We are trying to conduct a meta-analysis. One of the studies is providing Nagelkerke's R2 and p-value (and sample sizes for two groups) but not the actual effect size. Is there a way to convert this data to an effect size that we can use in a meta-analysis? Thanks!
Sal Mangiafico We haven't defined it a priori. But I assume we need to convert what we have to Cohen's d or Hedges' g at the end.
Isn't the Nagelkerke's R2 a measure of effect size in Polytomous Logistic Regression Models in itself?
Let me first say that I am always skeptical about converting among effect size statistics in the way that --- I suspect --- is done sometimes in meta analysis. First, even when the conversion is "valid" it inevitably assumes something about the distribution of the underlying population that went into the effect size statistic. Second, --- I suspect --- people use formulas to convert effect size statistics in ways that don't make sense. Like converting an r value from the correlation of two continuous variables to Cohen's d.
Okay, rant over.
If the Nagelkerke represents the the standardized effect size from two groups, then you can consider that an approximation of r-squared. You could take the square root of that, and use the r-to-Cohen's-d conversion. Nagelkerke is probably as close an approximation to r-squared as the conversion of r to Cohen's d.
For more on Sal Mangiafico 's first paragraph, he states "Some pseudo R-squared measures may not be appropriate or useful for some model types" in the help files for his function nagelkerke (in rcompanion). The different pseudo Rs map differently to the different aspects of the OLS R. A short table that I have found useful is in:
https://stats.oarc.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/ So, Sal this is mostly a question for you. If my goal was to convert to d, do you think one of the pseudo Rs is more appropriate. As many are based on L, presumably Mete Ercis could translate between these if there is enough information in the papers for the meta-analysis.
Hi, Daniel Wright . Oh, who knows ? ... I think the only case in which it makes sense to convert an r-squared to Cohen's d is when the r-squared is based on the comparison of a continuous variable across two groups, like point biserial correlation. In that case, I imagine an appropriate pseudo r-square would be similar to the r-square. As mentioned, I'm pretty skeptical of all this conversion-among-effect-size stuff. It would be interesting to see if partial eta-square or eta-square could be converted to Cohen's d among groups in, say, a one-way anova. But I think the only way to approach the problem reasonably is start with the raw data and calculate the actual desired effect size.
Thanks Sal Mangiafico . In the future more data should be available with lots of journals/funding sources requiring it!
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