xtmelogit multilevel analysis, all level 1 variable coefficients are exactly the same despite varying level 2 variables

[Peggy Fan]

Hi, I've run into this conundrum that I am not sure if it is a mathematical question or it is a Stata question.
I am using xtmelogit for 2-level, random intercepts models. The models take a long time to run due to same size and the number of the parameters. I ran a base model saved as matrix(a) and used that for subsequent models.

The command I use is

xtmelogit participation i.highested female C_age religious statist_only C_lngdp C_ln_population elf C_religion_pc || newid3:, laplace from(a, skip)

level 1 variables are individual characteristics, and level 2 variables are country characteristics.
The level 2 variables of interest (Statist, Corporatist, Statist-Corporatist, Liberal) are all dummy variables. As you can see, the coefficients for all level 2 vary across the models, but the coefficient and standard error for the level 1 variables are exactly the same. I don't know why this is happening. Anyone has any ideas?

[Stephen Jenkins]

Are you 100% sure that

the coefficient and standard error for the level 1 variables are exactly the same

. You appear to have shown the result of an estimates table command or some user-written equivalent (but you don't tell us!), and only 3 decimal places are shown for coefficient estimates and SEs. Perhaps there are differences apparent in the 4th or 5th decimal place? In any case, if you have a very large number of level-1 observations, one expects precise results for the statistics associated with the level-1 predictors ... but not necessarily the level-2 predictors (it depends on the level-2 sample size). I would also be very wary of any results based on estimation using the 'Laplace' method. I might use them to derive starting values for a second round of estimation but not for the 'final' results: it is 'well known' that you get better estimates for this sort of model using methods such as adaptive quadrature (the default in Stata).

Whatever, you might be advised to look at: ‘Regression analysis of cross-national differences using multi-level data: a cautionary tale’, Working Paper 2013-14. Colchester: Institute for Social and Economic Research, University of Essex. https://www.iser.essex.ac.uk/publications/working-papers/iser/2013-14. Also IZA Discussion Paper No. 7583, http://ftp.iza.org/dp7583.pdf

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[Peggy Fan]

Hi,
Sorry that I've violated several rules on this forum. I'm in the process of changing my username, and I knew the image file wasn't ideal but I could not find where I could post the code correctly, so thank you for pointing me to section 12 of the FAQ.

My level 1 observations are 255,197, level 2 country sample is 89. I understand the inherent problems with a dataset like this and I'm prepared to spell out the limitations of my findings. But the article you've provided is very helpful for my write-up, thank you.

Another question- would you suggest using "laplace" for the first round of estimation (a base model), and use the matrix derived but without "laplace" for the final estimation of the models? I resorted to "laplace" because the estimation of each model was taking hours and I was seeking alternatives that could be more efficient. But any suggestions are welcome as my knowledge of those estimation methods is quite limited.