I am doing a study about an intervention targeting pupils of schools, in different cities. Thus, it is a multilevel structure and I am using mixed models for regression analyses. Contextual factors, related with cities, could be explanatory variables for the outcome. In this manner, the variable “city” is a proxy of such contextual factors. But, the variable “city” is also a clustering variable of the multilevel model.
Now, the question:
Is it appropriate to include the clustering variable “city” as confounder variable in the multilevel mixed models when “city” is also included as a hierarchical cluster variable?
Thank you very much.
Andrés.
Andres - revised answer
Probabaly not as if you include city as a categorical variable it will have to be as a set of n-1 dummies. I would suggest that if you think that being in particular cities is important and that you have quite a few of them (say more than 15) that you include as a third level so that pupils are nested in schools nested within cities. This would be an efficient way of doing it.You can then include observed variables for schools and cities in the fixed part of the model. If there are say only three cities I would use a two level model and include 2 dummies for the cities and possibly cross level interactions with the pupil variables.
You could also use the pupil variables to derive contextual variables for the schools of these can be measured directly. One simple way to do this that reduces measurement error is to have a two level model with the pupil predictor variables at the response and estimate the precision-weighted school effect - see this RGate paper
Do multilevel models ever give different results?.
https://www.researchgate.net/publication/252146040_Do_multilevel_models_ever_give_different_results?ev=prf_pub
I have placed a training manual on Research gate and there is a chapter on a three level model - if you have few schools and cities I would consider estimating the models with Bayesian MCMC procedure - this is also consider in the training materials
see
https://www.researchgate.net/publication/260771330_Developing_multilevel_models_for_analysing_contextuality_heterogeneity_and_change_using_MLwiN_Volume_1_%28updated_June_2014%29?ev=prf_pub
Best wishes and succesful modelling!
Kelvyn
Article Do multilevel models ever give different results?.
Book Developing multilevel models for analysing contextuality, he...
Andrés,
Another possibility (assuming you are estimating a 3-level model) is to group-mean-center the outcomes by city, in addition to considering the clustering.
Though it looks as though Kelvyn is much more on top of this than I am, and can likely weigh in on the pros and cons.
Pat
I with Andy Bell have wriiten this paper on the use of group mean centering and placed it on Research Gate
Explaining Fixed Effects: Random Effects modelling of Time-Series Cross-Sectional and Panel Data; Andrew Bell Kelvyn Jones
https://www.researchgate.net/publication/233756428_Explaining_Fixed_Effects_Random_Effects_modelling_of_Time-Series_Cross-Sectional_and_Panel_Data
We are highly in favour of doing this and include group mean and the variable that has been grouped centred
Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...
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