Stata’s mixed for fitting linear multilevel models supports survey data. Sampling weights and robust/cluster standard errors are available.
Sampling weights are handled differently by mixed:
See [ME] mixed and, in particular, section Survey data in that entry for all the technical details.
We demonstrate using mixed to fit a two-level model for data from a two-stage sampling design with sampling weights at both stages. Schools were sampled at the first stage, students at the second.
. webuse pisa2000 (Programme for International Student Assessment (PISA) 2000 data) . mixed isei female high_school college one_for both_for test_lang [pw=w_fstuwt] || id_school:, pweight(wnrschbw) pwscale(size) nolog Mixed-effects regression Number of obs = 2,069 Group variable: id_school Number of groups = 148 Obs per group: min = 1 avg = 14.0 max = 28 Wald chi2(6) = 187.23 Log pseudolikelihood = -1443093.9 Prob > chi2 = 0.0000 (Std. err. adjusted for 148 clusters in id_school)
|isei||Coefficient std. err. z P>|z| [95% conf. interval]|
|female||.59379 .8732886 0.68 0.497 -1.117824 2.305404|
|high_school||6.410618 1.500337 4.27 0.000 3.470011 9.351224|
|college||19.39494 2.121145 9.14 0.000 15.23757 23.55231|
|one_for||-.9584613 1.789947 -0.54 0.592 -4.466692 2.54977|
|both_for||-.2021101 2.32633 -0.09 0.931 -4.761633 4.357413|
|test_lang||2.519539 2.393165 1.05 0.292 -2.170978 7.210056|
|_cons||28.10788 2.435712 11.54 0.000 23.33397 32.88179|
|Random-effects parameters||Estimate std. err. [95% conf. interval]|
|var(_cons)||34.69374 8.574865 21.37318 56.31617|
|var(Residual)||218.7382 11.22111 197.8147 241.8748|
In the above, we specified the student-level weights using standard Stata weight syntax [pw=w_fstuwt] and the school-level weights with the pweight(wnrschbw) option as part of the school random-effects equation. We also specified pwscale(size) to rescale the student-level weights using one of three available methods.
Sampling weights imply robust standard errors, and in the case of mixed, standard errors are clustered at the highest level (schools in this example) unless you specify otherwise.
See [ME] mixed for more details.