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I would like to conduct a meta-analysis to investigate the interaction of three variables:hair color (dark/light), gender (male/female) and size (continuous).

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I have three studies reporting effect sizes for the difference in size between light and dark hair:

my_data_1 <- data.frame(studies = c("study_1","study_2","study_3"),
group_1 = c(rep("light_hair",3)),
group_2 = c(rep("dark_hair",3)),
outcome = c(rep("size", 3)),
smd = c(1.2,1.3,0.8),
var_smd = c(0.2,0.23,0.15))

> my_data_1

  studies    group_1   group_2 outcome smd var_smd
1 study_1 light_hair dark_hair    size 1.2    0.20
2 study_2 light_hair dark_hair    size 1.3    0.23
3 study_3 light_hair dark_hair    size 0.8    0.15

Three studies reporting effect size for the difference in size between male and female:

my_data_2 <- data.frame(studies = c("study_4","study_5","study_6"),
group_1 = c(rep("male", 3)),
group_2 = c(rep("female", 3)),
outcome = c(rep("size", 3)),
smd = c(1.8,0.9,1.55),
var_smd = c(0.25,0.35,0.1))

> my_data_2

   studies group_1 group_2 outcome  smd var_smd
1 study_4    male  female    size 1.80    0.25
2 study_5    male  female    size 0.90    0.35
3 study_6    male  female    size 1.55    0.10

Three studies reporting effect sizes for the difference in gender between light and dark hair:

my_data_3 <- data.frame(studies = c("study_7","study_8","study_9"),
light_male = c(10,10,20),
light_female = c(5,7,12),
dark_male = c(15,7,14),
dark_female = c(19,21,25))
my_data_3 <- escalc(ai=light_male, bi=light_female, ci=dark_male,
di=dark_female, data=my_data_3, measure="OR2D")

> my_data_3

   studies light_male light_female dark_male dark_female     yi
1 study_7         10            5        15          19 0.5125
2 study_8         10            7         7          21 0.8023
3 study_9         20           12        14          25 0.6013
      vi
1 0.1275
2 0.1317
3 0.0744

All studies represent independent samples!

I would like to set up one multivariate meta-analytic model to investigate the mutual influence of the three factors hair color, gender and size. Could somebody point me to potential statistical approaches to this as well as potential implementations in R (metafor, gemtc, metaSEM)?

jokel
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    I don't understand the effect sizes for the difference in gender between light and dark hair. Gender is dichotomous, so what are those effect sizes supposed to represent? – Wolfgang Feb 11 '14 at 00:53
  • To add to the comment by @Wolfgang, it's not clear hear what the overall outcome variable is in your toy example. Based on your example data, your outcome variable is sometimes `size` and sometimes `gender`, which doesn't really make sense. – Patrick S. Forscher Feb 11 '14 at 02:13
  • Thank you for your comments! I tried to updated my question to make it more clear. – jokel Feb 11 '14 at 19:35
  • @jokel Your code for `my_data_3$SMD` and `my_data_3$SMD_var` is not correct. It should be `my_data_3$SMD – Wolfgang Feb 11 '14 at 22:09
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    This aside, this transformation only makes sense if we can imagine an underlying continuum for gender. If gender is supposed to reflect biological sex here, then this doesn't really apply. – Wolfgang Feb 11 '14 at 22:18
  • Thanks for the comments - I corrected the post. My hope was to bring the studies to some sort of common metric to allow combining them in one multivariate model. But there seems to be no way? – jokel Feb 11 '14 at 22:56
  • Your edits do help some, but it's still unclear to me what your meta-analytic question is. For example, you say that you have three effect sizes reporting the difference in `size` between light and dark hair. Size of what? You also say that you have three effect sizes reporting the difference in `size` between males and females. Again, size of what, and is this the same size that is measured for people with light and dark hair? – Patrick S. Forscher Feb 12 '14 at 01:18
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    Meta-analysis is useful when you have a well-defined question and when the population of studies that you retrieve all clearly bear on that well-defined question. Based on your toy example, it's not clear to me that the question that you're investigating is well-defined. – Patrick S. Forscher Feb 12 '14 at 01:19

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