6: Fixed & Random Summaries with Generic InputFixed and random-effects overall or summary effects for any kind of effect size

Meta-analysis in R with Metafor

Overall Summary

The Metafor program uses inverse variance weights to combine study ES into an overall or summary effect size

You can specify Fixed (common) effects analysis or Random (varying) effects analysis

If RE, you can choose from several methods for estimating the random effects variance component (REVC). Different REVC, weight, summary.

The method statement specifies both fixed or random and which REVC estimator you want

The effect sizes input to metafor may be transformed in various ways

The measure option tells metafor what transformation you want

Simplest Example

The default model is a generic, random effects analysis using a restricted maximum likelihood algorithm to estimate the REVC

You just input yi (the effect size for each study), vi (sampling variance for each study), and the name of the dataset. Note that to Metafor, yi means generic ES and vi means generic variance. You can choose any names you like for the input variables (e.g., yi= d, yi=Di, yi=gymsocks; whatever you named it in your Excel sheet).

Metafor computes the overall summary.

You tell R to print the result.

R code: McNatt

McNatt DB: Ancient Pygmalion joins contemporary management: A meta-analysis of the result. Journal of Applied Psychology 2000, 85:314-322.

Example of running a generic effect size and variance

Choice of Method

For fixed effects: method=“FE”

The choices for random effects (estimators of REVC), method = :

“HS” - Hunter & Schmidt

“HE” – Hedges

“DL” – DerSimonian-Laird

“SJ” – Sidik-Jonkman

“ML” – Maximum likelihood

“REML” – Restricted maximum likelihood

“EB” – Empirical Bayes

R code: McNatt

RE with DerSimonian-Laird estimator

Fixed Effects

Generic Input and “Measure=”If you use generic input, you compute the transformation you want (if any) and tell Metafor to use that effect size as yi. Metafor does not know or care what kind of effect size you pick. You must be sure that the variance input (vi) matches the effect size (yi) that you input. Don’t input the log odds as the effect along with the variance of the odds ratio; both yi and vi must be either log or not log.

If you use generic input, you must transform to another metric after the analysis if you want a different scale. For example, if you input data coded as Fisher’s z to yi, the results will be in z, and you will have to convert back to r if that is what you want to present. Or if you input log(odds ratio) to yi, then the analysis will be done in log odds, and you must convert back to odds if that is what you want to report.

If you use preferred formats for mean difference, correlations, or binary studies, you can instruct Metafor with the “measure=” command to make a transformation. This is discussed in the next two videos.