[R-sig-ME] Help with interpreting one fixed-effect coefficient

[Simon Harmel]

Could you please apply your logic step by step to the three coefficients?



On Sun, Sep 26, 2021 at 1:39 AM Juho Kristian Ruohonen
<juho.kristian.ruohonen using gmail.com> wrote:
>
> In my view, your logic is slightly oversimplified (i.e. incorrect). Regression models do not estimate coefficients by holding predictors constant exclusively at the reference category. They do something more general, namely estimate coefficients by holding predictors constant at any value at which variation is observed in the values of the other predictors.
>
> su 26. syysk. 2021 klo 9.03 Simon Harmel (sim.harmel using gmail.com) kirjoitti:
>>
>> Dear Juho and other List Members,
>>
>> My problem is the logic of interpretation. Assuming no interaction, a
>> categorical-predictors-only model, and aside from the intercept which
>> captures the mean for reference categories (in this case, boys in the
>> mixed schools), I have learned to interpret any main effect coef for a
>> categorical predictor by thinking of that coef. as something that can
>> differ from its reference category to affect "y" ***holding any other
>> categorical predictor in the model at its reference category***.
>>
>> By this logic, "schgendboy-only" main effect coef should mean diff.
>> bet. boys (held constant at the reference category) in boy-only vs.
>> mixed schools (which shows "schgendboy-only" can differ from its
>> reference category i.e, mixed schools).
>>
>> By this logic, "sexgirls" main effect coef should mean diff. bet.
>> girls vs. boys (which shows "sexgirls" can differ from its reference
>> category i.e, boys) in mixed schools (held constant at the reference
>> category).
>>
>> Therefore, by this logic, "schgendgirl-only" main effect coef should
>> mean diff. bet. boys (held constant at the reference category) in
>> girl-only vs. mixed schools (which shows "schgendgirl-only" can differ
>> from its reference category i.e, mixed schools).
>>
>> My question is that is my logic of interpretation incorrect? Or are
>> there exceptions to my logic of interpretation of which interpreting
>> "schgendgirl-only" coef is one?
>>
>> Thank you very much,
>> Simon
>>
>> On Sun, Sep 26, 2021 at 12:00 AM Juho Kristian Ruohonen
>> <juho.kristian.ruohonen using gmail.com> wrote:
>> >
>> > Fellow student commenting here...
>> >
>> > As you suggest, schgendgirl-only can only ever apply to female students. Strictly speaking, it's the estimated mean difference between a student of any sex in a girls-only school and a similar student in a mixed school. But since such comparisons are only observed between girls, the estimate is necessarily informed by girl data only. So your intended interpretation of the coefficient is correct.
>> >
>> >
>> > su 26. syysk. 2021 klo 0.27 Simon Harmel (sim.harmel using gmail.com) kirjoitti:
>> >>
>> >> Dear Colleagues,
>> >>
>> >> Apologies for crossposting (https://stats.stackexchange.com/q/545975/284623).
>> >>
>> >> I've two categorical moderators i.e., students' ***sex*** (`boys`,
>> >> `girls`) and the ***school-gender system*** (`boy-only`, `girl-only`,
>> >> `mixed`) in a model like: `y ~ sex + schoolgend`.
>> >>
>> >> My coefs are below. I can interpret three of the coefs but wonder how
>> >> to interpret the third one from the top (.175)?
>> >>
>> >> Assume "intrcpt" represents the boys' mean in mixed schools.
>> >>
>> >>                          Estimate
>> >> (Intercept)             -0.189
>> >> schgendboy-only   0.180
>> >> schgendgirl-only    0.175
>> >> sexgirls                  0.168
>> >>
>> >> My interpretations of the coefficients are as follows:
>> >>
>> >>             "(Intercept)": mean of y for boys in mixed schools = -.189
>> >>  "schgendboy-only": diff. bet. boys in boy-only vs. mixed schools = +.180
>> >>   "schgendgirl-only": diff. bet. ???????????????????????????? = +.175
>> >>                 "sexgirls": diff. bet. girls vs. boys in mixed schools = +.168
>> >>
>> >> If my interpretation logic for all other coefs is correct, then, this
>> >> third coef. must mean:
>> >>
>> >> diff. bet. boys in girl-only vs. mixed schools = +.175! (which makes no sense!)
>> >>
>> >> ps. I know I will end-up interpreting +1.75 as: diff. bet. girls in
>> >> girl-only vs. mixed schools BUT this doesn't follow the interpretation
>> >> logic for other coefs PLUS there are no labels in the output to show
>> >> what's what!
>> >>
>> >> Many thanks,
>> >> Simon
>> >>
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