I would be very grateful if someone could offer some ideas or point to relevant literature on the calculation of partial correlation coefficients (PCCs) using estimates from multi-level analyses.
Currently we are conducting a meta-analysis which draws on data from multiple regression models and uses PCC as a common effect size metric. So, for every relevant coefficient estimate included in our meta-analysis we are estimating a PCC. Some of the models included in our meta-analysis come from multi-level analyses. Our predictors of interest are at level 1, so is the outcome measure.
The regular formula for estimating PCC is the following (Stanley and Doucouliagos 2012):
r=t/sqrt(t²+df), where t is the t-statistic of a regression coefficient and df is degrees of freedom.
To estimate PCCs, we are using escalc function from metafor package in R. Using this function, one has to provide the number of predictors, total sample size and the t-statistic as inputs.
We are a bit unsure about the correct way to estimate PCCs using estimates from multi-level models, given that the calculation of degrees of freedom in multi-level models is different from that applied in single-level regression. In particular, I am wondering what figure we should provide for mi argument (total number of predictors) when estimating PCCs from multi-level models. Should we take the sum of level 1 and level 2 predictors? Should we take into account the number of level 2 units when specifying this argument? Perhaps escalc is not suitable for calculating PCCs when coefficient estimates come from multi-level models at all?
Any help would be greatly appreciated – thank you very much for your time.
