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?