Comparing Total MEs across models

Example 5.2.e of Mize and Han (2025): mediation/attenuation with a multi-category outcome

With a nominal or ordinal outcome, each predictor has one marginal effect per outcome category. The Total ME of Mize and Han (2025) summarizes them in one number: the sum of the absolute effects, divided by two. The totalme option of mecompare adds it above the per-category effects; with two models, the Difference row tests whether the Total ME changed.

Here the question is whether the total effect of a college degree on self-rated health shrinks once family income is in the model. The outcome has five ordered categories and is fit with a multinomial logit on the 2000–2021 GSS. Store the model without income and the model with it, and name both in models().

use "https://tdmize.github.io/data/data/cda_gss", clear
(cda_gss.dta |  GSS 1972-2021 CDA - Categorical Data Analysis | date created 2023)
drop if missing(healthR, college, race4, age, woman, parent, married, faminc)
(22,943 observations deleted)
drop if year < 2000 | year > 2021
(26,611 observations deleted)

. 
quietly mlogit healthR i.college i.race4 c.age i.woman i.parent i.married, vce(robust)
estimates store basemod
. 
quietly mlogit healthR i.college i.race4 c.age i.woman i.parent i.married c.faminc, vce(robust)
estimates store medmod
mecompare i.college, models(basemod medmod) totalme
Predicting: Pr(healthR)

Marginal effects and cross-model differences (N_basemod=19292) (N_medmod=19292)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
college                          |                                       
    College Deg - No Col Deg     |                                       
                    Total ME     |                                       
                         basemod |     1      0.159      0.006      0.000
                          medmod |     2      0.118      0.007      0.000
                      Difference |     3      0.041      0.003      0.000
                  Poor - basemod |     4     -0.047      0.003      0.000
                   Poor - medmod |     5     -0.033      0.003      0.000
               Poor - Difference |     6     -0.015      0.002      0.000
                  Fair - basemod |     7     -0.112      0.006      0.000
                   Fair - medmod |     8     -0.085      0.006      0.000
               Fair - Difference |     9     -0.027      0.002      0.000
                  Good - basemod |    10      0.024      0.008      0.003
                   Good - medmod |    11      0.021      0.009      0.015
               Good - Difference |    12      0.003      0.003      0.301
             Excellent - basemod |    13      0.135      0.007      0.000
              Excellent - medmod |    14      0.097      0.008      0.000
          Excellent - Difference |    15      0.038      0.003      0.000

The first block is the Total ME of a college degree in each model and the Difference: the part of the college effect that family income accounts for. The blocks beneath it are the effects of college on each health category, which show where the attenuation comes from. metest gives the attenuation as a proportion of the baseline Total ME:

metest (1 - 2) / 1
                                 |  estimate         se     pvalue 
---------------------------------+--------------------------------
college_TotME                    |                                
    (basemod - medmod) / basemod |     0.260      0.020      0.000

totalme college, models(basemod medmod) gives the same difference. The totalme option also works for continuous predictors (with amount()) and for nominal predictors (a Total ME inequality); the Options page has an example of each.

Reference

Mize, Trenton D. and Bing Han. 2025. “Inequality and Total Effect Summary Measures for Nominal and Ordinal Variables.” Sociological Science 12: 115–157.

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