Zero-inflated ordered logit regression (ziologit): results on individual outcomes

[Adelio Antunes]

Hi everyone,
I am using the new ziologit function in Stata 17 to assess the determinants of the level of expenditure of households on a discretionary product (e.g. tobacco). I am interested in the individual effects on each outcome (level). I know that I can test individual probabilities using the margins command with the contrast(at) option, or with the post option followed by a Wald test (as in the below code). However, it would be easier if one could see the individual results of regressions for each outcome. I could not find an option for that.

My questions:

1. Would such individual results for outcomes have a sense? If so:
2. Is there an option with the ziologit command, or postestimation, to generate these results? If not, in alternative:
3. Would running the regression on one outcome (akin to zero-inflated logit, I guess), give correct results? I guess not, given that Ziologit estimates a single model based on two equations, and the model would then be “shorter”.
4. If none of the above: What would be the correct the most effective way to test all independent [dummy] variables across outcomes?

. use https://www.stata-press.com/data/r17/tobacco
(Fictional tobacco consumption data)
 
. ziologit tobacco education income i.female, inflate(income education i.parent) or
 
Iteration 0:   log likelihood = -15977.364  (not concave)
Iteration 1:   log likelihood =  -13149.83  (not concave)
Iteration 2:   log likelihood = -12467.245 
Iteration 3:   log likelihood = -11039.218 
Iteration 4:   log likelihood = -9929.2298 
Iteration 5:   log likelihood = -9715.1143 
Iteration 6:   log likelihood = -9703.2464 
Iteration 7:   log likelihood = -9703.2168 
Iteration 8:   log likelihood = -9703.2168 
 
Zero-inflated ordered logit regression                 Number of obs =  15,000
                                                       Wald chi2(3)  = 3147.70
Log likelihood = -9703.2168                            Prob > chi2   =  0.0000
 
------------------------------------------------------------------------------
     tobacco | Odds ratio   Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
tobacco      |
   education |   1.663763   .0157788    53.68   0.000     1.633122    1.694978
      income |   1.792544   .0205068    51.02   0.000     1.752799    1.833191
             |
      female |
     Female  |   .5881507    .034156    -9.14   0.000     .5248755     .659054
-------------+----------------------------------------------------------------
inflate      |
      income |   .8798818   .0062032   -18.15   0.000     .8678073    .8921242
   education |   .8682758   .0043147   -28.42   0.000     .8598602    .8767738
             |
      parent |
    Smoking  |   3.280066   .1736572    22.44   0.000     2.956768    3.638714
       _cons |   13.69758   1.584661    22.62   0.000     10.91866    17.18378
-------------+----------------------------------------------------------------
       /cut1 |    5.85957    .104449                      5.654853    6.064286
       /cut2 |   11.14187   .1945483                      10.76056    11.52318
       /cut3 |    14.3632   .2495117                      13.87417    14.85224
------------------------------------------------------------------------------
Note: Estimates are transformed only in the first 2 equations to odds ratios.
Note: _cons estimates baseline odds.
 
 
. margins, at(female=(0 1)) contrast(at)
 
Contrasts of predictive margins                         Number of obs = 15,000
Model VCE: OIM
 
1._predict: Pr(tobacco=0), predict(pmargin outcome(0))
2._predict: Pr(tobacco=1), predict(pmargin outcome(1))
3._predict: Pr(tobacco=2), predict(pmargin outcome(2))
4._predict: Pr(tobacco=3), predict(pmargin outcome(3))
 
1._at: female = 0
2._at: female = 1
 
------------------------------------------------
             |         df        chi2     P>chi2
-------------+----------------------------------
_at@_predict |
          1  |          1       83.08     0.0000
          2  |          1       79.31     0.0000
          3  |          1       79.96     0.0000
          4  |          1       83.52     0.0000
      Joint  |          3       84.91     0.0000
------------------------------------------------
 
. margins, at(female=(0 1)) post
 
Predictive margins                                      Number of obs = 15,000
Model VCE: OIM
 
1._predict: Pr(tobacco=0), predict(pmargin outcome(0))
2._predict: Pr(tobacco=1), predict(pmargin outcome(1))
3._predict: Pr(tobacco=2), predict(pmargin outcome(2))
4._predict: Pr(tobacco=3), predict(pmargin outcome(3))
 
1._at: female = 0
2._at: female = 1
 
------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
_predict#_at |
        1 1  |   .6177199   .0037014   166.89   0.000     .6104653    .6249744
        1 2  |   .6491048   .0038512   168.55   0.000     .6415567     .656653
        2 1  |   .2604932   .0030529    85.33   0.000     .2545097    .2664767
        2 2  |   .2453202   .0029757    82.44   0.000     .2394879    .2511524
        3 1  |   .0736063   .0019345    38.05   0.000     .0698146    .0773979
        3 2  |   .0653043   .0017719    36.86   0.000     .0618315    .0687771
        4 1  |   .0481807   .0015966    30.18   0.000     .0450513    .0513101
        4 2  |   .0402707   .0015138    26.60   0.000     .0373036    .0432377
------------------------------------------------------------------------------
 
. test 1._predict#1._at=2._predict#1._at
 
 ( 1)  1bn._predict#1bn._at - 2._predict#1bn._at = 0
 
           chi2(  1) = 3177.28
         Prob > chi2 =    0.0000

[Adelio Antunes]

No human response but here is what AI tells us:
No, you cannot obtain separate coefficients for each outcome in a ZIOL model. The ZIOL model assumes that the outcomes are ordered and have a common set of coefficients for the main model. If you want to obtain separate coefficients for each outcome, you may consider using a multinomial logit model or a zero-inflated multinomial logit model instead. However, these models do not account for the ordinal nature of the outcome variable and may have different assumptions and limitations.