Different model types

Example 6.5 of Mize, Doan, and Long (2019): ordinal versus nominal

Marginal effects are on the scale of the outcome – here, probabilities of each party-identification category – so they can be compared across different types of models if both predict the same quantity. This example fits an ordered logit and a multinomial logit to the same five-category party identification variable with the same predictors, and asks whether the two models imply different effects of age. If they do, it is evidence the ordering imposed by the ordinal model is incorrect.

use "https://tdmize.github.io/data/data/gss_cme", clear
(gss_cme.dta | GSS 1972 - 2016 Weighted | 2018-07-10)
drop if year < 2010
(53,043 observations deleted)
drop if missing(partyid5, woman, edyrs, age, parent, married, faminc, employed, region4, year)
(1,244 observations deleted)
quietly ologit partyid5 c.age##c.age i.woman c.edyrs i.parent i.married i.race ///
               c.faminc i.employed i.region4 i.year, vce(robust)
estimates store ordinal
quietly mlogit partyid5 c.age##c.age i.woman c.edyrs i.parent i.married i.race ///
               c.faminc i.employed i.region4 i.year, vce(robust)
estimates store nominal

Age enters with a squared term, so the marginal effect depends on where the change starts. start(age=20) and amount(10) define the effect as the change in each probability from age 20 to age 30, with the other variables held at their means:

mecompare age, models(ordinal nominal) start(age=20) amount(10) uncentered covariates(atmeans)
Predicting: Pr(partyid5)
Marginal effects and cross-model differences (N_ordinal=8179) (N_nominal=8179)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
age + 10 (uncentered)            |                                       
            Strong Dem - ordinal |     1      0.020      0.004      0.000
            Strong Dem - nominal |     2      0.032      0.003      0.000
         Strong Dem - Difference |     3     -0.012      0.003      0.000
              Democrat - ordinal |     4      0.023      0.005      0.000
              Democrat - nominal |     5     -0.010      0.011      0.352
           Democrat - Difference |     6      0.034      0.009      0.000
           Independent - ordinal |     7     -0.003      0.000      0.000
           Independent - nominal |     8     -0.000      0.010      0.965
        Independent - Difference |     9     -0.003      0.010      0.796
            Republican - ordinal |    10     -0.024      0.005      0.000
            Republican - nominal |    11     -0.031      0.011      0.003
         Republican - Difference |    12      0.007      0.009      0.436
          Strong Repub - ordinal |    13     -0.016      0.004      0.000
          Strong Repub - nominal |    14      0.010      0.003      0.003
       Strong Repub - Difference |    15     -0.026      0.004      0.000

Each outcome category gets its own block. A significant Difference means the ordinal model’s proportional-odds assumption changes the conclusion for that category.

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