Convergence not achieved

[Ziyue Wang]

I am employing a zero inflated negative binomial model. The dependent variable is the days of catching diarrhea, with 6087 observations and 5775 is zero. My indenpendent variables are as below shows. I also add year fixed effect, city fixed effect and year-city fixed effect. this is the code :
zinb diarheal_days latrine1 drinking_water handwashing water_collection5 purify gender age head_education household_income floor household_size water_access i.city i.year i.city##i.year, inflate(_cons) cluster(village) nolog

Stata could report the result but it always shows 'Convergence not achieved'. however, when I repalce the i.city with i.province, stata does not report 'Convergence not achieved'. There are six provicnes and 69 cities.
My question is
1. Could the results with 'Convergence not achieved' be used?
2. If not, how to fix this problem?

Thank you!

HH has clean Latrine (0/1)

HH has improved drinking water source (0/1)

Availability of Soap at handwashing area (0/1)

Total water collection time(minutes)

Always purify water(0/1)

Water availability in residence (0/1)

Household income (BDT/yr)

Age(yrs)

Head_education

Gender(male=1)

Floor (0/1)

Household size(persons)

[Carlo Lazzaro]

Ziyue:
welcome to this forum.
It may be that using -i.province- instead of -i.city-makes your data less sparse and, as such, the MLE converges. I would go this way.

[Weiwen Ng]

Adding to what Carlo said: you are using a zero-inflated model. This means that you are modeling the probability that a household always has zero diarrhea days as well as the count of days given that they aren’t a structural zero. The zero inflation assumption magnifies any issues you had with sparsity, and sparsity can cause convergence issues.

in addition, if a household is a structural zero, you’re saying that it is essentially immune to diarrhea. If you would not feel comfortable defending that statement on substantive grounds, then I would think about just fitting an ordinary count model. I would not feel completely comfortable defending the zero inflation assumption in this context.