Inequality in categorical models

Example 4.2.b of Mize and Han (2025)

Because the statistic is built from predictions, it works the same way after a binary logit, where the predictions are probabilities. This example summarizes several nominal and binary predictors of conservative identification at once: gender, race-ethnicity, and subjective class.

use "https://tdmize.github.io/data/data/cda_gss", clear
(cda_gss.dta |  GSS 1972-2021 CDA - Categorical Data Analysis | date created 2023)
keep if year == 2021
(64,814 observations deleted)
drop if missing(conserv, race4, woman, class, age)
(424 observations deleted)

. 
logit conserv i.woman i.race4 i.class
Iteration 0:  Log likelihood = -2250.6348  
Iteration 1:  Log likelihood = -2208.9154  
Iteration 2:  Log likelihood = -2208.4707  
Iteration 3:  Log likelihood = -2208.4707  

Logistic regression                                     Number of obs =  3,608
                                                        LR chi2(7)    =  84.33
                                                        Prob > chi2   = 0.0000
Log likelihood = -2208.4707                             Pseudo R2     = 0.0187

--------------------------------------------------------------------------------
       conserv | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
---------------+----------------------------------------------------------------
         woman |
        Women  |     -0.326      0.073   -4.477   0.000       -0.469      -0.183
               |
         race4 |
        Black  |     -0.841      0.140   -6.006   0.000       -1.115      -0.567
        Other  |     -0.420      0.166   -2.527   0.011       -0.745      -0.094
     Hispanic  |     -0.549      0.125   -4.374   0.000       -0.794      -0.303
               |
         class |
working class  |     -0.053      0.141   -0.379   0.705       -0.329       0.222
 middle class  |     -0.019      0.138   -0.139   0.890       -0.290       0.251
  upper class  |     -0.131      0.218   -0.601   0.548       -0.557       0.296
               |
         _cons |     -0.406      0.138   -2.953   0.003       -0.676      -0.137
--------------------------------------------------------------------------------
meinequality woman race4 class
ME Inequality Estimates (N = 3608)

                         |   Estimate   Std. err.           z       P>|z| 
-------------------------+-----------------------------------------------
ME Inequality            |                                               
                   woman |      0.070       0.016       4.466       0.000 
                   race4 |      0.108       0.013       7.991       0.000 
                   class |      0.012       0.017       0.701       0.484

Class has no overall effect on conservative identification. Racial-ethnic groups differ by about 11 percentage points on average. For a binary variable such as woman the ME inequality is simply the absolute value of its marginal effect, which puts binary and multi-category predictors on the same footing for comparison.

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