mixed - Stata

18 mixed — Multilevel mixed-effects linear regression
Random-effects Parameters Estimate Std. Err. [95% Conf. Interval]
region: Identity
state: Identity
var(_cons) .0014506 .0012995 .0002506 .0083957
var(_cons) .0062757 .0014871 .0039442 .0099855
Notes:
var(Residual) .0013461 .0000689 .0012176 .0014882
LR test vs. linear regression: chi2(2) = 1154.73 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
1. Our model now has two random-effects equations, separated by ||. The first is a random intercept
(constant only) at the region level (level three), and the second is a random intercept at the state
level (level two). The order in which these are specified (from left to right) is significant—mixed
assumes that state is nested within region.
2. The information on groups is now displayed as a table, with one row for each grouping. You can
suppress this table with the nogroup or the noheader option, which will suppress the rest of the
header, as well.
3. The variance-component estimates are now organized and labeled according to level.
After adjusting for the nested-level error structure, we find that the highway and water components
of public capital had significant positive effects on private output, whereas the other public buildings
component had a negative effect.
Technical note
In the previous example, the states are coded 1–48 and are nested within nine regions. mixed
treated the states as nested within regions, regardless of whether the codes for each state were unique
between regions. That is, even if codes for states were duplicated between regions, mixed would
have enforced the nesting and produced the same results.
The group information at the top of the mixed output and that produced by the postestimation
command estat group (see [ME] mixed postestimation) take the nesting into account. The statistics
are thus not necessarily what you would get if you instead tabulated each group variable individually.
Model (7) extends in a straightforward manner to more than three levels, as does the specification
of such models in mixed.
Blocked-diagonal covariance structures
Covariance matrices of random effects within an equation can be modeled either as a multiple of
the identity matrix, as diagonal (that is, Independent), as exchangeable, or as general symmetric
(Unstructured). These may also be combined to produce more complex block-diagonal covariance
structures, effectively placing constraints on the variance components.