Melogit does not converge and encounters a flat region in a longitudinal sample

[Josefine Johnson]

Dear Stata Users,

I am encountering a problem with converging a melogit-model. I have a longitudinal sample of the SHARE survey (Survey on Health, Aging and Retirement in Europe) in where respondents (variable: mergeid) were asked multiple times across waves (variable: wave) in different countries (variable: country). I want to assess if tobacco consumption (binary variable: pres_smoke) was somehow influeced across time and changed.

Therefore, I want to do a multilevel model with mergeid at the 2nd level and country and the 3rd level. I am actually not so much interested in differences between the participants, but since my data is not independent, because respondents were asked multiple times, I have to specify that in my model so that the assumption of independence for my logistic regression is not violated.

However, even for my simplest model, in where I only include the dependent variable for smoking and the ID-variable at the 2nd level, I am getting an error term that the model cannot be improved and a flat region is encountered. In the forum I already read some great tips, but so far they did not work for my model.

So for example, I already used a logit model before and saved the values of it in a matrix to use them as starting values. I also tried to increace the tolerance value and tried different techniques.

bysort mergeid: gen mergeid_n = _n ==1
replace mergeid_n = sum(mergeid_n)
 
xtset mergeid_n wave

logit pres_smoke mergeid_n
matrix b = e(b)
melogit pres_smoke  || mergeid_n: ,or from(b, skip) tolerance(1e-15) technique(bfgs) /*iter(500)*/

bysort mergeid: gen mergeid_n = _n ==1
replace mergeid_n = sum(mergeid_n)
 
xtset mergeid_n wave

logit pres_smoke mergeid_n
matrix b = e(b)
melogit pres_smoke  || mergeid_n: ,or from(b, skip) tolerance(1e-15) technique(nr 5 bhhh 5) /*iter(500)*/

I have the feeling that I am encountering problems because the number of groups is very high, because it is a very large dataset. The number of respondents is around 130 000 people with multiple measures, so I have around 130 000 groups for mergeid at the higher level. This also the reason why I tried different techniques like the method of Broyden-Fletcher-Goldfarb-Shanno (bfgs), but it did not help so far.

Also the meqrlogit model did not work:

meqrlogit pres_smoke  || mergeid_n: ,or from(b, skip)  technique(bfgs) difficult /*iter(500)*/

Another reason could be that there are not so many differences between the respondents. Like I said, based on my hypotheses I am not really interested in the random effect for the respondents, but for my understanding I need to include the ID variable so that I do not violate the assumption of independence. I know that I could calculate other models instead of the multilevel model, but I would like to do a multilevel analysis because I want to include variables at the country level as a next step.

So far, I am out of ideas at the moment, and I am very much looking forward to any ideas of other Stata users. I apologize for not using the dataex command, but the data of SHARE is confidential and I am not allowed to share it anywhere.

Kind regards,
Josefine

[Andrew Musau]

There are no guarantees that you will get convergence with maximum likelihood. But you may try gllamm from SSC which implements adaptive quadrature. From the Wiki entry:

Generally, adaptive algorithms are just as efficient and effective as traditional algorithms for "well behaved" integrands, but are also effective for "badly behaved" integrands for which traditional algorithms may fail.

ssc install gllamm, replace

I think that cmp from SSC also implements this numerical integration method, but I have not tried it out. For an illustration of gllamm, see https://www.statalist.org/forums/for...on-encountered, but be sure to specify the correct link function in your case.

[Josefine Johnson]

Thank you @Andrew Musau
I will look into it!