I'm doing a meta-analysis which involves some multiple logistic regression. As it's a meta-analysis, I'm compiling data from various studies, which therefore differ slightly in their methodology. One particular aspect of methodology is likely to affect the response variable, and I therefore decided to include it as a random effect in my models.
However, now I'm being asked to provide more information about the likely effect of this predictor. Is it significant? How strong is the effect? The only way I can think to do so is to treat it as a fixed effect and see if adding/removing it improves the model or not, using F tests to compare models (they are quasi-binomial models). However, I had a feeling that treating variables as both random and fixed variables was wrong - it should be one of the other. I've never quite got a grip on the difference between the two, and would appreciate any advice. Thanks
edit: Here's a bit more info about my study. In my meta-analysis I'm comparing the results of other studies to my own study. The response in the model is the similarity in the data. Regarding this particular aspect of methodology, I used "method A". If all the other studies used "method A" it would be fine, but some used "method A", some "method B", some "method C" and some "method D". Each different method will introduce bias, but may do so to a different degree. Hope that makes sense.