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  • Question About Using Standardized Binary Logistic Regression Coefficients to Compute Marginal Effects in Stata

    Hello, everybody,
    I have a question about standardized binary logistic regression coefficients-- I know that I can get odds ratio with the Stata commands below

    use https://stats.idre.ucla.edu/stat/stata/dae/binary.dta, clear
    logit admit gre gpa i.rank, or
    Also, I know if I use the command below
    margins, dydx(*)

    I can compute marginal effect. However, my current project asks me to compute marginal effects using standardized regression coefficients.
    I don't know if this request is correct and how it can be realized in Stata. Thank you for your help!
    Last edited by smith Jason; 06 Dec 2022, 14:59.

  • #2
    You might find some helpful material via the links below. I'll mention Richard Williams by name in case he has anything to add to his notes (2nd link above).
    --
    Bruce Weaver
    Email: [email protected]
    Web: http://sites.google.com/a/lakeheadu.ca/bweaver/
    Version: Stata/MP 18.0 (Windows)

    Comment


    • #3
      I'm puzzled by the desire to compute marginal effects using standardized coefficients. Why would you want to do that? A big advantage of marginal effects is expressing things in meaningful metrics, and it seems like standardizing coefficients would work against that.

      Do you just want X-Standardization? Then I suspect standardizing the Xs yourself and then running logistic regression is the easiest.

      If you want XY standardization, then I suspect you'd have to do algebraic manipulations on the margins output like I show in the L04 handout Bruce listed.

      But again, are you really really really sure this is what you want to do?

      As a sidelight, Y-standardization gets discussed in my recently published Social Science Research Piece, "Comparing logit & probit coefficients between nested models."

      https://www.sciencedirect.com/scienc...49089X22001132

      If you want it and can't download for free, either contact me or see the earlier working paper version at

      https://papers.ssrn.com/sol3/papers....act_id=4105726
      Abstract

      Social scientists are often interested in seeing how the estimated effects of variables change once other variables are controlled for. For example, a simple analysis may reveal that income differs by race – but why does it differ? To answer such a question, a researcher might estimate a model where race is the only independent variable, and then add variables such as education to subsequent models. If the original estimated effect of race declines, this may be because race affects education, which in turn affects income. What is not universally realized is that the interpretation of such nested models can be problematic when logit or probit techniques are employed with binary dependent variables. Naïve comparisons of coefficients between models can indicate differences where none exist, hide differences that do exist, and even show differences in the opposite direction of what actually exists. We discuss why problems occur and illustrate their potential consequences. Proposed solutions, such as Linear Probability Models, Y-standardization, the Karlson/Holm/Breen method, and marginal effects, are explained and evaluated.
      -------------------------------------------
      Richard Williams, Notre Dame Dept of Sociology
      Stata Version: 17.0 MP (2 processor)

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

      Comment


      • #4
        Originally posted by Richard Williams View Post
        I'm puzzled by the desire to compute marginal effects using standardized coefficients. Why would you want to do that? A big advantage of marginal effects is expressing things in meaningful metrics, and it seems like standardizing coefficients would work against that.

        Do you just want X-Standardization? Then I suspect standardizing the Xs yourself and then running logistic regression is the easiest.

        If you want XY standardization, then I suspect you'd have to do algebraic manipulations on the margins output like I show in the L04 handout Bruce listed.

        But again, are you really really really sure this is what you want to do?

        As a sidelight, Y-standardization gets discussed in my recently published Social Science Research Piece, "Comparing logit & probit coefficients between nested models."

        https://www.sciencedirect.com/scienc...49089X22001132

        If you want it and can't download for free, either contact me or see the earlier working paper version at

        https://papers.ssrn.com/sol3/papers....act_id=4105726
        Abstract

        Social scientists are often interested in seeing how the estimated effects of variables change once other variables are controlled for. For example, a simple analysis may reveal that income differs by race – but why does it differ? To answer such a question, a researcher might estimate a model where race is the only independent variable, and then add variables such as education to subsequent models. If the original estimated effect of race declines, this may be because race affects education, which in turn affects income. What is not universally realized is that the interpretation of such nested models can be problematic when logit or probit techniques are employed with binary dependent variables. Naïve comparisons of coefficients between models can indicate differences where none exist, hide differences that do exist, and even show differences in the opposite direction of what actually exists. We discuss why problems occur and illustrate their potential consequences. Proposed solutions, such as Linear Probability Models, Y-standardization, the Karlson/Holm/Breen method, and marginal effects, are explained and evaluated.
        Thank you all for your response.
        I am new to this area and my intuition told me that using standardized logistic regression coefficients to compute marginal effects is unreasonable.
        However, the project leader insists that I have to compute marginal effects using standardized coefficients. (The guy doesn't understand statistics and just know very few knowledge)
        I don't know what to say and how to say under this circumstance.

        Comment


        • #5
          Standardized coefficients and marginal effects are two different approaches to making results easier to interpret. But, I’ve never seen both used together, can you ask the leader to give you examples of where this has been done? I’ve never tried it, and am not even sure how to do it, so I suppose it is possible I am overlooking something. But, to me it sounds very peculiar.
          -------------------------------------------
          Richard Williams, Notre Dame Dept of Sociology
          Stata Version: 17.0 MP (2 processor)

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

          Comment


          • #6
            Originally posted by Richard 1692305
            Standardized coefficients and marginal effects are two different approaches to making results easier to interpret. But, I’ve never seen both used together, can you ask the leader to give you examples of where this has been done? I’ve never tried it, and am not even sure how to do it, so I suppose it is possible I am overlooking something. But, to me it sounds very peculiar.
            Thank you, Professor Richard.
            The project leader finally told me that he doesn't know this and just think of whether it can be done with standardized logistic regression coefficients.

            Comment


            • #7
              Even in ordinary least squares (OLS) models, where standardized regression coefficients are often reported, there is reason for caution. The following is a note I wrote for myself when reviewing John Fox's book on regression and GzLMs. Perhaps you will find it helpful.


              In his book "Applied Regression Analysis and Generalized Linear Models" (2008, Sage), John Fox is very cautious about the use of standardized regression coefficients. He gives this interesting example. When two variables are measured on the same scale (e.g.,years of education, and years of employment), then relative impact of the two can be compared directly. But suppose those two variables differ substantially in the amount of spread. In that case, comparison of the standardized regression coefficients would likely yield a very different story than comparison of the raw regression coefficients. Fox then says:

              "If expressing coefficients relative to a measure of spread potentially distorts their comparison when two explanatory variables are commensurable [i.e., measured on the same scale], then why should the procedure magically allow us to compare coefficients [for variables] that are measured in different units?" (p. 95)

              Good question!

              A page later, Fox adds the following:

              "A common misuse of standardized coefficients is to employ them to make comparisons of the effects of the same explanatory variable in two or more samples drawn from different populations. If the explanatory variable in question has different spreads in these samples, then spurious differences between coefficients may result, even when _unstandardized_ coefficients are similar; on the other hand, differences in unstandardized coefficients can be masked by compensating differences in dispersion." (p. 96)

              And finally, this comment on whether or not Y has to be standardized:

              "The usual practice standardizes the response variable as well, but this is an inessential element of the computation of standardized coefficients, because the _relative_ size of the slope coefficients does not change when Y is rescaled." (p. 95)


              --
              Bruce Weaver
              Email: [email protected]
              Web: http://sites.google.com/a/lakeheadu.ca/bweaver/
              Version: Stata/MP 18.0 (Windows)

              Comment

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