Functions to compute best linear unbiased predictions (BLUPs) of the random effects for objects of class "rma.uni" and "". Corresponding standard errors and prediction interval bounds are also provided.

# S3 method for rma.uni
ranef(object, level, digits, transf, targs, ...)
# S3 method for
ranef(object, level, digits, transf, targs, verbose=FALSE, ...)



an object of class "rma.uni" or "".


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.


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.


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.


optional arguments needed by the function specified under transf.


logical to specify whether output should be generated on the progress of the computations (the default is FALSE).


other arguments.


For objects of class "rma.uni", an object of class "list.rma". The object is a list containing the following components:


predicted values.


corresponding standard errors.

lower bound of the prediction intervals.


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 function.

For objects of class "", a list of data frames with the same components as described above.


For best linear unbiased predictions that combine the fitted values based on the fixed effects and the estimated contributions of the random effects, see blup.

For predicted/fitted values that are based only on the fixed effects of the model, see fitted and predict.

Equal-effects models do not contain random study effects. The BLUPs for these models will therefore be 0.

When using the transf argument, the transformation is applied to the predicted values and the corresponding interval bounds. The standard errors are then set equal to NA and are omitted from the printed output.

By default, a standard normal distribution is used to construct the prediction intervals. When the model was fitted with test="t", test="knha", test="hksj", or test="adhoc", then a t-distribution with \(k-p\) degrees of freedom is used.

To be precise, it should be noted that the function actually computes empirical BLUPs (eBLUPs), since the predicted values are a function of the estimated variance component(s).


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.

Raudenbush, S. W., & Bryk, A. S. (1985). Empirical Bayes meta-analysis. Journal of Educational Statistics, 10(2), 75–98.

Robinson, G. K. (1991). That BLUP is a good thing: The estimation of random effects. Statistical Science, 6(1), 15–32.

Searle, S. R., Casella, G., & McCulloch, C. E. (1992). Variance components. Hoboken, NJ: Wiley.

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1–48.

See also

rma.uni and for functions to fit models for which BLUPs of the random effects can be computed.

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


### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg,

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

### BLUPs of the random effects
#>       pred     se   pi.ub 
#> 1  -0.0857 0.4092 -0.8877  0.7163 
#> 2  -0.5372 0.3638 -1.2501  0.1758 
#> 3  -0.2724 0.4296 -1.1144  0.5696 
#> 4  -0.6834 0.2176 -1.1099 -0.2568 
#> 5   0.4272 0.2606 -0.0835  0.9378 
#> 6  -0.0700 0.1942 -0.4506  0.3105 
#> 7  -0.5294 0.3759 -1.2662  0.2073 
#> 8   0.7174 0.1882  0.3485  1.0863 
#> 9   0.2077 0.2665 -0.3146  0.7300 
#> 10 -0.5326 0.2837 -1.0886  0.0234 
#> 11  0.3609 0.2046 -0.0401  0.7618 
#> 12  0.4298 0.4491 -0.4504  1.3100 
#> 13  0.5678 0.2821  0.0149  1.1207