xtreg and xtmixed: recap
We have the standard regression model (here with only one x):
but think that the data are clustered, and that the intercept (c0) might be different
for different clusters
… where the S-variables are dummies per cluster.
Because k can be large, this is not always feasible to estimate. Instead we estimate:
… with the delta normally distributed with zero mean and variance to be estimated.
And this you can do with xtreg
xtset <clustervariable>
xtreg y x1
… and by doing this, we are trying to take into
account the fact that the errors are otherwise not
independent.
But, it might be that you want to test also whether
the coefficient of x1 varies across the clusters.
What if c1 varies as well?
The same argument applies. We already had:
… and now make the c1 coefficient dependent on the cluster (“random slopes”)
This is not feasible to estimate, so instead we want to model:
… with zeta a normally distributed variable with zero mean and variance to be estimated
And this you can do with xtmixed
xtmixed y x1 || <clustervar>:
is just like the xtreg command, but if you want
random slopes for x1, you add x1 after the “:”
xtmixed y x1 || <clustervar>: x1
Your output then gives you estimates for the
variance (or standard deviation) of delta and zeta.
xtmixed can deal with nested clusters as well
(“classes within schools”)
Again the same kind of argument applies. We already had:
… and we want separate constant terms per class and per school
So we estimate instead:
… where delta is again a normally distributed variable at the school level with zero
mean and variance to be estimated, and tau is a normally distributed variable at the
class level with zero mean and variance to be estimated.
And this you can do with xtmixed as well
xtmixed y x1 || school: || class:
Remember to put the bigger cluster on the left!
Horrors
xtmixed finds its estimates using an iterative process.
That can complicate matters:
– it might not converge
– it might converge but to the wrong values
– it might converge to different estimates for different algorithms
in the iterative process
You have only a couple of weapons against that:
– run again using a different algorithm (use option “, mle”)
– Allow estimation of correlations as well (use option,
“cov(unstr)”)
– run the dummy-variant (with lots of dummies) anyway
In principle, I will try to make sure that such issues will not
occur, but I cannot be sure. This is also something you can precheck yourselves.
Splitting up variables (within vs across clusters)
Basically this is completely unrelated to the previous.
The important thing is that it can be done in
clustered data, and can lead to different
interpretations (see before)
There are two separate issues:
- which coefficients do you want to vary per cluster?
- which variables do you want to include?
Splitting up variables is related to the second
question, not the first.