Nested logit models and mediation/attenuation

Example 6.2 of Mize, Doan, and Long (2019)

One of the most common cross-model questions is whether an effect changes when controls are added, such as in tests of mediation/attenuation. Here the effect of a college degree on the probability of being very happy is compared across four nested logits: the bivariate model, then a full set of controls, then wages, then occupational prestige. Unlike logit coefficients, marginal effects – here, changes in the predicted probability – can be compared across models without the problem of rescaling.

use "https://tdmize.github.io/data/data/gss_cme", clear
(gss_cme.dta | GSS 1972 - 2016 Weighted | 2018-07-10)
drop if year < 2000
(38,116 observations deleted)
drop if employed != 1
(9,556 observations deleted)
drop if missing(vhappy, college, wages, occprest, age, married, parent, woman, conserv, reltrad)
(5,578 observations deleted)
quietly logit vhappy i.college, vce(robust)
estimates store m1
quietly logit vhappy i.college i.married i.parent i.woman i.conserv ///
              i.reltrad i.year c.age##c.age, vce(robust)
estimates store m2
quietly logit vhappy i.college c.wages i.married i.parent i.woman i.conserv ///
              i.reltrad i.year c.age##c.age, vce(robust)
estimates store m3
quietly logit vhappy i.college c.wages c.occprest i.married i.parent i.woman ///
              i.conserv i.reltrad i.year c.age##c.age, vce(robust)
estimates store m4
mecompare college, models(m1 m2 m3 m4)
Predicting: Pr(vhappy)
Marginal effects across models (N_m1=9216) (N_m2=9216) (N_m3=9216) (N_m4=9216)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
college                          |                                       
    College Deg - No Col Deg     |                                       
                              m1 |     1      0.072      0.010      0.000
                              m2 |     2      0.060      0.011      0.000
                              m3 |     3      0.036      0.011      0.001
                              m4 |     4      0.019      0.012      0.103

Use metest to calculate the cross-model tests. Here, whether the effect diminishes in each subsequent model.

metest, clear
metest 1 - 2, add
                                 |  estimate         se     pvalue 
---------------------------------+--------------------------------
college                          |                                
                         m1 - m2 |     0.012      0.004      0.003 
metest 2 - 3, add
                                 |  estimate         se     pvalue 
---------------------------------+--------------------------------
college                          |                                
                         m1 - m2 |     0.012      0.004      0.003 
                         m2 - m3 |     0.024      0.004      0.000 
metest 3 - 4, add
                                 |  estimate         se     pvalue 
---------------------------------+--------------------------------
college                          |                                
                         m1 - m2 |     0.012      0.004      0.003 
                         m2 - m3 |     0.024      0.004      0.000 
                         m3 - m4 |     0.017      0.004      0.000

With two models, the Difference row is printed directly:

mecompare college, models(m1 m2)
Predicting: Pr(vhappy)
Marginal effects and cross-model differences (N_m1=9216) (N_m2=9216)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
college                          |                                       
    College Deg - No Col Deg     |                                       
                              m1 |     1      0.072      0.010      0.000
                              m2 |     2      0.060      0.011      0.000
                      Difference |     3      0.012      0.004      0.003
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