mixed - Stata

36 mixed — Multilevel mixed-effects linear regression
The R.varname notation is equivalent to giving a list of overparameterized (none dropped)
indicator variables for use in a random-effects specification. When you specify R.varname, mixed
handles the calculations internally rather than creating the indicators in the data. Because the set of
indicators is overparameterized, R.varname implies noconstant. You can include factor variables in
the fixed-effects specification by using standard methods; see [U] 11.4.3 Factor variables. However,
random-effects equations support only the R.varname factor specification. For more complex factor
specifications (such as interactions) in random-effects equations, use generate to form the variables
manually, as we demonstrated in example 6.
Technical note
Although we were able to fit the crossed-effects model (8), it came at the expense of increasing the
column dimension of our random-effects design from 2 in model (5) to 57 in model (8). Computation
time and memory requirements grow (roughly) quadratically with the dimension of the random effects.
As a result, fitting such crossed-effects models is feasible only when the total column dimension is
small to moderate.
Reexamining model (8), we note that if we drop u i , we end up with a model equivalent to (4),
meaning that we could have fit (4) by typing
instead of
. mixed weight week || _all: R.id
. mixed weight week || id:
as we did when we originally fit the model. The results of both estimations are identical, but the
latter specification, organized at the cluster (pig) level with random-effects dimension 1 (a random
intercept) is much more computationally efficient. Whereas with the first form we are limited in how
many pigs we can analyze, there is no such limitation with the second form.
Furthermore, we fit model (8) by using
. mixed weight week || _all: R.week || _all: R.id
as a direct way to demonstrate the R. notation. However, we can technically treat pigs as nested
within the all group, yielding the equivalent and more efficient (total column dimension 10) way
to fit (8):
. mixed weight week || _all: R.week || id:
We leave it to you to verify that both produce identical results. See Rabe-Hesketh and Skrondal (2012)
for additional techniques to make calculations more efficient in more complex models.
Example 11
As another example of how the same model may be fit in different ways by using mixed (and
as a way to demonstrate covariance(exchangeable)), consider the three-level model used in
example 4:
y jk = X jk β + u (3)
k
+ u (2)
jk + ɛ jk