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

[Juho Kristian Ruohonen]

 (Intercept): with all predictors at zero, an average student is estimated
to have a response value of -0.18.
schgendboy-only: on average, students in boys-only schools are estimated to
have response values 0.180 units higher than otherwise comparable students
in a mixed-sex schools.
schgendgirl-only: on average, students in girls-only schools are estimated
to have response values  0.175 units higher than otherwise comparable
students in a mixed-sex schools.
sexgirl: on average, female students are estimated to have response values
0.168 units higher than otherwise comparable male students.

su 26. syysk. 2021 klo 9.57 Simon Harmel (sim.harmel using gmail.com) kirjoitti:

> 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
> >> >>
> >> >> _______________________________________________
> >> >> R-sig-mixed-models using r-project.org mailing list
> >> >> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

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