a way to do it in one through margins, contrast.

logit intent_b group##educ
margins educ, dydx(group) post
contrast educ, atequations

Output:

. logit intent_b group##educ

Iteration 0:  Log likelihood = -5386.1972  
Iteration 1:  Log likelihood = -5326.3177  
Iteration 2:  Log likelihood = -5326.2313  
Iteration 3:  Log likelihood = -5326.2313  

Logistic regression                                     Number of obs =  8,103
                                                        LR chi2(8)    = 119.93
                                                        Prob > chi2   = 0.0000
Log likelihood = -5326.2313                             Pseudo R2     = 0.0111

--------------------------------------------------------------------------------------------------------------------
                                          intent_b | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
---------------------------------------------------+----------------------------------------------------------------
                                             group |
                                      Treatment 1  |  -.0227693   .1043158    -0.22   0.827    -.2272246     .181686
                                      Treatment 2  |   .0744928   .1027005     0.73   0.468    -.1267966    .2757821
                                                   |
                                              educ |
            Short-cycle tertiary or some tertiary  |  -.3777486    .102155    -3.70   0.000    -.5779687   -.1775285
                                         Tertiary  |   .2209682   .0974774     2.27   0.023     .0299161    .4120204
                                                   |
                                        group#educ |
Treatment 1#Short-cycle tertiary or some tertiary  |   .0695456   .1437746     0.48   0.629    -.2122475    .3513386
                             Treatment 1#Tertiary  |   .0646161    .139141     0.46   0.642    -.2080953    .3373274
Treatment 2#Short-cycle tertiary or some tertiary  |  -.0529544   .1437266    -0.37   0.713    -.3346533    .2287445
                             Treatment 2#Tertiary  |  -.0677267   .1376612    -0.49   0.623    -.3375376    .2020842
                                                   |
                                             _cons |  -.4554755   .0723716    -6.29   0.000    -.5973213   -.3136298
--------------------------------------------------------------------------------------------------------------------

. margins educ, dydx(group) post

Conditional marginal effects                             Number of obs = 8,103
Model VCE: OIM

Expression: Pr(intent_b), predict()
dy/dx wrt:  2.group 3.group

--------------------------------------------------------------------------------------------------------
                                       |            Delta-method
                                       |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
---------------------------------------+----------------------------------------------------------------
1.group                                |  (base outcome)
---------------------------------------+----------------------------------------------------------------
2.group                                |
                                  educ |
             Upper secondary or below  |   -.005393    .024705    -0.22   0.827    -.0538139    .0430279
Short-cycle tertiary or some tertiary  |   .0099681   .0210726     0.47   0.636    -.0313334    .0512696
                             Tertiary  |   .0103429   .0227564     0.45   0.649    -.0342588    .0549446
---------------------------------------+----------------------------------------------------------------
3.group                                |
                                  educ |
             Upper secondary or below  |   .0178302   .0245789     0.73   0.468    -.0303436    .0660039
Short-cycle tertiary or some tertiary  |   .0045676   .0213205     0.21   0.830    -.0372199    .0463551
                             Tertiary  |   .0016691   .0226137     0.07   0.941    -.0426529    .0459912
--------------------------------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. contrast educ, atequations

Contrasts of conditional marginal effects                Number of obs = 8,103
Model VCE: OIM

Expression: Pr(intent_b), predict()
dy/dx wrt:  2.group 3.group

------------------------------------------------
             |         df        chi2     P>chi2
-------------+----------------------------------
1b.group     |
        educ |  (omitted)
-------------+----------------------------------
2.group      |
        educ |          2        0.28     0.8675
-------------+----------------------------------
3.group      |
        educ |          2        0.26     0.8772
------------------------------------------------

.

Edit: if you're wondering the point of this example, the group variable doesn't correspond to any actual group assignment (participants were randomized into two groups but I wanted to make this work for a more general case for other reasons).

[Jean-Michel Galarneau]

Something like what is below should display the predicted probability (after logistic if I recall the manual correctly) of each treatment at each level of education. You should use factor notation in your logistic regression so that it makes life easier for margins.

margins i.treatment,at(education=(1 2 3))

below will give you the effects of each treatment, relative to the reference category, by level of education.

margins r.treatment,at(education=( 1 2 3))

And for the adjacent comparisons.

margins r.treatment,at(education=( 1 2 3))

[Jean-Michel Galarneau]

adjacent should be

margins ar.treatment,at(education=( 1 2 3))