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  • Manually created interaction terms (dummy*dummy) versus # command in logit

    Dear Members,

    I am having a little bit of trouble in interpreting interaction effects between dummies in the context of a logit model.

    I have logit model where dependent variable Y is probability of being in favour of animal cloning, then I have a categorical independent variable support ranking support for government on a 1-4 scale, and female which is a dummy for gender (female=1, male=0), plus controls. I am interested in looking at interaction effects between support and female with respect to Y.

    There's two main points to my question.

    A)
    Now, in the context of a non-linear model, I am aware that interpreting interaction effects has been the subject of a big debate essentially between two options:
    1) using -inteff- command, (Norton, Wang and Ai, 2004)
    2) using -margins- which is a more up-to-date version with respect to -mfx- and should take care of the issues that -inteff- was originally set up for
    ----I am struggling to understand what would be the best approach to go for, is -margins- yielding misleading estimates of both size and direction of the interaction's ME or is it just less accurate or what?

    B)
    In order to circumvent the issue above, I opted to create dummies for each category of support:
    support1=1 when an individual has level of support=1
    support2=1 when an individual has level of support=2
    support3=1 when an individual has level of support=3
    support4=1 when an individual has level of support=4
    Then I manually created the interaction effects with female:
    support1fem = support1*female
    support2fem = support2*female
    support3fem = support3*female
    support4fem = support4*female

    All of these four newly created variable should, in theory, be dummies themselves since they can only ever take value of 0 or zero (they are the products of two dummies)

    I then run the regression:

    logit support2 support3 support4 female support2fem support3fem support4fem
    (support1 is the default group)

    And computed marginal effects with -margins, dydx(*) atmeans- command. I am then interpreting, for example in the case of the support2fem interaction variable, their ME as being "the over and above effect of being female on the probability that Y=1, given a level 2 support category" (compared to a male with a level 1 support category).

    Am I interpreting this correctly by using -margins- on manually computed interaction terms between two dummies?

    Thank you so much for your help in advance!

  • #2
    Welcome to the Stata Forum / Statalist.

    I believe that best approach is using the factor notation. For example, for the interaction (plus main effects) between 2 categorical variables, we could use the - regress y i.catvar1##i.catvar2 - command.

    To end, - margins - will demand the use of factor notation in the regression as well.
    Best regards,

    Marcos

    Comment


    • #3
      Dear Marcos,

      thank you for the swift reply!

      I guess my problem is, if I do use the ##, when I then do -margins-, in the context of a logit rather than linear model, the interpretation of the ME on the interaction term would be problematic, at least according to Norton, Wang and Ai (2004). I don't really understand how to go about tackling this issue with the -inteff- command, especially considering that, at least to me, there does not seem to be a consensus on the topic.
      I thought that re-coding the categorical variable into dummies, and then interacting manually each category dummy with female could circumvent the issue by allowing me to have a correct ME on the manually computed variable (support2fem). Am I doing this correctly?
      Thank you!

      Comment


      • #4
        The following may help you to understand why you need to use factor variable notation if you want to use margins:

        https://www3.nd.edu/~rwilliam/stats3/Margins01.pdf

        -------------------------------------------
        Richard Williams, Notre Dame Dept of Sociology
        Stata Version: 17.0 MP (2 processor)

        EMAIL: [email protected]
        WWW: https://www3.nd.edu/~rwilliam

        Comment


        • #5
          I believe this text will be helpful to you: https://www3.nd.edu/~rwilliam/stats/Margins01.pdf
          Best regards,

          Marcos

          Comment


          • #6
            The results produced by margins when you do not use factor variable notation are spurious/wrong and should not be interpreted. Arguably, there is not even such thing as the marginal effect of an interaction term. You will find this discussion by Vince Wiggins interesting.

            Best
            Daniel

            Comment


            • #7
              You may also find this discussion by Martin Buis in reference to the paper you cited in post #1 interesting, if you have not already seen it.

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