This question has an UPDATE.
There is a nice answer HERE regarding how to interpret regression coefficients when predictors each consist of two categories in
R. But imagine we have students' sex (
girls) and the school-gender system (
mixed) in a model like:
y ~ sex + schoolgend.
Here, we expect 4 coefficients. I wonder how to interpret the third coefficient (+.175 see below)?
(Intercept) represents the
boys mean in
Estimate (Intercept) -0.189 schgendboy-only 0.180 schgendgirl-only 0.175 <-- This one! 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. (
schgendgirl-only) 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!
It seems that
schgendgirl-only can meaninglessly represent: diff. bet. boys in girl-only vs. mixed schools just like it can meaningfully represent: diff. bet. girls in girl-only vs. mixed schools
The reason is that the two coefficients are exactly equal. Here is a reproducible
R demonstration (results are shown to 4 decimal places):
library(R2MLwiN) # For the dataset library(lme4) # For Model fitting library(emmeans) # For pairwise contrasts data("tutorial") Form <- normexam ~ 1 + standlrt + schgend + sex + (standlrt | school) model <- lmer(Form, data = tutorial, REML = FALSE) emmeans(model, pairwise~schgend+sex)$contrast #contrast estimate SE df z.ratio p.value #mixedsch boy - boysch boy -0.17986 0.0991 Inf -1.814 0.4565 #mixedsch boy - girlsch boy -0.17482 0.0788 Inf -2.219 0.2287<--This coef. equals #mixedsch boy - mixedsch girl -0.16826 0.0338 Inf -4.975 <.0001 #mixedsch boy - boysch girl -0.34813 0.1096 Inf -3.178 0.0186 #mixedsch boy - girlsch girl -0.34308 0.0780 Inf -4.396 0.0002 #boysch boy - girlsch boy 0.00505 0.1110 Inf 0.045 1.0000 #boysch boy - mixedsch girl 0.01160 0.0997 Inf 0.116 1.0000 #boysch boy - boysch girl -0.16826 0.0338 Inf -4.975 <.0001 #boysch boy - girlsch girl -0.16322 0.1058 Inf -1.543 0.6361 #girlsch boy - mixedsch girl 0.00656 0.0928 Inf 0.071 1.0000 #girlsch boy - boysch girl -0.17331 0.1255 Inf -1.381 0.7388 #girlsch boy - girlsch girl -0.16826 0.0338 Inf -4.975 <.0001 #mixedsch girl - boysch girl -0.17986 0.0991 Inf -1.814 0.4565 #mixedsch girl - girlsch girl -0.17482 0.0788 Inf -2.219 0.2287<--This coef. #boysch girl - girlsch girl 0.00505 0.1110 Inf 0.045 1.0000