xtreg and xtmixed: recap

1
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.
2
And this you can do with xtreg

• xtset ltclustervariablegt
• 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.

3
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
4
And this you can do with xtmixed

• xtmixed y x1 ltclustervargt
• is just like the xtreg command, but if you want
  random slopes for x1, you add x1 after the
• xtmixed y x1 ltclustervargt x1
• Your output then gives you estimates for the
  variance (or standard deviation) of delta and
  zeta.

5
(No Transcript)
6
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.
7
And this you can do with xtmixed as well

• xtmixed y x1 school class
• Remember to put the bigger cluster on the left!

8
(No Transcript)
9
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 pre-check yourselves.

10
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.