[R-sig-ME] Multilevel logit and sample size (mixed models)

[Linus Holtermann]

Hello,

I want to estimate a complex hierarchical multilevel logit model with spatial structure.
The model is a two-level-model wtih random slopes for some variables and cross-level interaction effects (the excact form of the model is not yet specified). I have 20 regions (upper Level) which contain several districts (lower Level). The dependent variable is employment growth at district-level.
The multilevel logit model should include at least three variables at the upper Level and eight variables at the lower Level.
I am a little bit concerned that my sample size is too small to produce reliable Point estimates and Standard Errors for such a complex model.

There are two Options:

1.) Choosing larger district Areas for which more relevant data is avaidable, resulting in:
20 regions with number of districts per region varying from 3 to 40 (Average number of districts per Region: 13)

2.) Choosing smaller district Areas, resulting in:
20 regions with number of districts per region varying from 8 to 400 (Average number of districts per Region: 60)

I like to use larger districts, because more data are avaidable. Is the sample size too small for the multilevel model? In literature this topic is discussed controversially. Some authors say you need at least 50 Groups with an average number of 50 memebers per group in a multilevel model with dichotomous data. Ohter claim that at least 20 Groups with minimum 5 members per group are sufficient. Is there a test for minimum sample size for multilevel models in R? Would an MCMC-approach help me to produce more reliable estimates?


Off Topic: Has someone try to incorporate spatial effects (spatial lag or spatial error) in multilevel models? Is that possible?

Mit freundlichen Grüßen
 
 
Linus Holtermann
Hamburgisches WeltWirtschaftsInstitut gemeinnützige GmbH (HWWI)
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