[R-meta] Meta-analysis of linear and non-linear associations: R2 as the “effect size”?

[Werner, M.A. (Marlene)]

Dear all,

I have a question regarding meta-analysis of effect sizes of associations.
I was wondering whether it is possible to somehow quantitatively summarize results across studies that modelled the association between two variables "linearly" (e.g. using simple linear regression) vs. others that modelled the association "non-linearly" (e.g. polynomials or splines). One variable is continuous (hormone concentration) and the other is ordinal (self-report of well-being).
For instance, would it be possible to meta-analyze the (adjusted) R2 as the "effect size"? If so, how would one go about the meta-analytic steps?
I figured that meta-analysis of proportions might be applicable, but then I would need the counts on which the proportion is based, which is not directly available for this �proportion�, especially not in the non-linear case.

I started thinking about meta-analyzing "explained variance" in the first place because I cannot summarize the "regression coefficients" across these models; �non-linear models� include several coefficients, whereas �linear models� only provide one.
Then again, R2 is not really applicable as a goodness of fit measure for non-linear models. So which other "summary statistic" to use that is available and comparable for these models, even when comparing them in a non-quantitative way? Would the Standard Error of the Regression be an option? But how to standardize it to make it comparable across studies?

I would be very grateful for any ideas or pointers! Thanks in advance!

(Note that I have posted the same q on stackexchange: https://stats.stackexchange.com/questions/513164/meta-analysis-of-linear-and-non-linear-associations-r2-as-the-effect-size?; I hope that is ok!)

All the best,

Marlene Werner

Drs. M.A. (Marlene) Werner  |  PhD candidate
Department of Gynaecology and Obstetrics / Sexology and Psychosomatic Gynaecology
Location AMC | H4-236 | Meibergdreef 9, 1105 AZ Amsterdam
E: m.a.werner using amsterdamumc.nl<mailto:m.a.werner using amsterdamumc.nl>
www.amsterdamumc.nl<http://www.amsterdamumc.nl/>

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