I have recently completed my multilevel logistic analyses (MCMC method), using 11 countries and around 25,000 respondents. I initially computed the null model, then introduced the person-level variables, to finally also include country-level characteristics. As I was hoping for, once I account for the country-level variables, the level-2 variance drops considerably (from 0.748 to 0.105).
When presenting the results, however, I show not only the variance estimates at the country level, but also the country-level variance as a percentage of the total variance. To my understanding, however, multilevel logistic models do not provide a direct estimate of first-level variance. The lower level variance is automatically constrained to the value of pi^2/3 =3.29. The estimated total variance is therefore the sum of the level-2 variance + 3.29.
To my understanding, however, there are ways to estimate first-level variance, namely "model linearisation", "simulation" or the "latent variable approach". I was therefore wondering whether you could help me calculate the lower-level variances and whether you could advice me on which is the best method to do so?
Is there a Stata do-file to do so using runmlwin?
I hope I made myself clear enough in explaining my issue.
As always, I very much appreciate your attention and time, and value your comments! Of course, if it is not possible (or does not make much sense) to estimate the level-1 variance, please just let me know
Best regards, giodje12