Total ME inequalities for nominal independent variables
Example 5.3 of Mize and Han (2025)
With a nominal outcome and nominal independent variables there are two layers of summary. On each outcome category, the effect of a nominal predictor is the ME inequality of meinequality – the average absolute difference in that category’s probability across the predictor’s groups. The Total ME inequality then sums those across the outcome categories. Here race-ethnicity and degree, both nominal, predict self-rated health.
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, race4, age, woman, parent, married, faminc, degree)(22,943 observations deleted)drop if year < 2000 | year > 2021(26,611 observations deleted)
. mlogit healthR i.race4 c.age i.woman i.parent i.married c.faminc i.degreeIteration 0: Log likelihood = -22624.777
Iteration 1: Log likelihood = -21538.636
Iteration 2: Log likelihood = -21388.465
Iteration 3: Log likelihood = -21382.092
Iteration 4: Log likelihood = -21382.055
Iteration 5: Log likelihood = -21382.055
Multinomial logistic regression Number of obs = 19,292
LR chi2(36) = 2485.44
Prob > chi2 = 0.0000
Log likelihood = -21382.055 Pseudo R2 = 0.0549
-------------------------------------------------------------------------------------------
healthR | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------------------+----------------------------------------------------------------
Poor |
race4 |
Black | -0.192 0.100 -1.915 0.056 -0.389 0.005
Other | 0.184 0.178 1.035 0.301 -0.164 0.532
Hispanic | -0.270 0.118 -2.289 0.022 -0.501 -0.039
|
age | 0.024 0.002 12.070 0.000 0.020 0.028
|
woman |
Women | 0.025 0.071 0.347 0.729 -0.115 0.164
|
parent |
Parent | 0.072 0.091 0.794 0.427 -0.106 0.250
|
married |
Married | -0.271 0.080 -3.370 0.001 -0.428 -0.113
faminc | -0.025 0.002 -10.036 0.000 -0.030 -0.020
|
degree |
high school | -0.896 0.086 -10.477 0.000 -1.064 -0.729
associate/junior college | -1.207 0.158 -7.632 0.000 -1.517 -0.897
bachelor's | -1.644 0.144 -11.391 0.000 -1.926 -1.361
graduate | -1.775 0.194 -9.130 0.000 -2.155 -1.394
|
_cons | -1.876 0.151 -12.392 0.000 -2.173 -1.580
--------------------------+----------------------------------------------------------------
Fair |
race4 |
Black | 0.162 0.057 2.855 0.004 0.051 0.274
Other | 0.192 0.101 1.914 0.056 -0.005 0.390
Hispanic | 0.230 0.062 3.713 0.000 0.109 0.352
|
age | 0.012 0.001 9.789 0.000 0.010 0.014
|
woman |
Women | -0.006 0.040 -0.154 0.878 -0.085 0.073
|
parent |
Parent | -0.048 0.050 -0.948 0.343 -0.146 0.051
|
married |
Married | -0.140 0.044 -3.152 0.002 -0.227 -0.053
faminc | -0.008 0.001 -9.442 0.000 -0.010 -0.006
|
degree |
high school | -0.521 0.058 -8.917 0.000 -0.636 -0.407
associate/junior college | -0.722 0.088 -8.170 0.000 -0.896 -0.549
bachelor's | -1.024 0.077 -13.221 0.000 -1.175 -0.872
graduate | -1.078 0.094 -11.454 0.000 -1.262 -0.893
|
_cons | -0.638 0.089 -7.176 0.000 -0.813 -0.464
--------------------------+----------------------------------------------------------------
Good | (base outcome)
--------------------------+----------------------------------------------------------------
Excellent |
race4 |
Black | -0.150 0.057 -2.656 0.008 -0.262 -0.039
Other | -0.352 0.090 -3.890 0.000 -0.529 -0.174
Hispanic | -0.109 0.061 -1.792 0.073 -0.228 0.010
|
age | -0.011 0.001 -9.245 0.000 -0.013 -0.009
|
woman |
Women | 0.067 0.036 1.862 0.063 -0.004 0.137
|
parent |
Parent | -0.140 0.044 -3.209 0.001 -0.226 -0.055
|
married |
Married | 0.072 0.040 1.797 0.072 -0.007 0.150
faminc | 0.005 0.001 8.929 0.000 0.004 0.006
|
degree |
high school | 0.198 0.074 2.683 0.007 0.053 0.342
associate/junior college | 0.321 0.092 3.496 0.000 0.141 0.501
bachelor's | 0.470 0.080 5.860 0.000 0.313 0.627
graduate | 0.640 0.086 7.410 0.000 0.471 0.809
|
_cons | -0.554 0.092 -6.001 0.000 -0.735 -0.373
-------------------------------------------------------------------------------------------totalme race4 degreeTotal ME Estimates (N = 19292)
| Estimate Std. err. z P>|z|
-------------------------+-----------------------------------------------
race4 |
total ME Ineq. | 0.047 0.007 6.937 0.000
-------------------------+-----------------------------------------------
degree |
total ME Ineq. | 0.116 0.006 20.894 0.000 totalme calculates a summary inequality measure for each categorical predictor. The default is weighted by the share of the sample in each pair of groups compared; unweighted gives every pairwise comparison the same weight, and all reports both. To test whether the two Total ME inequalities differ from each other, run the same comparison through mecompare with its totalme option and use metest on the two rows.