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edited Nov 28, 2013 at 22:53

thesixmax

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I am currently working on a random intercept multilevel model using the European Social Survey round 6 dataset. It is a 2-level model with individuals (level 1) nested within countries (level 2). To simplify things, let's look atimagine the following regression:

where the dependent variable is trust in the European Parliament on a scale from 0-10, and the level-1 predictor is gender. In the data set, there exists two weights exists:

My question is: do I need to specify the population size weights when I run the multilevel model? I clearlytend to get different results. Below is the regression only usingwith design weights apllied (I am using Stata):

And here is the regression usingwith both design weights, population size weights and scaling applied:

I can't figure out how the population weights influence the ML estimates. In theThe official documentation for ESS, they write the following documentation says:

The question is, whether I actually just compare countries, or compare them to an overall mean. The latter seems for me to be correct, as the parameter estimates actually relate to the overall mean $\mu_{00}$. But I may be wrong. The Stata manual has an extensive section on weighting here but it did not clear things up for me. Any suggestions?

I am currently working on a random intercept multilevel model using the European Social Survey round 6 dataset. It is a 2-level model with individuals (level 1) nested within countries (level 2). To simplify things, let's look at the following regression:

where the dependent variable is trust in the European Parliament on a scale from 0-10, and the level-1 predictor is gender. In the data set, two weights exists:

My question is: do I need to specify the population size weights when I run the multilevel model? I clearly get different results. Below is the regression only using design weights (I am using Stata):

And here is the regression using both design weights, population size weights and scaling:

I can't figure out how the population weights influence the ML estimates. In the official documentation for ESS, they write the following:

The question is, whether I actually just compare countries, or compare them to an overall mean. The latter seems for me to be correct, as the parameter estimates actually relate to the overall mean $\mu_{00}$. But I may be wrong. The Stata manual has an extensive section on weighting here but it did not clear things up for me. Any suggestions?

I am currently working on a random intercept multilevel model using the European Social Survey round 6 dataset. It is a 2-level model with individuals (level 1) nested within countries (level 2). To simplify things, imagine the following regression:

where the dependent variable is trust in the European Parliament on a scale from 0-10, and the level-1 predictor is gender. In the data set, there exists two weights:

My question is: do I need to specify the population size weights when I run the multilevel model? I tend to get different results. Below is the regression with design weights apllied (I am using Stata):

And here is the regression with both design weights, population size weights and scaling applied:

I can't figure out how the population weights influence the ML estimates. The official ESS documentation says:

The question is, whether I actually just compare countries, or compare them to an overall mean. The latter seems to be correct, as the parameter estimates actually relate to the overall mean $\mu_{00}$. But I may be wrong. The Stata manual has an extensive section on weighting here but it did not clear things up for me. Any suggestions?

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edit approved Nov 28, 2013 at 22:05

Roberto Ferrer

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where the dependent variable is 'trust in the European Parliament'trust in the European Parliament on a scale from 0-10, and the level-1 predictor is gendergender. In the data set, two weights exists:

Design weightDesign weight: The design weights are inclusion probabilities for individuals $i$ in countries $j$. The design weight corrects for slightly different probabilities of selection, thereby making the sample more representative of a ‘true’ sample of individuals from each country.
Population size weightsPopulation size weights: The population size weight makes an adjustment to ensure that each country is represented in proportion to its population size. The population size weight is calculated as PWEIGHT= [Population size]/[(Net sample size in data file)*10 000]

My question is now -: do I need to specify the population size weights when I run the multilevel model? I clearly get different results. Below is the regression only using design weights (I am using STATAStata):

And here is the regression using both deisgndesign weights, population size weights and scaling:

The question is, whether I actually just compare countries, or compare them to an overall mean. The latter seems for me to be correct, as the parameter estimates actually relate to the overall mean $\mu_{00}$. But I may be wrong. The STATAStata manual has an extensive section on weighting here but it did not clear things up for me. Any suggestions?

where the dependent variable is 'trust in the European Parliament' on a scale from 0-10, and the level-1 predictor is gender. In the data set, two weights exists:

Design weight: The design weights are inclusion probabilities for individuals $i$ in countries $j$. The design weight corrects for slightly different probabilities of selection, thereby making the sample more representative of a ‘true’ sample of individuals from each country.
Population size weights: The population size weight makes an adjustment to ensure that each country is represented in proportion to its population size. The population size weight is calculated as PWEIGHT= [Population size]/[(Net sample size in data file)*10 000]

My question is now - do I need to specify the population size weights when I run the multilevel model? I clearly get different results. Below is the regression only using design weights (I am using STATA):

And here is the regression using both deisgn weights, population size weights and scaling:

The question is, whether I actually just compare countries, or compare them to an overall mean. The latter seems for me to be correct, as the parameter estimates actually relate to the overall mean $\mu_{00}$. But I may be wrong. The STATA manual has an extensive section on weighting here but it did not clear things up for me. Any suggestions?

where the dependent variable is trust in the European Parliament on a scale from 0-10, and the level-1 predictor is gender. In the data set, two weights exists:

Design weight: The design weights are inclusion probabilities for individuals $i$ in countries $j$. The design weight corrects for slightly different probabilities of selection, thereby making the sample more representative of a ‘true’ sample of individuals from each country.
Population size weights: The population size weight makes an adjustment to ensure that each country is represented in proportion to its population size. The population size weight is calculated as PWEIGHT= [Population size]/[(Net sample size in data file)*10 000]

My question is: do I need to specify the population size weights when I run the multilevel model? I clearly get different results. Below is the regression only using design weights (I am using Stata):

And here is the regression using both design weights, population size weights and scaling:

The question is, whether I actually just compare countries, or compare them to an overall mean. The latter seems for me to be correct, as the parameter estimates actually relate to the overall mean $\mu_{00}$. But I may be wrong. The Stata manual has an extensive section on weighting here but it did not clear things up for me. Any suggestions?

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asked Nov 28, 2013 at 21:19

thesixmax

125
2
7

Multiple weights in multilevel models

I am currently working on a random intercept multilevel model using the European Social Survey round 6 dataset. It is a 2-level model with individuals (level 1) nested within countries (level 2). To simplify things, let's look at the following regression:

$Y_{ij}=\beta_{0j}+\beta_{1j}X_{ij}+e_{ij}$

where the dependent variable is 'trust in the European Parliament' on a scale from 0-10, and the level-1 predictor is gender. In the data set, two weights exists:

Design weight: The design weights are inclusion probabilities for individuals $i$ in countries $j$. The design weight corrects for slightly different probabilities of selection, thereby making the sample more representative of a ‘true’ sample of individuals from each country.
Population size weights: The population size weight makes an adjustment to ensure that each country is represented in proportion to its population size. The population size weight is calculated as PWEIGHT= [Population size]/[(Net sample size in data file)*10 000]

My question is now - do I need to specify the population size weights when I run the multilevel model? I clearly get different results. Below is the regression only using design weights (I am using STATA):

. xtmixed trstep gndr [pw = dweight]|| land:, mle var 

Obtaining starting values by EM: 

Performing gradient-based optimization: 

Iteration 0:   log pseudolikelihood =  -92442,22  
Iteration 1:   log pseudolikelihood =  -92442,22  (backed up)

Computing standard errors:

Mixed-effects regression                        Number of obs      =     39923
Group variable: land                            Number of groups   =        24

                                                Obs per group: min =       579
                                                               avg =    1663,5
                                                               max =      2711


                                                Wald chi2(1)       =      5,91
Log pseudolikelihood =  -92442,22               Prob > chi2        =    0,0151

                                  (Std. Err. adjusted for 24 clusters in land)
------------------------------------------------------------------------------
             |               Robust
      trstep |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        gndr |   ,1147821   ,0472334     2,43   0,015     ,0222063    ,2073578
       _cons |   4,144926    ,117911    35,15   0,000     3,913825    4,376027
------------------------------------------------------------------------------

------------------------------------------------------------------------------
                             |               Robust           
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
land: Identity               |
                  var(_cons) |   ,3184852   ,0689119      ,2084065    ,4867066
-----------------------------+------------------------------------------------
               var(Residual) |    5,93535   ,2514202      5,462477    6,449158
------------------------------------------------------------------------------

And here is the regression using both deisgn weights, population size weights and scaling:

. xtmixed trstep gndr [pw = dweight]|| land:, mle var pweight(pweight) pwscale(size)

Obtaining starting values by EM: 

Performing gradient-based optimization: 

Iteration 0:   log pseudolikelihood = -81334,099  
Iteration 1:   log pseudolikelihood =  -81333,24  
Iteration 2:   log pseudolikelihood =  -81333,24  

Computing standard errors:

Mixed-effects regression                        Number of obs      =     39923
Group variable: land                            Number of groups   =        24

                                                Obs per group: min =       579
                                                               avg =    1663,5
                                                               max =      2711


                                                Wald chi2(1)       =     10,73
Log pseudolikelihood =  -81333,24               Prob > chi2        =    0,0011

                                  (Std. Err. adjusted for 24 clusters in land)
------------------------------------------------------------------------------
             |               Robust
      trstep |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        gndr |   ,1680609   ,0513105     3,28   0,001     ,0674942    ,2686276
       _cons |   3,745146   ,1854299    20,20   0,000      3,38171    4,108582
------------------------------------------------------------------------------

------------------------------------------------------------------------------
                             |               Robust           
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
land: Identity               |
                  var(_cons) |   ,2645594   ,0598105      ,1698583     ,412059
-----------------------------+------------------------------------------------
               var(Residual) |   6,070198   ,3532338      5,415894    6,803549
------------------------------------------------------------------------------

I can't figure out how the population weights influence the ML estimates. In the official documentation for ESS, they write the following:

When comparing data from two or more countries but without reference to the average (or combined total) of those countries, only the design weight need be applied. When comparing data of two or more countries and with reference to the average (or combined total) of those countries, both design and population size weights should be applied. (ESS Documentation)

The question is, whether I actually just compare countries, or compare them to an overall mean. The latter seems for me to be correct, as the parameter estimates actually relate to the overall mean $\mu_{00}$. But I may be wrong. The STATA manual has an extensive section on weighting here but it did not clear things up for me. Any suggestions?

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Multiple weights in multilevel models