Comparing ME inequalities across models
Example 4.3.b of Mize and Han (2025): tests of mediation/attenuation
How much of the racial-ethnic inequality in an outcome is accounted for by education and wealth? Fit the model with and without those variables, store both, and name them in models(): meinequality reports the ME inequality from each model and tests the difference. The example uses a count of functional limitations from the Health and Retirement Study.
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)
. nbreg iadl i.race4cat, vce(robust)Fitting Poisson model:
Iteration 0: Log pseudolikelihood = -13500.189
Iteration 1: Log pseudolikelihood = -13500.189
Fitting constant-only model:
Iteration 0: Log pseudolikelihood = -11635.217 (not concave)
Iteration 1: Log pseudolikelihood = -10469.899
Iteration 2: Log pseudolikelihood = -10464.788
Iteration 3: Log pseudolikelihood = -10464.788
Fitting full model:
Iteration 0: Log pseudolikelihood = -10457.949
Iteration 1: Log pseudolikelihood = -10457.922
Iteration 2: Log pseudolikelihood = -10457.922
Negative binomial regression Number of obs = 15,609
Wald chi2(3) = 16.82
Dispersion: mean Prob > chi2 = 0.0008
Log pseudolikelihood = -10457.922 Pseudo R2 = 0.0007
-------------------------------------------------------------------------------------
| Robust
iadl | Coefficient std. err. z P>|z| [95% conf. interval]
--------------------+----------------------------------------------------------------
race4cat |
Non-Hispanic Black | 0.162 0.054 2.990 0.003 0.056 0.268
Hispanic | 0.218 0.061 3.552 0.000 0.098 0.339
Other | 0.104 0.106 0.978 0.328 -0.104 0.312
|
_cons | -1.189 0.031 -38.169 0.000 -1.250 -1.128
--------------------+----------------------------------------------------------------
/lnalpha | 1.884 0.029 1.827 1.941
--------------------+----------------------------------------------------------------
alpha | 6.582 0.191 6.217 6.968
-------------------------------------------------------------------------------------est store basemod. nbreg iadl i.race4cat i.collegeB c.wealth_w c.income_w, vce(robust)Fitting Poisson model:
Iteration 0: Log pseudolikelihood = -12622.528
Iteration 1: Log pseudolikelihood = -12602.681
Iteration 2: Log pseudolikelihood = -12602.675
Iteration 3: Log pseudolikelihood = -12602.675
Fitting constant-only model:
Iteration 0: Log pseudolikelihood = -11635.217 (not concave)
Iteration 1: Log pseudolikelihood = -10469.899
Iteration 2: Log pseudolikelihood = -10464.788
Iteration 3: Log pseudolikelihood = -10464.788
Fitting full model:
Iteration 0: Log pseudolikelihood = -10239.46
Iteration 1: Log pseudolikelihood = -10157.912
Iteration 2: Log pseudolikelihood = -10136.224
Iteration 3: Log pseudolikelihood = -10136.199
Iteration 4: Log pseudolikelihood = -10136.199
Negative binomial regression Number of obs = 15,609
Wald chi2(6) = 225.65
Dispersion: mean Prob > chi2 = 0.0000
Log pseudolikelihood = -10136.199 Pseudo R2 = 0.0314
---------------------------------------------------------------------------------------
| Robust
iadl | Coefficient std. err. z P>|z| [95% conf. interval]
----------------------+----------------------------------------------------------------
race4cat |
Non-Hispanic Black | -0.150 0.056 -2.697 0.007 -0.260 -0.041
Hispanic | -0.187 0.063 -2.988 0.003 -0.310 -0.064
Other | -0.028 0.100 -0.282 0.778 -0.225 0.168
|
collegeB |
bachelor's or higher | -0.362 0.071 -5.087 0.000 -0.501 -0.222
wealth_w | -0.000 0.000 -0.830 0.406 -0.000 0.000
income_w | -0.010 0.001 -11.485 0.000 -0.012 -0.009
_cons | -0.437 0.051 -8.498 0.000 -0.538 -0.337
----------------------+----------------------------------------------------------------
/lnalpha | 1.643 0.035 1.575 1.712
----------------------+----------------------------------------------------------------
alpha | 5.173 0.182 4.829 5.542
---------------------------------------------------------------------------------------est store medmod. meinequality race4cat, models(basemod medmod)ME Inequality Estimates (N_basemod = 15609 , N_medmod = 15609)
| Estimate Std. err. z P>|z|
-------------------------+-----------------------------------------------
race4cat ME Ineq. |
Model 1 (basemod) | 0.046 0.012 3.919 0.000
Model 2 (medmod) | 0.038 0.011 3.353 0.001
Cross-Model Diff. | 0.009 0.022 0.389 0.698 The Difference row is the reduction in racial-ethnic inequality once education, wealth, and income are in the model, with its standard error and p-value: the part of the inequality those variables account for.
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