[R] Metafor multilevel metaregression: total variance increases when moderator added?

[Duncan, Laura]

Hi there,

I am running a two level multilevel meta-regression of 170 estimates nested within 3 informants nested within 26 studies. I run the null model to get a pooled estimate with random effects at the informant level and study level.

Then I test a series of potential moderators (one at a time, given small number of studies and adjust p-values for multiple testing). I use:
(sum(Model1$sigma2) - sum(Model2$sigma2)) / sum(Model1$sigma2)
to compute the proportional reduction in the total variance from here:
http://stackoverflow.com/questions/22356450/getting-r-squared-from-a-mixed-effects-multilevel-model-in-metafor

For one moderator, I get a negative value for reduced total variance and an unexpected negative coefficient. Based on Wolfgang's response in the link above this is possible "depending on the size of your dataset, those variance components may not be estimated very precisely and that can lead to such counter-intuitive results".

I am trying to diagnose why this model is not being estimated properly and why I am getting an unexpected negative result. When I remove the second level from the model and run a single-level random effects models of 170 estimates nested within 26 studies, the coefficient is positive and as we would expect.

Does anyone have any suggestions for what might be going on or how I might diagnose the problem with this model?

Thanks,
Laura

Laura Duncan, M.A.
Research Coordinator
Offord Centre for Child Studies
McMaster University

Tel: 905 525 9140 x21504
Fax: 905 574 6665
duncanlj at mcmaster.ca
ontariochildhealthstudy.ca<www.ontariochildhealthstudy.ca>
offordcentre.com

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