Tests across three or more models

Example 6.2 of Mize, Doan, and Long (2019), with all four models

With three or more models, mecompare lists each model’s marginal effects and reports no differences; metest can be used to test the comparisons you choose. The four nested logits of Example 6.2:

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

Rows 1-4 are the effect of college in models 1-4. 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

And whether it is the same in all four models:

metest 1 = 2 = 3 = 4
Tests of equality

                                 |      chi2         df     pvalue 
---------------------------------+--------------------------------
college                          |                                
               m1 = m2 = m3 = m4 |    60.094      3.000      0.000
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