Multilevel models
Students nested in schools: mixed-effects logit
mecompare works after multilevel models such as melogit. The marginal effects average over the random effects (the default prediction), so they are changes in predicted probabilities, as after an ordinary logit.
The example uses wave 1 of Add Health: about 5,800 students in 132 schools. The outcome is being a current smoker. The predictors are sex, age, race, and whether the student’s mother has a college degree, plus a school-level variable: the share of students in the school whose mother has a college degree.
use "https://tdmize.github.io/data/data/ah_si_2026", clear(ah-si.dta | Add Health Waves 1-6: Cleaned for MCAP SI)keep if wave == 1(22,963 observations deleted)rename cluster school
drop if missing(smoker, male, age, race, momeduc)(679 observations deleted)generate momcollege = momeduc >= 4
bysort school: egen school_momcollege = mean(momcollege). quietly melogit smoker i.male c.age i.race i.momcollege c.school_momcollege || school:
estimates store multilevelWith no variable listed before the comma, mecompare computes marginal effects for every predictor. Age and the school’s share of college-educated mothers are changed by one standard deviation:
mecompare, models(multilevel) amount(sd)Predicting: Marginal predicted mean
Marginal effects (N_multilevel=5825)
| ME # Estimate SE P>|z|
---------------------------------+---------------------------------------
male |
Male - Female |
multilevel | 1 0.010 0.011 0.338
---------------------------------+---------------------------------------
age + SD (centered) |
multilevel | 2 0.061 0.006 0.000
---------------------------------+---------------------------------------
race |
Black - White |
multilevel | 3 -0.167 0.013 0.000
Latinx - White |
multilevel | 4 -0.085 0.020 0.000
Asian - White |
multilevel | 5 -0.129 0.028 0.000
Other - White |
multilevel | 6 0.000 0.047 1.000
---------------------------------+---------------------------------------
momcollege |
1 - 0 |
multilevel | 7 -0.060 0.012 0.000
---------------------------------+---------------------------------------
school momcollege + SD (centered |
multilevel | 8 -0.008 0.008 0.335Black students are 16.7 percentage points less likely to smoke than White students. A student whose mother has a college degree is 6.0 points less likely to smoke, but the share of college-educated mothers in the school adds little beyond that: a one standard deviation increase is associated with a 0.8 point reduction (p = .34).
Ordinary and multilevel logit
The coefficients of a multilevel logit are on a different scale than those of an ordinary logit, so they cannot be compared directly; the marginal effects can. Here the same model is fit as an ordinary logit, which ignores the schools, and compared with the multilevel logit. Fit both models without vce(robust): mecompare clusters the standard errors on school.
quietly logit smoker i.male c.age i.race i.momcollege c.school_momcollege
estimates store ordinary. mecompare, models(ordinary multilevel) amount(sd)NOTE: mecompare clusters the standard errors on the highest-level group of the multilevel or panel m
> odel(s), so they will differ from the models' own. Fit every model without vce(robust); mecompare
> supplies the clustering.
Predicting: Default prediction for each model
Marginal effects and cross-model differences (N_ordinary=5825) (N_multilevel=5825)
| ME # Estimate Robust SE P>|z|
---------------------------------+---------------------------------------
male |
Male - Female |
ordinary | 1 0.010 0.012 0.381
multilevel | 2 0.010 0.011 0.370
Difference | 3 -0.000 0.001 0.977
---------------------------------+---------------------------------------
age + SD (centered) |
ordinary | 4 0.067 0.007 0.000
multilevel | 5 0.061 0.007 0.000
Difference | 6 0.006 0.003 0.013
---------------------------------+---------------------------------------
race |
Black - White |
ordinary | 7 -0.176 0.014 0.000
multilevel | 8 -0.167 0.014 0.000
Difference | 9 -0.010 0.005 0.042
Latinx - White |
ordinary | 10 -0.112 0.022 0.000
multilevel | 11 -0.085 0.023 0.000
Difference | 12 -0.027 0.009 0.004
Asian - White |
ordinary | 13 -0.134 0.034 0.000
multilevel | 14 -0.129 0.034 0.000
Difference | 15 -0.005 0.007 0.509
Other - White |
ordinary | 16 -0.005 0.041 0.907
multilevel | 17 0.000 0.045 1.000
Difference | 18 -0.005 0.008 0.564
---------------------------------+---------------------------------------
momcollege |
1 - 0 |
ordinary | 19 -0.061 0.010 0.000
multilevel | 20 -0.060 0.010 0.000
Difference | 21 -0.001 0.001 0.329
---------------------------------+---------------------------------------
school momcollege + SD (centered |
ordinary | 22 -0.011 0.010 0.262
multilevel | 23 -0.008 0.010 0.405
Difference | 24 -0.003 0.002 0.153Most effects are nearly the same in the two models. The ordinary logit gives somewhat larger effects of age and race: for example, its Latinx–White difference is 11.2 percentage points, compared with 8.5 in the multilevel logit (the difference of 2.7 points has p = .004).