Zero-inflated ordered logit model interpretation Consider this Stata code and selected results:
use https://stats.idre.ucla.edu/stat/data/hsb2, clear

generate honcomp = (write >=60)
logit honcomp female read science

Iteration 0:   log likelihood = -115.64441
Iteration 1:   log likelihood = -84.558481
Iteration 2:   log likelihood = -80.491449
Iteration 3:   log likelihood = -80.123052
Iteration 4:   log likelihood = -80.118181
Iteration 5:   log likelihood = -80.11818

This is a listing of the log likelihoods at each iteration. (Remember that logistic regression uses maximum likelihood, which is an iterative procedure.)  The first iteration (called iteration 0) is the log likelihood of the “null” or “empty” model; that is, a model with no predictors. At the next iteration, the predictor(s) are included in the model.  At each iteration, the log likelihood increases because the goal is to maximize the log likelihood.  When the difference between successive iterations is very small,  the model is said to have “converged”, iteration is stopped and the results are displayed.
The above is from https://stats.idre.ucla.edu/stata/output/logistic-regression-analysis/.
There is also an option of fitting a zero-inflated ordered logit model.
. ziologit tobacco education income i.female, inflate(income education i.parent)
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

This output is from https://www.stata.com/new-in-stata/zero-inflated-ordered-logit/.
There appears to be one model computation being performed here, since there is only one iteration output.

*

*Is there just one model being fitted here that provide simultaneously all the coefficients for the tobacco and inflate portions? If this is correct how is this done?


*What relevance is “not concave”? Does it matter if it is or is not concave?


*In the link, there is also /cut1, /cut2 and /cut3. What do these represent?

The zero-inflated original logit has a single likelihood that represents the likelihood of all the parameters being estimated. There are not two likelihoods for the two portions of the model. There is a single estimation procedure over all the parameters. This is why at each iteration you see only a single likelihood. This is done by writing down the likelihood for all the parameters in a single expression and maximizing this value. The two components of the model are estimated simultaneously and depend on each other. It's not the case that each unit is used twice; each unit contributes exactly once to the likelihood.
The /cut1, /cut2, and /cut3 in the output are the cutpoints in the ordinal logit model. See help ologit for more details. These are the equivalents of the intercept in a binary logistic regression. The probability that the linear predictor plus error falls between the cutpoints is the probability of receiving the corresponding value of the outcome (given that you are not in the inflation group).
