st: indicators of nesting versus xtmelogit

[Noah Friedkin <friedkin@soc.ucsb.edu>]

The data I am analyzing are longitudinal, consisting of individuals  
located in 4 cities across 17 time periods. I.e., each individual  
contributes 17 observations, and each observation occurs in one of  
4X17=68 settings. I am not concerned with the effects of these  
settings, but instead with a set of individual-level predictors x1,  
x2, x3 of the  binary responses y of individuals in their city-time  
contexts. There are three credible approaches to the analysis of these  
observations:

(1)  xtmelogit y x1 x2 x3 || city: || time:
(2) logit y x1 x2 x3 c2 c3 c4 t2 t3  … t17, where c2-c4 and t2-t17 are  
indicator variables with city 1 and time 1 as the omitted settings
(3) logit y x1 x2 x3 c1t2 c1t3 … c1t17 c2t1 c2t2 … c2t17 … c4t1 c4t2  
…c4t17 where c_t_ are indicator variables with c1t1 as the omitted  
setting

Model 2 is a popular approach. Model 3 appears closer to model 1.  
However, my sense is that models 2-3 are excessively conservative and  
potentially misleading in allowing (what may be viewed as) meaningless  
“nuisance” associations to affect the estimates for x1, x2, and x3.  
Model 1 seems preferable.

Question 1. What are the pros and cons of these three models?

I am assuming that model 1 is equivalent to allowing different  
intercepts for each sity-time group of observations. I'm also assuming  
that the estimated random effects for the 68 city-time groups are not  
constrained, so that (for example) they might be found to be all  
positive values that monotonically increase with time.

Question2. Are both of my assumptions about model 1 correct, or is my  
understanding of model 1 flawed?

Comments on the above two questions would be much appreciated.










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