# Meta-regression with dependent variables of different types

The textbook examples of metaregression I demonstrate how to combine coefficients when the dependent variable has the one distribution (for instance, exclusively binomial or exclusively continuous).

Is there a method of combining regression coefficients for a meta-regression when the dependent variables are a mix of distributions: for instance, counts, ordinal and continuous?

• If the dependent variables are that different, is it even reasonable to combine effect sizes in a meta-analysis? Aug 23, 2011 at 12:13
• I guess that's about the answer to my question! Thanks Andy
– tom
Aug 24, 2011 at 3:35

This situation can easily arise in areas like health where people often present their data as categorisations of essentially continuous underlying variables. If the binary outcome as been presented as a (log) odds ratio and the continuous as mean differences then dividing the log odds by 1.65 (due to Cox) or by pi / \sqrt(3) converts to mean differences depending on assumptions about the distribution (and they are almost identical anyway. If you are using metafor in R these are available there. You may also be interested in

@article{haddock98,
author = {Haddock, C K and Ridnskopf, D and Shadish, W R},
title = {Using odds ratios as effect sizes for meta--analysis
of dichotomous data: a primer on methods and issues},
journal = {Psychological Methods},
year = {1998},
volume = {3},
pages = {339--353},
keywords = {meta-analysis}
}


for an introductory account and

@ARTICLE{chinn00,
author = {Chinn, S},
year = 2000,
title = {A simple method for converting an odds ratio to effect size for use
in meta--analysis},
journal = {Statistics in Medicine},
volume = 19,
pages = {3127--3131},
keywords = {meta-analysis}
}


who gives a worked example