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

Simon Harmel @|m@h@rme| @end|ng |rom gm@||@com
Sun Sep 26 08:03:41 CEST 2021


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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