Possible methods to assess model fit of a two-part glm

[Luis Mijares Castaneda]

Hello, I have the following model shown below, a two-part model where the first equation is a probit and the second equation is a gamma regression. As the title of my question states, are there any commands/models I can use to assess how well the model fit the data? My outcome was out-of-pocket dental costs; this was a traditional over-inflated zero with a large right-skewed healthcare expenditure variable. The data is survey weighted, so I know traditional MLE-based methods like LR test and estat are unavailable. Any help would be greatly appreciated.

svy:twopm oopdental_costs `contrls', firstpart(probit) secondpart(glm, family(gamma) link(log))

[John Mullahy]

What departures from good fit are of greatest concern in your application?

There are many ways to assess model fit, and many are often reported in published research.

But—in my humble opinion—various goodness-of-fit statistics are typically reported more as a matter of convention than because they provide useful decision-relevant information to the analyst or to the people using the results the analyst produces.

[Luis Mijares Castaneda]

I probably should have written out the full model. I was thinking of testing for heteroskedasticity or anything else that could undermine the model

local contrls i.inc_d i.male i.race i.age_cat2 i.education  i.veteran i.mothered ///
  i.QuantHI i.Quant_wealth i.dentalinsurance i.dentalvisit i.endentulism ///
  i.smoke_now c.chronicdisease 
 
svy: twopm oopdental_costs `contrls', firstpart(probit) secondpart(glm, family(gamma) link(log))