meglm vs gllamm for two-stage survey design with final weight only

[Hillel Alpert]

I appreciate a recommendation on the best model (meglm or gllamm) to use for trended (time-series) analysis of data consisting of:

Complex (two-stage) sampling survey data, combined from 20 sites (states), each sampled and administrated separately over multiple years.

Each observation has a psu, stratum, and final weight, although not separate level 1 and level 2 weights.

In an ideal world, I would want to account for the complex survey design variables as well as the random effects or clustering by state.

I gather that the stratification variable cannot be used in the gllamm, and possibly the mixed effects model either. However, I could adjust for stratification variables (e.g. sex, race).

Thanks for your thoughts on this.

[Hillel Alpert]

A follow-up question which perhaps someone could answer is what is the essential difference between gllamm and meglm (or melogit, for example) in context of weighted survey data?