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  • Interpeting interaction estimation reuslts from regressions

    Hi all,

    My name is GrĂ¡inne Gibson and I am currently doing my masters dissertation on the effect of Single-Sex schooling on adolescents non-cognitive and well-being outcomes in Ireland. I have attached a screenshot of my results and I just want to make sure I have the correct interpretation. If you take the coefficient for the interaction between gender and single_sex gender being 1=female 0=otherwise, my estimated coefficient is -1.1052387. I am wondering if I interpret this as 'attending a SS school in Ireland decreases a student competitiveness by 1.105 percentage points" ? Later I run the predictive margins and see the difference between boys in Single-Sex schools and boys in co-ed and receive a positive and significant coefficient (0.947482) which again I would like to interpret correctly. "Boys in SS schools are on average .0947 more competitive than their co-ed counterparts"? for females, it is negative and insignificant.

    I would appreciate any advice
    Attached Files

  • #2
    apologies for the title spelling errors ** Interpreting interaction estimation results from regression analysis.

    Comment


    • #3
      This does not look quite right. If Table 5 shows the margins derived from the full model in Table 4, then the interaction terms is too extreme. Effect of SS is 0.0947 in males and -0.0105 in female; if this is true the interaction term's beta coefficient should be the difference of these two numbers, -1.105 seems too big in absolute magnitude.

      Looking at the model, I wonder if it "female" and "single_sex" are also in the model. Right now they seem to have been omitted. You'd need both of them back to formally test an "interaction between sex and single_sex", otherwise you're just testing a dummy variable where 1 is female in single sex school and 0 is all other combinations. Try using either of these instead:

      Code:
      reg y i.female##i.single_sex
      * or this:
      reg y i.female i.single_sex i.female#i.single_sex
      Here is an example showing how the interaction term can be recovered from the margins, which I was not able to do with the data presented in two tables in #1:

      Code:
      sysuse nlsw88, clear
      
      reg wage i.collgrad##i.union, noheader
      
      margins collgrad#union
      
      display (10.47342-10.11737)-(7.823589-6.36869)
      Results:
      Code:
      . reg wage i.collgrad##i.union, noheader
      -------------------------------------------------------------------------------------
                     wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
      --------------------+----------------------------------------------------------------
                 collgrad |
            college grad  |   3.748679   .2453873    15.28   0.000     3.267418     4.22994
                          |
                    union |
                   union  |   1.454899   .2462993     5.91   0.000     .9718493    1.937949
                          |
           collgrad#union |
      college grad#union  |  -1.098846   .4553523    -2.41   0.016    -1.991897   -.2057956
                          |
                    _cons |    6.36869   .1158806    54.96   0.000     6.141421    6.595958
      -------------------------------------------------------------------------------------
      
      .
      . margins collgrad#union
      
      Adjusted predictions                            Number of obs     =      1,878
      Model VCE    : OLS
      
      Expression   : Linear prediction, predict()
      
      --------------------------------------------------------------------------------------------
                                 |            Delta-method
                                 |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
      ---------------------------+----------------------------------------------------------------
                  collgrad#union |
      not college grad#nonunion  |    6.36869   .1158806    54.96   0.000     6.141421    6.595958
         not college grad#union  |   7.823589   .2173362    36.00   0.000     7.397342    8.249835
          college grad#nonunion  |   10.11737   .2163021    46.77   0.000      9.69315    10.54159
             college grad#union  |   10.47342   .3160629    33.14   0.000     9.853549    11.09329
      --------------------------------------------------------------------------------------------
      
      .
      . display (10.47342-10.11737)-(7.823589-6.36869)
      -1.098849
      I don't have any advice on the interpretation for now given the inconsistency between the model.
      Last edited by Ken Chui; 29 Jul 2021, 07:06.

      Comment


      • #4
        Hi Ken,

        Thank you for your response. I do see what you mean about 'female' and 'single_Sex' being omitted however they were in the regression output from stata which I have attached. Have I reported the incorrect co-efficient in my table above for the interaction estimate. Stat gives -.2989675 for female and 1.single sex .0947482 ?
        Attached Files

        Comment


        • #5
          These are my derived predictive margins form my regression. From here I ran .. "lincom 1.female#1.single_sex - 1.female#0.single_sex" and "lincom 0.female#1.single_sex - 0.female#0.single_sex" which is to comapre males in \single sex vrs males in co-ed and the first command was for the female differances.
          Attached Files

          Comment


          • #6
            #4 and #5 look fine. In #4 the interaction's coefficient is only -0.1052387. But in your table 4 it says -1.1052387. I wonder if you created that table manually and added a "1" by mistake?

            If female and single_sex are in the regression, then they should be tabulated as well. The culprit seems to be the table 4 having errors, it may need to be revised more carefully.

            Comment


            • #7
              Thank you Ken!

              I see now I added the one so I will recheck all tables. Can I ask you then how I interpret the (-.102387) and also why I may need "female" and "single_sex" included in my tables also if I have the interaction co-efficient ? I am not sure if I am speaking in percentage point terms such as "attending a SS school decreases a students competitiveness by -.1052387 percentage points however we see from the predictive margins that on average males are more competitive than females?

              Comment


              • #8
                I see now I added the one so I will recheck all tables. Can I ask you then how I interpret the (-.102387)
                The -0.1052387 is the "difference in difference", basically the difference in the effect of going to single_sex school between males and females. If you compute the difference between the two differences typed in Table 5 of #1, you'll get:
                Code:
                display -0.0104904 - 0.0947482
                and that's your interaction's beta coefficient.

                and also why I may need "female" and "single_sex" included in my tables also if I have the interaction co-efficient ?
                I work in biomedical field so am not sure if the practice applies to yours, check with your advisors. Generally, we don't omit the beta coefficients of the variables that were used to compute the interaction term. Reasons include: i) having them would allow readers to reconstruct the four adjusted means for all the gender x single_sex combinations, and ii) not having them would trigger questions from readers and reviewers (e.g. like what I asked in #2) because they'd think that you did not put them in the model.

                I am not sure if I am speaking in percentage point terms such as "attending a SS school decreases a students competitiveness by -.1052387 percentage points however we see from the predictive margins that on average males are more competitive than females?
                If COMPETE is measured in percent ranging from 0 to 100, then "percent point" is a correct interpretation as the extra effect from the interaction is still additive. I'd perhaps describe the findings as: we found that among girls, whether going to a single sex school or co-ed was not associated with COMPETE (report the female mean difference here). However, boys attending single sex school, on average, performed better than those in co-ed (report the male mean difference here). And this beneficial effect for boys is significantly bigger than that of the girls (effect for girl - effect for boy = report the interaction, or difference in difference here).

                Notice that just because the interaction is negative does not mean girl going to single sex schools got a decrease in performance. It can also be that the boys got a much larger positive effect. That's the tricky thing about difference in difference, it can be even be negative while both groups got benefit. That's another reason why you need to report the coefficient for gender and single_sex as well.
                Last edited by Ken Chui; 30 Jul 2021, 08:09.

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