Multilevel models with survey data

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:

1. Weights can (and should be) specified at every model level unless you wish to assume equiprobability sampling at that level.

2. Weights at lower model levels need to indicate selection conditional on selection of the higher-level cluster and not merely indicate overall selection.

3. The scaling of weights at lower levels needs to be considered. Unlike a standard analysis where the scale of the sampling weights is not an issue (only their relative sizes matter), in multilevel models weight scales need to be made "consistent" across lower-level clusters.

See [ME] mixed and, in particular, the Survey data section 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)




             
 
 
               Robust

        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







                             
 
 
               Robust           

  Random-effects parameters  
 
   Estimate   std. err.     [95% conf. interval]

 
 
 

id_school: Identity          
 

                  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.