[R-meta] Question about explained variance at 2nd and 3rd level

[Willemijn van Eldik]

Dear colleagues,

Gratefully, I am making use of your R Package Metafor to conduct a three-level meta-analysis. I have a question and I hope that you can help me with this question.
Shortly, I am conducting several meta-analyses for the association between the interparental relationship and children’s problem behavior. The ES of interest is r (z-transformed) and my dataset concerns 1601 ES from 206 independent samples.
I am conducting several univariate moderator analyses, mostly using categorical moderator (dummies).

I would like to extract from the moderator analysis how much variance one moderator explains at the 2nd and 3rdlevel. My assumption is that I can use the sigma-components, to compare nested models, to calculate this amount of explained variance. Following this reasoning, I would have expected the sigma-component to become smaller in significant moderator models, compared to the overall model (without moderators). However, the sigma-components are not consistently becoming smaller when a significant moderator is added to the model. Neither are the sigma-components consistent in amount, e.g. getting larger, is some models including a non-significant moderator.
Based on these observations of the output, I am hestitant to use the sigma-components to  evaluate the explained variance by a moderator on each level. My first assumption was that this was caused by missing values in moderator analyses. However, this shows even when no missing values are present. But maybe I missed something or are mistaken somewhere.

My questions are;
-         -  Is it true that this is caused by missing values and the consequence that these models are not comparable with a different N?
-          - Is there another reason (in case there are no missing values)?
-          - And most important: is there another way of evaluating the explained variance by a moderator?

Thanking you in advance,

Best regards,
Willemijn van Eldik
​
PhD Candidate

Erasmus University Rotterdam
Department of Psychology, Education & Child Studies, ESSB
Location Mandeville (T) 16, Burg. Oudlaan 50, Room T16-15
Postbus 1738
3000 DR  Rotterdam
E: vaneldik at essb.eur.nl<mailto:vaneldik at essb.eur.nl> T: 0031104089730


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