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st: indicators of nesting versus xtmelogit


From   Noah Friedkin <friedkin@soc.ucsb.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: indicators of nesting versus xtmelogit
Date   Tue, 21 Oct 2008 18:49:45 -0700

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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