Unable to reach maximum likelihood in GSEM multinomial cross-classified model

[Michael Sinnige]

Dear,

As this is my first post in this forum and of this kind, I might miss some conventions used in this forum. Please inform me of any mistake in this.

My question is about a multinomial multilevel regression analysis using gsem (mlogit). We have several models with three levels. One of the models is a cross-classified model. It is this model with which we run into an issue. Stata does not seem to be able to calculate the maximum likelihood (it stops at 300 iterations). Stata can compute the simpler model. For the cross-classified model, I have tried using the outcome of the simpler model as starting values, but that provides no solution (same calculation problem).

Simpler model (Stata can calculate this model)

gsem (i.uitstroombinnentweejaartot_nom <- i.year c.leeftijd_beslissing1 c.leeftijd_sq c.doorlooptijd_nieuw2 sq_proc_duur native_counselor i.family_composition opvangcap_2log i.urbanisation lnGDP_cap_PPP2 GDP_growth freedom_PTaveragemin1 freedom_PTaverageverschil CorruptionPerceptionIndex i.EUvisa i.potentialEUMember i.schengenvisarequired M1[Number]@1 M2[Number>countryyear]@1), nocapslatent difficult latent(M1 M2) mlogit

Cross-classified model (which Stata is not able to calculate)

gsem (i.uitstroombinnentweejaartot_nom <- i.year c.leeftijd_beslissing1 c.leeftijd_sq c.doorlooptijd_nieuw2 sq_proc_duur native_counselor i.family_composition opvangcap_2log i.urbanisation lnGDP_cap_PPP2 GDP_growth freedom_PTaveragemin1 freedom_PTaverageverschil CorruptionPerceptionIndex i.EUvisa i.potentialEUMember i.schengenvisarequired M1[Number]@1 M2[corop]@1 M3[Number>countryyear]@1), nocapslatent difficult latent(M1 M2 M3) mlogit

Additional information
- The dataset consists of 15.680 observations
- Level 2 variable (countryyear) has approximately 450 different values. Level 3 (Number, which represents a country) variable has 102 different values
- Level 2 variable (corop) has approximately 41 different values
- I am using Stata 18 on Windows 10
- I have tried interpreting the hessian matrix; this is, however, too complex for me without assistance.

Is there anything I can do so that State can find the maximum likelihood?

Kind regards,
Michael Sinnige

[Clyde Schechter]

Non-convergence problems can be difficult and frustrating. Sometimes there is no choice but to simplify the model. But there are a few things worth trying.

1. Is the log likelihood stuck on the same number from some point on in the iteration log? Or going around in cricles after some point? If either of these is the case, rerun the model adding the -iterate(#)- option, choosing # to be a number that gets you just past that stall point. You will get interim "results" at the end of that--these results are not correct and are not usable, but can be helpful in understanding what's going wrong. Are there any variables whose coefficient(s) or standard error(s) are either ridiculously large in magnitude, or, in the case of the standard error(s) very close to zero? If so, that (those) variable(s) are problematic and will probably have to be removed from the model.

2. Although usually we advise people to simplify the model and then build back one step at a time until you get the fullest model that still converges, there is one complexification that is worth trying: add -cov(M1*M2) cov(M2*M3) cov(M1*M3)- to your model. By default these covariances are not estimated but are assumed to be 0. If that's too far from reality, it can make the model fail to converge. Allowing -gsem- to estimate them may make it possible to estimate your model.

Other Forum members who have more experience with -gsem- than I do may have other ideas as well, and I hope they will chime in.

[Michael Sinnige]

Thank you for your quick and helpful response! I will try your suggestions.