I'm interested in conducting an individual patient data (IPD) meta-analysis in which the main outcome of interest is a correlation coefficient between and IV and DV.
The IV is measured slightly differently across studies, and conversion to make them all match is not possible. Clearly, I can still do a two-stage IPD meta-analysis based on correlation coefficients calculated for each study individually. I would also like to conduct a one-stage IPD analysis using linear mixed modeling (with random intercepts and/or slopes by study) for a few reasons: to more flexibly model an important covariate, to assess whether the relationship between IV and DV is linear, and to model aggregation bias (per Stewart et al. 2012).
Given the heterogeneity in the IV measures, is this still possible?
Added plot to demonstrate the problem.
Would it make sense, in this case, to standardize the variables within-study before conducting IPD meta-analysis? I'm worried that such an approach would lose across-study effects X.