Comparing ME inequalities across models
Examples 4.3.b and 4.3.a of Mize and Han (2025): nested models, and separate samples
The ME inequality of Mize and Han (2025) summarizes the effect of a nominal predictor in one number: the average absolute difference in the outcome across its categories. The meinequality option of mecompare adds it to the table; with two models, the Difference row tests whether the inequality changed. This page shows nested models and models fit to separate samples. The same examples, run with the meinequality command, are on the meinequality pages.
Nested models: how much of a racial-ethnic inequality is accounted for by SES?
How much of the racial-ethnic inequality in functional limitations is accounted for by education, wealth, and income? The outcome is a count of limitations in instrumental activities of daily living from the Health and Retirement Study. Fit the model with and without those variables, store both, and name them in models().
use "https://tdmize.github.io/data/data/cda_hrs", clear(cda_hrs.dta | Health & Retirement Study 2020)drop if missing(iadl, race4cat, collegeB, wealth_w, income_w)(114 observations deleted)
. quietly nbreg iadl i.race4cat, vce(robust)
estimates store basemod. quietly nbreg iadl i.race4cat i.collegeB c.wealth_w c.income_w, vce(robust)
estimates store medmodmecompare i.race4cat, models(basemod medmod) meinequalityPredicting: Predicted mean of iadl
Marginal effects and cross-model differences (N_basemod=15609) (N_medmod=15609)
| ME # Estimate Robust SE P>|z|
---------------------------------+---------------------------------------
race4cat |
ME Inequality |
basemod | 1 0.046 0.012 0.000
medmod | 2 0.038 0.011 0.001
Difference | 3 0.009 0.022 0.698
Non-Hispani - Non-Hispan |
basemod | 4 0.053 0.018 0.004
medmod | 5 -0.049 0.018 0.006
Difference | 6 0.102 0.008 0.000
Hispanic - Non-Hispanic |
basemod | 7 0.074 0.022 0.001
medmod | 8 -0.060 0.019 0.002
Difference | 9 0.134 0.010 0.000
Other - Non-Hispanic Whi |
basemod | 10 0.033 0.036 0.349
medmod | 11 -0.010 0.034 0.776
Difference | 12 0.043 0.011 0.000The first block is the ME inequality in each model and the Difference: the reduction in racial-ethnic inequality once education, wealth, and income are in the model. The blocks beneath it are the contrasts with the base category. metest gives the reduction as a proportion of the baseline inequality:
metest (1 - 2) / 1 | estimate se pvalue
---------------------------------+--------------------------------
race4cat_MEineq |
(basemod - medmod) / basemod | 0.187 0.436 0.667 meinequality race4cat, models(basemod medmod) gives the same difference.
Separate samples: has the effect of religion changed over time?
When the two models are fit to different samples – different groups, or different time periods – add the groups option. Here the question is whether religious-tradition differences in willingness to let a gay man speak in public were larger before 1980 than after 2010. Two logits are fit, one per period, and groupnames() labels the rows.
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(spkhomo, reltrad, age, woman)(30,806 observations deleted)
. quietly logit spkhomo i.reltrad c.age i.woman if year < 1980, vce(robust)
estimates store premod. quietly logit spkhomo i.reltrad c.age i.woman if year >= 2010, vce(robust)
estimates store postmodmecompare i.reltrad, models(premod postmod) groups groupnames(Pre1980 Post2010) ///
meinequality(unweighted)Predicting: Pr(spkhomo)
Marginal effects and cross-model differences (N_Pre1980=5593) (N_Post2010=8226)
| ME # Estimate Robust SE P>|z|
---------------------------------+---------------------------------------
reltrad |
Unwgt ME Ineq. |
Pre1980 | 1 0.156 0.011 0.000
Post2010 | 2 0.072 0.007 0.000
Difference | 3 0.083 0.013 0.000
Mainline Pr - Evangelica |
Pre1980 | 4 0.212 0.017 0.000
Post2010 | 5 0.118 0.011 0.000
Difference | 6 0.094 0.021 0.000
Black Prote - Evangelica |
Pre1980 | 7 0.075 0.026 0.004
Post2010 | 8 -0.003 0.018 0.883
Difference | 9 0.078 0.032 0.014
Catholic - Evangelical |
Pre1980 | 10 0.205 0.018 0.000
Post2010 | 11 0.094 0.011 0.000
Difference | 12 0.111 0.021 0.000
Jewish - Evangelical |
Pre1980 | 13 0.366 0.030 0.000
Post2010 | 14 0.150 0.017 0.000
Difference | 15 0.216 0.034 0.000
Other Faith - Evangelica |
Pre1980 | 16 0.176 0.038 0.000
Post2010 | 17 0.070 0.017 0.000
Difference | 18 0.107 0.042 0.011
Nonaffiliat - Evangelica |
Pre1980 | 19 0.325 0.025 0.000
Post2010 | 20 0.125 0.010 0.000
Difference | 21 0.200 0.027 0.000The Difference row tests whether the inequality changed. It is significantly smaller after 2010 than before 1980: religious traditions have converged on this question.
unweighted compares the marginal effects alone; the default weighted version would also reflect the change in the religious makeup of the GSS between the two periods. meinequality(all) reports both.
Reference
Mize, Trenton D. and Bing Han. 2025. “Inequality and Total Effect Summary Measures for Nominal and Ordinal Variables.” Sociological Science 12: 115–157.