mixed - Stata

12 mixed — Multilevel mixed-effects linear regression
6. The second estimation table shows the estimated variance components. The first section of the
table is labeled id: Identity, meaning that these are random effects at the id (pig) level and that
their variance–covariance matrix is a multiple of the identity matrix; that is, Σ = σuI. 2 Because
we have only one random effect at this level, mixed knew that Identity is the only possible
covariance structure. In any case, the variance of the level-two errors, σu 2 , is estimated as 14.82
with standard error 3.12.
7. The row labeled var(Residual) displays the estimated variance of the overall error term; that
is, ̂σ 2 ɛ = 4.38. This is the variance of the level-one errors, that is, the residuals.
8. Finally, a likelihood-ratio test comparing the model with one-level ordinary linear regression, model
(4) without u j , is provided and is highly significant for these data.
We now store our estimates for later use:
. estimates store randint
Example 2
Extending (4) to allow for a random slope on week yields the model
and we fit this with mixed:
. mixed weight week || id: week
Performing EM optimization:
weight ij = β 0 + β 1 week ij + u 0j + u 1j week ij + ɛ ij (5)
Performing gradient-based optimization:
Iteration 0: log likelihood = -869.03825
Iteration 1: log likelihood = -869.03825
Computing standard errors:
Mixed-effects ML regression Number of obs = 432
Group variable: id Number of groups = 48
Obs per group: min = 9
avg = 9.0
max = 9
Wald chi2(1) = 4689.51
Log likelihood = -869.03825 Prob > chi2 = 0.0000
weight Coef. Std. Err. z P>|z| [95% Conf. Interval]
week 6.209896 .0906819 68.48 0.000 6.032163 6.387629
_cons 19.35561 .3979159 48.64 0.000 18.57571 20.13551
Random-effects Parameters Estimate Std. Err. [95% Conf. Interval]
id: Independent
var(week) .3680668 .0801181 .2402389 .5639103
var(_cons) 6.756364 1.543503 4.317721 10.57235
var(Residual) 1.598811 .1233988 1.374358 1.85992
LR test vs. linear regression: chi2(2) = 764.42 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estimates store randslope