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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?

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

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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

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