metafor (version 3.0-2)

blup: Best Linear Unbiased Predictions for 'rma.uni' Objects

Description

The function calculates best linear unbiased predictions (BLUPs) of the study-specific true effect sizes or outcomes by combining the fitted values based on the fixed effects and the estimated contributions of the random effects for objects of class "rma.uni". Corresponding standard errors and prediction interval bounds are also provided.

Usage

blup(x, …)
# S3 method for rma.uni
blup(x, level, digits, transf, targs, …)

Arguments

x

an object of class "rma.uni".

level

numeric value between 0 and 100 to specify the prediction interval level. If unspecified, the default is to take the value from the object.

digits

integer to specify the number of decimal places to which the printed results should be rounded. If unspecified, the default is to take the value from the object.

transf

optional argument to specify a function that should be used to transform the predicted values and interval bounds (e.g., transf=exp; see also transf). If unspecified, no transformation is used.

targs

optional arguments needed by the function specified under transf.

…

other arguments.

Value

An object of class "list.rma". The object is a list containing the following components:

pred

predicted values.

se

corresponding standard errors.

pi.lb

lower bound of the prediction intervals.

pi.ub

upper bound of the prediction intervals.

…

some additional elements/values.

The object is formatted and printed with print.list.rma.

References

Kackar, R. N., & Harville, D. A. (1981). Unbiasedness of two-stage estimation and prediction procedures for mixed linear models. Communications in Statistics, Theory and Methods, 10(13), 1249--1261. https://doi.org/10.1080/03610928108828108

Raudenbush, S. W., & Bryk, A. S. (1985). Empirical Bayes meta-analysis. Journal of Educational Statistics, 10(2), 75--98. https://doi.org/10.3102/10769986010002075

Robinson, G. K. (1991). That BLUP is a good thing: The estimation of random effects. Statistical Science, 6(1), 15--32. https://doi.org/10.1214/ss/1177011926

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1--48. https://doi.org/10.18637/jss.v036.i03

See Also

rma.uni, predict.rma, fitted.rma, ranef.rma.uni

Examples

# NOT RUN {
### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)

### meta-analysis of the log risk ratios using a random-effects model
res <- rma(yi, vi, data=dat)

### BLUPs of the true risk ratios for each study
blup(res, transf=exp)

### illustrate shrinkage of BLUPs towards the (estimated) population average
res <- rma(yi, vi, data=dat)
blups <- blup(res)$pred
plot(NA, NA, xlim=c(.8,2.4), ylim=c(-2,0.5), pch=19,
     xaxt="n", bty="n", xlab="", ylab="Log Risk Ratio")
segments(rep(1,13), dat$yi, rep(2,13), blups, col="darkgray")
points(rep(1,13), dat$yi, pch=19)
points(rep(2,13), blups, pch=19)
axis(side=1, at=c(1,2), labels=c("Observed\nValues", "BLUPs"), lwd=0)
segments(.7, res$beta, 2.15, res$beta, lty="dotted")
text(2.3, res$beta, expression(hat(mu)==-0.71), cex=1)
# }