The R package metafor offers various ways of back-transforming the results of a meta-analysis with a transformed effect size/outcome variable. In this case, I will refer to a reliability generalization meta-analysis using a random-effects model and coefficient alpha as the outcome variable, which has been transformed using with a Bonett transfromation 'ABT' using escalc.
The pooled estimate can be back-transformed using the predict() and transf functions. For example,
predict(model_name, transf=transf.iabt)
will provide a back-tranformed point estimate and confidence intervals.
My question is: How can one back-transform other aspects of an rma output that are not metric-free, such as tau and its confidence intervals, using the metafor package/R? I have tried summary(model_name, transf=transf.iabt) but that gives me the same results as summary(model_name). Perhaps I have misunderstood the calculation of tau-square, hence tau, which may be something that is not so easily 'back-transformable'.
Best Answer
You don't need to back-transform the estimate of $\tau^2$.
predict()gives you the prediction interval and its bounds can be back-transformed, so that tells you how much heterogeneity there is in the back-transformed scale.