metafor (version 4.6-0)

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

Description

Function to compute 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, ...)

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 the print function. To format the results as a data frame, one can use the as.data.frame function.

Arguments

x

an object of class "rma.uni".

level

numeric value between 0 and 100 to specify the prediction interval level (see here for details). If unspecified, the default is to take the value from the object.

digits

optional 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 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.

Author

Wolfgang Viechtbauer https://www.metafor-project.org

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 for the function to fit models for which BLUPs can be extracted.

predict and fitted for functions to compute the predicted/fitted values based only on the fixed effects and ranef for a function to compute the BLUPs based only on the random effects.

Examples

### 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$yi, pch=19)
points(rep(2,13), blups, pch=19)
axis(side=1, at=c(1,2), labels=c("Observed\nValues", "BLUPs"), lwd=0)
segments(0, res$beta, 2.15, res$beta, lty="dotted")
text(2.3, res$beta, substitute(hat(mu)==muhat, list(muhat=round(res$beta[[1]], 2))), cex=1)