Aggregating coefficients in a meta-analysis I have a question about the treatment of data in a meta-analysis.
It is quite common in this particular field for researchers to essentially use data twice for analysis: once as a normal bivariate correlation between variable A and B and then again in a multiple-regression context where they model the relationship between A and B as a quadratic function, while also including a couple of other predictors. Theoretically it makes more sense to treat the relationship as non-linear, but some researchers treat the relationship as linear, while others treat it as non-linear, while some even just report both, as mentioned above. 
What is the most appropriate way of dealing with this situation? Can I just aggregate the unstandardized coefficients, regardless of how the researchers treated the relationship?      
 A: If you are combining coefficients, you want those coefficients to be estimating, as far as possible, the same thing. If one study controls for some covariates, and another study does not, then it's possible that they are estimating very different effects. The relationship between height and weight in children, for example, is different to the relationship between height and weight in children, controlling for age.
Sometimes you might consider different sets of covariates to be attempts to estimate the same thing - but different covariates were relevant, or one study attempted to estimate an effect using a randomized trial, and a second attempted to use propensity scores.
The heterogeneity statistic might be useful if you do decide to combine studies, as might the use of study level moderators.
A: The main problem I foresee here apart from the issues of the comparability of the other covariates which Jeremy Miles has outlined in another answer is combining the linear and quadratic coefficients simultaneously. To do this you will need a multivariate meta-analysis which is not the main problem as that is available in standard statistical software like R and Stata. However you will also need the variance-covariance matrix of the coefficients (or at least the covariance for the linear and quadratic coefficients) and I suspect this will not have been published.
