Comparing Total MEs across models
Example 5.2.e of Mize and Han (2025): mediation/attenuation
Does the total effect of a college degree on self-rated health shrink once family income is in the model? Store the model without income and the model with it, and name both in models(): totalme reports the Total ME from each model and tests the difference.
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, college, race4, age, woman, parent, married, faminc)(22,943 observations deleted)drop if year < 2000 | year > 2021(26,611 observations deleted)
. mlogit healthR i.college i.race4 c.age i.woman i.parent i.married, vce(robust)Iteration 0: Log pseudolikelihood = -22624.777
Iteration 1: Log pseudolikelihood = -21801.971
Iteration 2: Log pseudolikelihood = -21756.528
Iteration 3: Log pseudolikelihood = -21756.104
Iteration 4: Log pseudolikelihood = -21756.104
Multinomial logistic regression Number of obs = 19,292
Wald chi2(24) = 1511.84
Prob > chi2 = 0.0000
Log pseudolikelihood = -21756.104 Pseudo R2 = 0.0384
---------------------------------------------------------------------------------
| Robust
healthR | Coefficient std. err. z P>|z| [95% conf. interval]
----------------+----------------------------------------------------------------
Poor |
college |
College Degree | -1.345 0.106 -12.732 0.000 -1.552 -1.138
|
race4 |
Black | 0.037 0.099 0.378 0.706 -0.156 0.231
Other | 0.292 0.175 1.664 0.096 -0.052 0.635
Hispanic | 0.092 0.115 0.804 0.421 -0.133 0.317
|
age | 0.029 0.002 15.258 0.000 0.025 0.033
|
woman |
Women | 0.065 0.071 0.928 0.353 -0.073 0.204
|
parent |
Parent | 0.090 0.092 0.976 0.329 -0.090 0.270
|
married |
Married | -0.659 0.076 -8.691 0.000 -0.808 -0.511
_cons | -3.339 0.120 -27.898 0.000 -3.574 -3.105
----------------+----------------------------------------------------------------
Fair |
college |
College Degree | -0.745 0.049 -15.208 0.000 -0.842 -0.649
|
race4 |
Black | 0.255 0.056 4.534 0.000 0.145 0.366
Other | 0.223 0.099 2.243 0.025 0.028 0.418
Hispanic | 0.397 0.060 6.584 0.000 0.279 0.515
|
age | 0.014 0.001 11.088 0.000 0.011 0.016
|
woman |
Women | 0.010 0.040 0.263 0.793 -0.067 0.088
|
parent |
Parent | -0.034 0.050 -0.675 0.499 -0.131 0.064
|
married |
Married | -0.296 0.042 -7.042 0.000 -0.379 -0.214
_cons | -1.355 0.071 -19.011 0.000 -1.495 -1.215
----------------+----------------------------------------------------------------
Good | (base outcome)
----------------+----------------------------------------------------------------
Excellent |
college |
College Degree | 0.450 0.037 12.030 0.000 0.376 0.523
|
race4 |
Black | -0.198 0.056 -3.541 0.000 -0.308 -0.089
Other | -0.330 0.091 -3.633 0.000 -0.508 -0.152
Hispanic | -0.172 0.060 -2.863 0.004 -0.289 -0.054
|
age | -0.011 0.001 -9.189 0.000 -0.013 -0.008
|
woman |
Women | 0.043 0.036 1.214 0.225 -0.027 0.113
|
parent |
Parent | -0.134 0.043 -3.103 0.002 -0.219 -0.049
|
married |
Married | 0.183 0.038 4.810 0.000 0.108 0.257
_cons | -0.262 0.062 -4.245 0.000 -0.383 -0.141
---------------------------------------------------------------------------------est store basemod. mlogit healthR i.college i.race4 c.age i.woman i.parent i.married c.faminc, vce(robust)Iteration 0: Log pseudolikelihood = -22624.777
Iteration 1: Log pseudolikelihood = -21613.16
Iteration 2: Log pseudolikelihood = -21511.395
Iteration 3: Log pseudolikelihood = -21504.44
Iteration 4: Log pseudolikelihood = -21504.414
Iteration 5: Log pseudolikelihood = -21504.414
Multinomial logistic regression Number of obs = 19,292
Wald chi2(27) = 1574.72
Prob > chi2 = 0.0000
Log pseudolikelihood = -21504.414 Pseudo R2 = 0.0495
---------------------------------------------------------------------------------
| Robust
healthR | Coefficient std. err. z P>|z| [95% conf. interval]
----------------+----------------------------------------------------------------
Poor |
college |
College Degree | -0.906 0.110 -8.257 0.000 -1.121 -0.691
|
race4 |
Black | -0.120 0.099 -1.211 0.226 -0.315 0.074
Other | 0.237 0.176 1.352 0.176 -0.107 0.581
Hispanic | -0.055 0.115 -0.475 0.635 -0.281 0.171
|
age | 0.026 0.002 14.021 0.000 0.022 0.029
|
woman |
Women | -0.022 0.071 -0.311 0.756 -0.162 0.118
|
parent |
Parent | 0.121 0.092 1.313 0.189 -0.060 0.301
|
married |
Married | -0.247 0.086 -2.883 0.004 -0.415 -0.079
faminc | -0.030 0.004 -7.730 0.000 -0.038 -0.022
_cons | -2.646 0.135 -19.648 0.000 -2.910 -2.382
----------------+----------------------------------------------------------------
Fair |
college |
College Degree | -0.567 0.051 -11.130 0.000 -0.667 -0.467
|
race4 |
Black | 0.191 0.056 3.385 0.001 0.080 0.301
Other | 0.219 0.101 2.176 0.030 0.022 0.416
Hispanic | 0.339 0.060 5.607 0.000 0.220 0.457
|
age | 0.013 0.001 10.461 0.000 0.010 0.015
|
woman |
Women | -0.027 0.040 -0.681 0.496 -0.105 0.051
|
parent |
Parent | -0.022 0.050 -0.447 0.655 -0.120 0.075
|
married |
Married | -0.141 0.045 -3.146 0.002 -0.228 -0.053
faminc | -0.009 0.001 -9.153 0.000 -0.011 -0.007
_cons | -1.118 0.074 -15.021 0.000 -1.264 -0.972
----------------+----------------------------------------------------------------
Good | (base outcome)
----------------+----------------------------------------------------------------
Excellent |
college |
College Degree | 0.331 0.040 8.318 0.000 0.253 0.409
|
race4 |
Black | -0.152 0.056 -2.696 0.007 -0.262 -0.041
Other | -0.340 0.091 -3.719 0.000 -0.519 -0.161
Hispanic | -0.134 0.060 -2.225 0.026 -0.251 -0.016
|
age | -0.011 0.001 -8.967 0.000 -0.013 -0.008
|
woman |
Women | 0.072 0.036 2.004 0.045 0.002 0.143
|
parent |
Parent | -0.148 0.043 -3.407 0.001 -0.233 -0.063
|
married |
Married | 0.076 0.040 1.925 0.054 -0.001 0.154
faminc | 0.005 0.000 9.788 0.000 0.004 0.006
_cons | -0.376 0.064 -5.915 0.000 -0.501 -0.252
---------------------------------------------------------------------------------est store medmod. totalme college, models(basemod medmod)Total ME Estimates (N_basemod = 19292 , N_medmod = 19292)
| Estimate Std. err. z P>|z|
-------------------------+-----------------------------------------------
college |
Model 1 (basemod) | 0.159 0.006 26.338 0.000
Model 2 (medmod) | 0.118 0.007 17.514 0.000
Cross-Model Diff. | 0.041 0.003 15.006 0.000 The Difference row is the part of the total college effect that family income accounts for, with its standard error.
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