mixed - Stata

mixed — Multilevel mixed-effects linear regression 13
Because we did not specify a covariance structure for the random effects (u 0j , u 1j ) ′ , mixed used
the default Independent structure; that is,
[ ] [ ]
u0j σ
2
Σ = Var = u0 0
u 1j 0 σu1
2
with ̂σ u0 2 = 6.76 and ̂σ u1 2 = 0.37. Our point estimates of the fixed effects are essentially identical to
those from model (4), but note that this does not hold generally. Given the 95% confidence interval
for ̂σ u1 2 , it would seem that the random slope is significant, and we can use lrtest and our two
stored estimation results to verify this fact:
. lrtest randslope randint
Likelihood-ratio test LR chi2(1) = 291.78
(Assumption: randint nested in randslope) Prob > chi2 = 0.0000
Note: The reported degrees of freedom assumes the null hypothesis is not on
the boundary of the parameter space. If this is not true, then the
reported test is conservative.
The near-zero significance level favors the model that allows for a random pig-specific regression
line over the model that allows only for a pig-specific shift.
(6)
Covariance structures
In example 2, we fit a model with the default Independent covariance given in (6). Within any
random-effects level specification, we can override this default by specifying an alternative covariance
structure via the covariance() option.
Example 3
We generalize (6) to allow u 0j and u 1j to be correlated; that is,
[ ] [ ]
u0j σ
2
Σ = Var = u0 σ 01
u 1j σ 01 σu1
2