Total MEs for a single model
Example 5.2.c of Mize and Han (2025)
Self-rated health has four ordered categories, so in a multinomial logit each predictor has four marginal effects – one per category – and it is not obvious which predictor matters most. The Total ME sums the absolute effects across the categories (and halves the sum) to give one summary of how much probability each predictor moves. This example uses the 2000–2021 GSS.
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 age married parent, amount(sd)Total ME Estimates (N = 19292)
| Estimate Std. err. z P>|z|
-------------------------+-----------------------------------------------
age |
+ SD (centered) | 0.051 0.003 16.847 0.000
-------------------------+-----------------------------------------------
married |
Married vs Not Married | 0.031 0.007 4.737 0.000
-------------------------+-----------------------------------------------
parent |
Parent vs No Children | 0.027 0.009 2.976 0.003 For continuous independent variables, custom amounts of change can be specified in the amount() option; here age changes by one standard deviation. The Total ME for a binary variable such as married or parent is built from its discrete change on each outcome category, so continuous and binary predictors are summarized on the same scale.