Effect size assumptions for meta-analysis

Question

As part of a project I needed to run separate multilevel proportional odds models independently for different years in my data using meta-analysis. I want to pool the estimates across studies. All continuous variables in my models were grand-mean centered and z-score transformed.

I have the luxury of every independent variable, as well as dependent variable, being the same in all of my analyses. I am not familiar with the proper effect size to use in these analyses for multilevel proportional odds models. In addition, I'm wondering how much the effect size matters given that everything in these models, aside from the sample sizes, are identical? I'm also already reporting my results in standard deviation units.

I've begun to wonder about this hypothetical... if all the variables in your models were identical, and your intention was not to generalize beyond your sampling frame, could you not use the an unstandardized metric in these analyses?

Answer 1

The usual approach in the situation where you have a number of predictors in your model would be to extract their coefficients which in this case would presumably be being analysed on the log scale. If you want to meta-analyse them all simultaneously you would then also extract the variance-covariance matrix for the coefficients from each primary analysis. Having all that to hand you would then use your favourite multivariate meta-analysis program to do the meta-analysis.

Your proposal to do an unweighted analysis is one which is practical in univariate meta-analysis but it is not clear to me how to do this while still taking account of the lack of independence between estimates of the coefficients.