# ranef

##### Best Linear Unbiased Predictions for 'rma.uni' and 'rma.mv' Objects

The function calculates best linear unbiased predictions (BLUPs) of the random effects for objects of class `"rma.uni"`

and `"rma.mv"`

. Corresponding standard errors and prediction interval bounds are also provided.

- Keywords
- models

##### Usage

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

##### Arguments

- object
an object of class

`"rma.uni"`

or`"rma.mv"`

.- 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`

; see also transf). If unspecified, no transformation is used.- targs
optional arguments needed by the function specified under

`transf`

.- verbose
logical indicating whether output should be generated on the progress of the computations (the default is

`FALSE`

).- …
other arguments.

##### Value

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

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

##### Note

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.rma`

and `predict.rma`

.

Fixed-effects models (with or without moderators) 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.

The normal distribution is used to calculate the prediction intervals. When the model was fitted with the Knapp and Hartung (2003) method (i.e., `test="knha"`

in the `rma.uni`

function), then the t-distribution with \(k-p\) degrees of freedom is used.

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

##### 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.

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. https://www.jstatsoft.org/v036/i03.

##### See Also

##### 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 random effects
ranef(res)
# }
```

*Documentation reproduced from package metafor, version 2.4-0, License: GPL (>= 2)*