GSEM and multilevel multinomial logistic regression

[Giovanni Borghesan]

Dear Statalists,
I'm trying to fit a multinomial multilevel logistic regression on the propensity for voting a populist party.
The data I'm using is the integrated European Social Survey dataset to which I added several country and year level variables (example with dataex below).
Even after reading several ( if not all the) examples provided by the manual I still can't figure out how to specify such a model with gsem.
This is because I don't understand how to specify the corresponding level for each variable. Individuals should be nested in countries and countries should be nested in years.

If I were to fit the model using xtmixed (as I didi until now) the model would be:
(In this case I reorganized the dependent variable to have just two outcomes)

quietly xtmixed PTV gndr agec edulvla polintr freehms attimm eminority       ///
                gincdif tvtotrlgdgr radical urban individualism income       ///
                c_socgloind c_persgloind c_infoglind c_cultgloind gdp        ///
                c_unemp c_gini c_cpi c_socspe imminfrate m_imp_comp if good  ///                                      
|| country:  c_socgloind c_persgloind c_infoglind c_cultgloind gdp c_unemp   ///
             c_gini c_cpi c_socspe imminfrate m_imp_comp,                    ///
|| year: c_socgloind c_persgloind c_infoglind c_cultgloind gdp c_unemp       ///
         c_gini c_cpi c_socspe imminfrate m_imp_comp,  var mle
est store model4
predict lfit4

Here is an example of the data:

clear
input float ptv double(gndr edulvla) long country float gdp double year
0 1 3 1 42058.75 2006
0 0 2 1 42058.75 2002
0 1 3 1 42058.75 2004
0 1 3 1 42058.75 2004
0 1 3 1 42058.75 2004
0 1 1 1 42058.75 2014
0 1 3 1 42058.75 2002
0 1 3 1 42058.75 2006
1 1 3 1 42058.75 2006
0 1 3 1 42058.75 2004
0 0 5 1 42058.75 2004
0 0 3 1 42058.75 2002
0 1 2 1 42058.75 2002
0 0 3 1 42058.75 2006
0 0 4 1 42058.75 2004
0 1 4 1 42058.75 2006
0 0 3 1 42058.75 2002
0 1 3 1 42058.75 2002
0 1 3 1 42058.75 2004
0 0 3 1 42058.75 2006
0 0 3 1 42058.75 2006
0 1 2 1 42058.75 2004
0 1 3 1 42058.75 2004
0 0 3 1 42058.75 2004
1 0 4 1 42058.75 2006
0 0 3 1 42058.75 2014
0 1 3 1 42058.75 2002
0 0 3 1 42058.75 2006
0 1 5 1 42058.75 2002
0 1 3 1 42058.75 2004
0 1 5 1 42058.75 2014
0 1 3 1 42058.75 2004
0 0 3 1 42058.75 2002
0 1 3 1 42058.75 2004
0 0 3 1 42058.75 2002
. 0 2 1 42058.75 2006
0 0 3 1 42058.75 2002
0 0 3 1 42058.75 2006
0 0 5 1 42058.75 2002
1 1 3 1 42058.75 2014
0 0 3 1 42058.75 2006
0 0 5 1 42058.75 2014
0 0 3 1 42058.75 2006
0 1 3 1 42058.75 2006
0 0 3 1 42058.75 2006
0 1 3 1 42058.75 2006
0 1 3 1 42058.75 2006
0 1 3 1 42058.75 2014
0 1 3 1 42058.75 2006
0 0 5 1 42058.75 2004
0 0 2 1 42058.75 2004
0 1 3 1 42058.75 2002
0 1 3 1 42058.75 2006
0 0 3 1 42058.75 2006
. 0 3 1 42058.75 2004
0 1 5 1 42058.75 2002
0 1 2 1 42058.75 2006
0 1 3 1 42058.75 2006
0 1 3 1 42058.75 2014
0 1 2 1 42058.75 2002
0 1 3 1 42058.75 2006
0 1 3 1 42058.75 2006
0 1 3 1 42058.75 2006
0 1 3 1 42058.75 2004
0 1 5 1 42058.75 2002
0 1 3 1 42058.75 2004
0 1 3 1 42058.75 2004
0 1 5 1 42058.75 2004
0 1 3 1 42058.75 2006
0 1 3 1 42058.75 2002
1 1 3 1 42058.75 2014
0 0 3 1 42058.75 2014
. 1 2 1 42058.75 2006
0 1 5 1 42058.75 2002
0 1 3 1 42058.75 2004
0 1 3 1 42058.75 2006
0 1 2 1 42058.75 2014
0 0 4 1 42058.75 2006
0 0 3 1 42058.75 2006
0 0 3 1 42058.75 2002
0 0 3 1 42058.75 2014
0 1 2 1 42058.75 2002
0 0 5 1 42058.75 2006
0 0 3 1 42058.75 2006
0 1 3 1 42058.75 2014
0 1 2 1 42058.75 2006
. 1 2 1 42058.75 2002
0 1 3 1 42058.75 2004
0 1 3 1 42058.75 2014
0 1 5 1 42058.75 2002
0 0 3 1 42058.75 2002
0 0 3 1 42058.75 2006
0 1 3 1 42058.75 2002
0 1 3 1 42058.75 2014
0 1 3 1 42058.75 2006
0 0 3 1 42058.75 2002
0 1 5 1 42058.75 2014
0 0 3 1 42058.75 2006
0 1 5 1 42058.75 2014
0 0 3 1 42058.75 2002
end
label values ptv ptv
label def ptv 0 "Not populist", modify
label def ptv 1 "Right wing populist", modify
label def ptv 2"Left wing populist", modify
label values gndr gndr
label def gndr 1 "Male", modify
label values edulvla edulvla
label def edulvla 1 "Less than lower secondary education (ISCED 0-1)", modify
label def edulvla 2 "Lower secondary education completed (ISCED 2)", modify
label def edulvla 3 "Upper secondary education completed (ISCED 3)", modify
label def edulvla 4 "Post-secondary non-tertiary education completed (ISCED 4)", modify
label def edulvla 5 "Tertiary education completed (ISCED 5-6)", modify
label values country country
label def country 1 "Austria", modify
label values year essround

Can someone help me? I don't need the full model, just the general rules for specifying it!

Thanks to everyone in advance also for your patience (first post!)

Giovanni

[Clyde Schechter]

Thank you for using -dataex- on your very first post! Unfortunately, your data example does not lend itself to solving your problem because you have only a single country included. Most people who would want to help you out with this would want to test their code before posting a response, and this example makes that impossible. Please post back with a different example that includes multiple countries and years. Also have the example include more than just 2 levels of your outcome variable. It would just waste your time and mine if I were to dash off some code that probably wouldn't work for you because it has not been tested on a realistic example.

Next, you say that you want countries nested within years, but the -xtmixed- model you show has years nested within countries. In fact, both of these models would be quite unusual (although possible): it would be more typical to have country and year effects crossed. Can you clarify what you really want?

By the way, if you are running a version of Stata recent enough to have -gsem-, then -xtmixed- has been renamed to -mixed-.

[Giovanni Borghesan]

Dear Clyde, thanks a lot for the answer.
I'm now posting a new example ( dataex ptv gndr country year if year > 2010 & country !=2, count(2500) ) that should provide both different years and different countries, I hope it will not be too long, if the new example is not good enough please let me know some other specific requirement and I will be happy to do so. Now, talking about the outcome variable, it only has three outcomes: 0 is "Not populist" 1 is "Right wing populist" and 2 "Left wing populist", maybe such an outcome variable would require a different method but I don't know sincerely. In regard to the order of the levels, my main interest would be to grasp the differences that rise within a country during time. For that reason I nested them in that order (yes, I made an error in the previous post). Anyway, I trust your experience so If you think that it should be required to have the effect of countries and years crossed together, let's do so!

Another thing I would like to underline is that theoretically speaking, I shouldn't need to specify any latent variable which I understand to be a thing in the -gsem- syntax.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float ptv double gndr long country double year
0  1 1 2014
0  0 1 2014
0  1 1 2014
1  1 1 2014
0  0 1 2014
0  1 1 2014
0  1 1 2014
1  1 1 2014
0  0 1 2014
0  1 1 2014
0  0 1 2014
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0  1 1 2014
0  0 1 2014
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0  0 3 2012
0  1 3 2014
0  0 3 2012
0  1 3 2012
1  1 3 2014
.  0 3 2012
0  0 3 2012
0  0 3 2012
0  1 3 2012
0  0 3 2012
0  0 3 2014
.  0 3 2012
0  0 3 2012
0  1 3 2014
1  0 3 2014
1  0 3 2014
0  1 3 2012
0  1 3 2014
.  1 3 2012
.  1 3 2014
.  1 3 2014
0  1 3 2012
1  1 3 2014
0  0 3 2014
2  0 3 2014
0  1 3 2014
0  1 3 2012
2  1 3 2014
0  1 3 2012
0  0 3 2014
0  0 3 2014
0  1 3 2014
0  0 3 2014
0  1 3 2014
0  1 3 2012
.  1 3 2012
0  0 3 2012
0  0 3 2012
1  1 3 2014
0  1 3 2014
.  0 3 2014
1  0 3 2014
.  1 3 2014
0  1 3 2012
0  0 3 2012
1  0 3 2014
0  0 3 2014
0  0 3 2014
0  1 3 2014
0  1 3 2014
0  1 3 2012
0  1 3 2012
0  1 3 2014
.  1 3 2014
0  1 3 2014
0  1 3 2012
.  1 3 2012
0  1 3 2014
0  0 3 2014
0  1 3 2014
1  1 3 2014
0  0 3 2012
.  1 3 2012
0  0 3 2014
0  0 3 2012
0  0 3 2014
0  0 3 2012
0  1 3 2012
0  0 3 2012
2  0 3 2014
0  1 3 2012
0  0 3 2014
1  0 3 2012
1  1 3 2014
1  0 3 2014
0  0 3 2014
0  0 3 2014
0  1 3 2012
0  1 3 2012
2  1 3 2014
.  1 3 2014
.  1 3 2014
0  1 3 2012
0  0 3 2012
0  1 3 2014
0  0 3 2012
0  0 3 2012
0  0 3 2014
.  0 3 2014
0  1 3 2012
1  1 3 2014
.  1 3 2012
1  0 3 2012
0  1 3 2014
.  1 3 2014
0  0 3 2014
0  0 3 2014
0  0 3 2014
0  0 3 2012
0  0 3 2014
0  1 3 2012
0  0 3 2014
1  1 3 2012
0  1 3 2012
0  0 3 2012
0  1 3 2014
0  0 3 2014
.  0 3 2012
0  0 3 2012
1  1 3 2014
0  1 3 2012
0  0 3 2012
0  1 3 2014
0  0 3 2012
.  0 3 2014
.  1 3 2012
0  1 3 2014
0  1 3 2012
0  0 3 2012
0  0 3 2014
0  0 3 2014
0  0 3 2012
0  1 3 2014
0  1 3 2012
0  0 3 2012
.  0 3 2012
1  0 3 2012
1  0 3 2012
0  1 3 2012
1  1 3 2012
1  1 3 2014
0  1 3 2012
1  1 3 2014
0  1 3 2012
0  1 3 2014
0  1 3 2012
0  1 3 2012
0  0 3 2012
0  0 3 2012
0  1 3 2012
0  0 3 2014
0  1 3 2012
.  1 3 2012
1  1 3 2012
0  1 3 2012
0  0 3 2012
0  0 3 2012
0  0 3 2012
0  0 3 2012
0  0 3 2014
1  1 3 2014
1  0 3 2014
1  0 3 2014
0  0 3 2012
0  0 3 2012
0  0 3 2012
1  1 3 2012
.  1 3 2012
0  1 3 2012
.  0 3 2014
1  1 3 2014
.  0 3 2014
0  0 3 2014
0  0 3 2012
0  1 3 2012
0  0 3 2012
.  0 3 2012
0  0 3 2012
.  0 3 2012
0  1 3 2012
1  0 3 2014
0  0 3 2012
0  0 3 2012
0  1 3 2014
.  0 3 2012
0  1 3 2014
0  1 3 2012
0  1 3 2012
0  0 3 2012
0  0 3 2014
0  0 3 2014
0  1 3 2014
0  0 3 2012
0  1 3 2012
1  1 3 2012
0  1 3 2014
.  1 3 2014
1  1 3 2014
0  0 3 2012
1  1 3 2014
0  1 3 2014
0  1 3 2012
0  1 3 2012
1  0 3 2014
0  1 3 2014
0  1 3 2012
0  1 3 2012
1  0 3 2014
0  1 3 2014
0  0 3 2012
0  0 3 2012
0  0 3 2012
0  1 3 2012
.  1 3 2012
0  0 3 2012
0  0 3 2012
0  1 3 2012
0  1 3 2012
2  1 3 2014
1  1 3 2014
0  1 3 2012
0  0 3 2012
.  0 3 2014
.  1 3 2014
0  1 3 2014
1  0 3 2014
0  0 3 2012
1  1 3 2014
0  1 3 2012
0  0 3 2012
0  0 3 2012
0  1 3 2012
0  1 3 2012
0  0 3 2012
0  1 3 2014
0  1 3 2014
0  0 3 2014
0  0 3 2014
0  0 3 2012
0  1 3 2014
1  0 3 2012
1  0 3 2012
1  1 3 2014
.  0 3 2014
0  0 3 2014
0  1 3 2012
0  0 3 2014
0  0 3 2012
0  0 3 2014
0  0 3 2012
0  0 3 2014
.  1 3 2012
0  1 3 2012
1  0 3 2014
0  0 3 2012
1  1 3 2014
0  1 3 2012
0  0 3 2014
0  0 3 2012
.  0 3 2012
0  0 3 2012
.  0 3 2014
.  1 3 2012
1  1 3 2014
0  0 3 2012
0  0 3 2014
.  0 3 2014
0  0 3 2012
0  0 3 2014
0  1 3 2014
0  1 3 2012
.  1 3 2014
0  1 3 2012
0  1 3 2014
0  0 3 2012
0  0 3 2012
0  0 3 2014
0  0 3 2014
1  1 3 2014
2  1 3 2014
0  1 3 2012
0  1 3 2014
0  0 3 2014
.  0 3 2014
0  1 3 2014
1  1 3 2014
1  1 3 2014
1  1 3 2014
0  1 3 2012
0  1 3 2012
0  0 3 2014
0  0 3 2012
0  0 3 2012
0  0 3 2012
0  1 3 2014
.  1 3 2014
0  0 3 2012
0  0 3 2012
0  0 3 2012
0  0 3 2012
0  1 3 2012
0  1 3 2012
0  0 3 2014
1  0 3 2014
.  1 3 2014
0  1 3 2014
0  0 3 2014
.  1 3 2014
0  1 3 2014
0  1 3 2012
0  0 3 2012
0  1 3 2012
0  0 3 2012
0  1 3 2014
0  0 3 2014
0  0 3 2014
0  1 3 2014
0  0 3 2012
0  1 3 2012
1  0 3 2012
0  0 3 2012
0  1 3 2014
0  0 3 2012
0  1 3 2012
0  1 3 2014
0  0 3 2012
0  0 3 2012
.  1 3 2014
1  1 3 2014
1  0 3 2012
0  0 3 2012
0  1 3 2012
0  1 3 2012
0  1 3 2014
0  1 3 2014
0  1 3 2012
0  1 3 2012
end
label values ptv ptv
label def ptv 0 "Not populist", modify
label def ptv 1 "Right wing populist", modify
label def ptv 2 "Left wing populist", modify
label values gndr gndr
label def gndr 1 "Male", modify
label def gndr .a "No answer", modify
label values country country
label def country 1 "Austria", modify
label def country 3 "Czech Republic", modify
label values year essround

Have a good day,
Giovanni

[Clyde Schechter]

Well, here are my thoughts. If you have a large number of countries, it is reasonable to treat country as a random effect. I would not do this for just a handful, but if you have a few dozen or more, then it makes some sense. For years, I am more skeptical about treating them as random effects. I suspect that you have only a small number of them, so you would not really be sampling year-space very well. But I'll leave that to you. Here's how I would do a random-effects multinomial logistic regression (yes, I think that's the right approach for this kind of outcome variable) with a random effect at the country level and leaving year as a fixed effect.

gsem (ptv <- i.gndr /*other predictors perhaps*/ i.year C[country], link(logit) family(multinomial))

The C[country] creates a latent variable that is the random effect at the country level. I do not understand your remark about not wanting to include any latent variables: a random effect is a latent variable.

This will not converge in your example which has only 2 countries, and also has only one year's worth of data for one of them. (But your example was good enough for me to play with it and test the code in some ways.)

If you really want to make year a random effect, and have it crossed with country, all you need to do is change i.year to Y[year].

And if you really want to make year a random effect nested within country, replace i.year with Y[country>year]. Understand if you go this route you are saying that there are some country specific effects on ptv that apply to individual countries across all time, and that these effects are more or less normally distributed, and that within each country there are also year-specific affects that apply to all voters in that country in that year, but the effects in a given year in one country are different from the effects in a different year in other countries, and these effects are also more or less normally distributed. I do have difficulty buying this as a data generating process, but I am not a political scientist, so it may be realistic. I am less troubled by this model having seen more of your data than I was initially, but still sceptical of it. I'm more inclined to think of time effects as being specific to the year but applying across countries in the same way. And, either way, if there are only a small number of years represented, using a random effects model is probably not helpful.

[Joseph Coveney]

If I were to fit the model using xtmixed (as I didi until now) the model would be:

quietly xtmixed . . . ///
|| country: c_socgloind c_persgloind c_infoglind c_cultgloind gdp c_unemp ///
c_gini c_cpi c_socspe imminfrate m_imp_comp, ///
|| year: c_socgloind c_persgloind c_infoglind c_cultgloind gdp c_unemp ///
c_gini c_cpi c_socspe imminfrate m_imp_comp

You ain't gonna fit that model. Nor anything like it. At least not before you've retired.

[Giovanni Borghesan]

Dear Clyde,
it works!
For a matter of completeness, the years in the sample are eight which I believe to be a sufficient number. In regard to the specifications of the time effect you are right, I have to discuss it with the supervisor. From now I'll just make different tries and I'll let you know. Anyway thanks for such a deep answer, you have clarified everything to me.

Answering to Joseph, it was just an example because the -mixed- syntax is way easier. Anyway doing this try actually worked, even if not meaningful, it just took a long time to converge.
Let's hope I won't do those things also after retirement.

Thanks to you all