[R-sig-ME] Methodological and practical issues about survey weights using lme4

[Fernando Pedro Bruna Quintas]

Dear list members,

I have two questions about the use of survey weights in multilevel models.

I have estimated a multilevel model about the effects of individual and cultural variables in well-being, using the European Social Survey. By �culture� I mean national aggregates of my level-1 indicators. Think of Yij as an indicator of wellbeing, Xij as an indicator of being individualistic (for instance) and Xj as the sample country mean of individualism, representing the degree of individualism in a national culture (contextual effect).

I have estimated the following simplified model:
lmer( Yij  ~ (Xij-Xj) + Xj + (1 | country) ) , data=databank)

A referee makes me the following comment: �Post stratication weights at individual level and at the higher-level national variables is a relevant issue. This issue of importance on MLM context as Stata instructions note https://www.stata.com/features/overview/multilevel-models-with-survey-data/. The authors seem to be using R but I would assume it includes similar options to include weights to all levels of the analysis. The literature on MLM includes recommendations for Fitting multilevel models in complex survey data with design weights and this needs to be referred and selection of weights justified.�

The information about weights in the survey I am using is in the following link:
https://www.europeansocialsurvey.org/methodology/ess_methodology/data_processing_archiving/weighting.html

My questions are the following:

  1.  A first questions is about general methodology, though applied to the analysis of the effects of level-two variables. I would appreciate references or links about when is appropriate to use survey weights, depending on the research question. I have data on 23 countries. My goal is to measure the effects of level-two (cultural variables). Therefore, I am not so much interested on concluding about big countries (Russia has 145 million of people!). I need variance to differentiate cultural effects in Belgium, Netherlands... However, If I do not use weights my conclusions are only about the particular sample published by the European Social Survey. Any thought?
  2.  Apart from that, and more generally for any other study, I would appreciate comments and references about using survey weights in lme4. I understand that I would have to change the calculation of all may level-one variables, which are defined as deviations to the national means. Additionally, I must consider reweighting national means of those variables, as well as other level-two variables. The estimation procedure has to be weighted... I would appreciate any practical comment about weighted estimation using survey data and lme4.

Thank you very much,

Fernando Bruna
Department of Economics
University of A Corunha (Coru�a), Spain


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