[R-meta] prediction intervals in multi-level meta-analysis models

[James Pustejovsky]

Dear meta-analysis folks,

I am using metafor to fit a multi-level meta-regression model. I want to
generate an 80% prediction interval for the effect size in a new study with
a given set of characteristics. Here's an example using the Konstantopoulos
data on effects modified school calendars:

library(metafor)
data("dat.konstantopoulos2011")

kon_fit <- rma.mv(yi = yi, V = vi, data = dat.konstantopoulos2011,
                  mods = ~ year,
                  random = ~ 1 | district / school,
                  sparse = TRUE)

predict(kon_fit, newmods = 2021, level = 80)

(This particular example is a bit extreme because it involves a massive
extrapolation forward in time, but this isn't relevant to my question.)

It looks like the prediction interval generated by metafor::predict()
incorporates three sources of variation: 1) uncertainty in the average
effect size estimate at the given value of the predictor, 2) estimated
between-district variation, and 3) estimated school-level variation.

My question is: does anyone know of any references on the methodology
behind constructing such prediction intervals (involving multiple variance
components)? The methods implemented in metafor seem very sensible, but I
can't seem to find anything in the literature about this stuff.

Kind Regards,
James

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