metafor (version 1.9-4)

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

Description

The function calculates best linear unbiased predictions (BLUPs) of the true 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 class 'rma.uni':
blup(x, level, digits, transf, targs, \dots)

Arguments

x

an object of class "rma.uni".

level

numerical value between 0 and 100 specifying the prediction interval level (if unspecified, the default is to take the value from the object).

digits

integer specifying 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 specifying the name of a function that should be used to transform the predicted values and interval bounds (e.g., transf=exp). 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 "list.rma" object is formated 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, 1249--1261. Raudenbush, S. W., & Bryk, A. S. (1985). Empirical Bayes meta-analysis. Journal of Educational Statistics, 10, 75--98. Robinson, G. K. (1991). That BLUP is a good thing: The estimation of random effects. Statistical Science, 6, 15--32. Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1--48. http://www.jstatsoft.org/v36/i03/.

See Also

rma.uni, predict.rma, fitted.rma

Examples

### load BCG vaccine data
data(dat.bcg)

### calculate log relative risks and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)

### meta-analysis of the log relative risks using a random-effects model
res <- rma(yi, vi, data=dat)
blup(res, transf=exp)

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