Non-convergence of probit model

[Christina Chara]

Hello,

I am investigating the determinants of educational mismatch using a panel dataset. My dependent variable is a dummy variable equal to zero if a respondent is well-matched and equal to one if they are mismatched. When I ran the probit and xtprobit models on my full sample (both static and dynamic specifications) I get results after less than 15 iterations. However, when I break down my sample into different career stage groups and try to run a separate regression for each group (approximately 900-1000 observations per group), the probit model produces thousands of iterations non-stop for some groups while for others it quickly converges. I would appreciate any insight as to why this happens with only a couple of the groups especially given that the equations and number of observations are the same and any advice as to whether there is a solution to this problem as if not I won't be able to make comparisons as to how the determinants of educational mismatch affect the likelihood of mismatch of respondents who are at different career stages.

Thanking you in advance.

[Richard Williams]

How rare is the less common event in each subsample? You could have 1000 observations but if only 5 or 10 of them experience the event you could have estimation problems.

[Christina Chara]

Thanks Richard,

Out of 1067 observations, 840 are mismatched==0 (78.73%) and 227 (21.27%) are not mismatched i.e. mismatched==1. This is actually the largest of my sub-groups and it has the largest number of y==1 compared to the other groups which converge when I use the probit commands

[Richard Williams]

Within each subgroup are there any variables that come close to being constants or that are super highly correlated with each other or with the dv? My guess is that it has something to do with the subsample compositions being different but without having the data it is heard to say. Maybe try running means and correlations for each subgroup.

[Clyde Schechter]

So, if I understand you correctly, in your non-convergent subgroup you have 227 vs 840 breakout on your dependent variable. Then the numbers of events in both categories should be adequate. Another possibility is that in your non-convergent subgroup you have near-collinearity or near-perfect prediction making it difficult to estimate the effect of one of your variables.

You don't describe how many variables you have in your models or what they are. Here is a suggestion. Try re-running the same model in your non-convergent subgroup, but use the -iterate()- option. Select a number of iterations that gets you several iterations past the point where Stata appears to be getting stuck. The estimation will stop there and Stata will show you the interim results. You may be able to identify some variable in the output that has an implausibly large (or implausibly small) coefficient, or an astronomical standard error. That variable (and there may be more than one) is the likely source of the problem. Examining the distributions of that variable at both levels of your outcome variable (restricted to the estimation sample, of course) may reveal that despite the 227 vs 840 breakout in the subgroup overall, in one of the cells defined by this troublesome variable the breakout is very lopsided and that you are asking Stata to estimate its effect even though there is almost no data on it. If you do find that, then you need to exclude that variable from your modeling, at least in the non-convergent subgroup.

[Christina Chara]

Many thanks for you helpful recommendations. I inspected the various explanatory variables using basic tabulations and the only variable that was suspicious was the health limitation variable that is broken down in 3 categories: Strongly Limited in activities because of health problems, Limited in activities because of health problems and Not limited. The first category had 11 observations in it, the second 36 while the third had 1019. When I dropped this variable the model converged after 16 iterations. Is there an absolute minimum in terms of relative cell size that should be met or a rule of thump so as for the probit model to converge?
Thanks again

[Clyde Schechter]

I'm not aware of any predictable limits or rules of thumb that apply. Often one just has to stumble onto these problems because how easy or hard it is to identify the coefficient of a variable also depends on what other variables are in the model.

If you are content with a model that excludes the health limitations variable, then I think you are fine. If not, you could try re-defining it into 2 categories by combining the first and second (if that seems reasonable substantively). While 47 vs 1019 is still pretty lopsided, you never know--you might get convergence and reasonable results if you try it. (Or not.)

[Christina Chara]

Thank you very much Clyde-this is indeed very helpful

[Christina Chara]

Hello again,

I encounter the same problem of non-stop iterations in my model described above, this time when I change from the probit to the xtprobit command (With the vce(cluster id) option). The probit model works fine but the panel xtprobit won't converge even if the variables in the regression are exactly the same. The models I am running are dynamic as I include the lag of the dependent variables as one of the explanatory variables. Given that all my explanatory variables are the same in both cases I am confused as to why the cross sectional pooled probit converges whereas the panel probit model (with clustering around the id variable to correct for serial correlation) won't converge.

Any insight will be greatly appreciated.

[Clyde Schechter]

Well, -xtprobit- is a different model. It has a different likelihood function and it includes parameters not found in -probit-. My suggestion is to again use the -iterate()- option to get Stata to stop somewhere in the point where it is getting stuck and look at the interim output. In this case, my hunch is that you will find that the estimate for /lnsig2u is problematic, perhaps heading towards negative infinity. Another possibility is that rho is very close to 1--which can also cause convergence problems. Another possibility is that by introducing lagged values of some independent variables as additional covariates you have introduced more near-collinearity. Either way, using the -iterate()- option is likely to help you pinpoint the problem.

[Christina Chara]

thank you very much Clyde-i changed the cut-off points that defined my sub-samples and everything works now