estimation of confidence intervals for melogit random effects

[Theodore Bartholomew]

Hi all,

I've tested a multilevel logistic model using melogit. I'm trying to understand how the 95% CI of the random effects are estimated. I'm curious about this as the random parameters and their confidence intervals are same when I run the model as it's baseline (melogit dv iv1 iv2 iv3 || cluster2: || cluster 1: iv2) and with the odds ratio specifier (melogit dv iv1 iv2 iv3 || cluster2: || cluster1: iv2, or). I've read through the FAQ about estimation of confidence intervals for logistic (https://www.stata.com/support/faqs/s...cs/delta-rule/) but am wondering how this is different for random parameters with melogit.

Related, my understanding is that we can assert significance of the random parameters if the confidence interval does not contain 1 for a multilevel logistic model (and by paying attention to likelihood ratio tests). Does significance identification by confidence interval not containing 1 apply even if the ,or option is not added to the model command?

Thanks!

[Clyde Schechter]

In a multi-level logistic model, the random effects parameters are presented differently from the coefficients of the fixed effects. The way in which they are calculated is too complicated to present here. If you wish to see the details, see the Methods and Formulas section of the -meglm- command chapter in the PDF manuals that are installed with your Stata. And, to be clear, the -or- option does not affect the output shown for the variance components.

To answer your question, no you would not test variance components for significance on the basis of a CI containing 1, as 1 is not the null value for these parameters. If you are going to do a significance test on the variance components, the best way to do that is to run the -melogit- twice, once with the variance component(s) of interest include, and once without, storing the estimates after each. Then use the -lrtest- command. A likelihood ratio test will be more appropriate than anything based on the CIs of the variance components.

[Theodore Bartholomew]

Thank you for your quick response, Clyde and direction toward the meglm chapter. I'll look into it. And thanks for your response regarding the likelihood ratio test being more appropriate. That was my understanding as well but have had an editor suggest that the likelihood ratio test would not be appropriate here, so was drawing the CI containing 1 as indicative of significance based on Sommet & Morselli's article (https://www.rips-irsp.com/articles/10.5334/irsp.90/).