Dear Statalisters,

I would like to know how to properly specify a temporal variable in within-between "hybrid" random effects models.

My model, a logistic regression concerning inter-state conflict initiation , takes the following form:

y: binary dependent variable (1 = conflict initiation)
z1: time-variant predictor
z2: time-variant predictor
t t2 t3 : cubic polynomial of years since conflict initiation

Following Schunck (2013), the within-between variables are constructed:
Code:
by cluster, sort: center z1, prefix(w) mean(b)
by cluster, sort: center z2, prefix(w) mean(b)
And an interaction between z1 and z2 may take the following form
Code:
gen wz1Xbz2 = wz1*bz2
by cluster, sort: center wz1Xbz2, prefix(w_) mean(b_)
And so the model takes the following form:
Code:
logit y wz1 bz1 wz2 bz2  w_wz1Xbz2  b_wz1Xbz2
The next step is to include t t2 t3 in the model, but I am unsure about how to do so. Specifically, is it correct to simply include these variables in the model like so:
Code:
logit y wz1 bz1 wz2 bz2  w_wz1Xbz2  b_wz1Xbz2  t t2 t3
Or do I instead need to generate mean and centred versions of these time variables as well (I am tending toward the former since it does make much sense to me to model peace years as a cluster-average or cluster-deviation)

Further to this, I would also like to include an interaction between ,say, wz1 and t t2 t3. But , of course, to do so, I first need to know how these time variables should be specified in the model.

Finally, I should add that t t2 t3 - as a running count of the number years since conflict - are distinct from the actual time series variable, which is simply the year of observation.

Any advice would be hugely appreciated.

Matthew