metafor (version 2.4-0)

residuals.rma: Residual Values based on 'rma' Objects

Description

The residuals, rstandard, and rstudent functions compute residuals, corresponding standard errors, and standardized residuals for models fitted with the rma.uni, rma.mh, rma.peto, and rma.mv functions.

Usage

# S3 method for rma
residuals(object, type="response", …)

# S3 method for rma.uni rstandard(model, digits, type="marginal", …) # S3 method for rma.mh rstandard(model, digits, …) # S3 method for rma.peto rstandard(model, digits, …) # S3 method for rma.mv rstandard(model, digits, cluster, …)

# S3 method for rma.uni rstudent(model, digits, progbar=FALSE, …) # S3 method for rma.mh rstudent(model, digits, progbar=FALSE, …) # S3 method for rma.peto rstudent(model, digits, progbar=FALSE, …) # S3 method for rma.mv rstudent(model, digits, progbar=FALSE, cluster, reestimate=TRUE, parallel="no", ncpus=1, cl=NULL, …)

Arguments

object

an object of class "rma" (for residuals).

type

the type of residuals which should be returned. For residuals, the alternatives are: "response" (default), "rstandard", "rstudent", and "pearson". For rstandard.rma.uni, the alternatives ares: "marginal" (default) and "conditional". See ‘Details’.

model

an object of class "rma" (for residuals) or an object of class "rma.uni", "rma.mh", "rma.peto", or "rma.mv" (for rstandard and rstudent).

cluster

optional vector specifying a clustering variable to use for computing cluster-level multivariate standardized residuals (only for "rma.mv" objects).

reestimate

logical indicating whether variance/correlation components should be re-estimated after deletion of the \(i\)th study/cluster when computing externally standardized residuals (the default is TRUE).

parallel

character string indicating whether parallel processing should be used (the default is "no"). For parallel processing, set to either "snow" or "multicore". See ‘Details’.

ncpus

integer specifying the number of processes to use in the parallel processing.

cl

optional snow cluster to use if parallel="snow". If not supplied, a cluster on the local machine is created for the duration of the call.

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).

progbar

logical indicating whether a progress bar should be shown (only for rstudent) (the default is FALSE).

other arguments.

Value

Either a vector with the residuals of the requested type (for residuals) or an object of class "list.rma", which is a list containing the following components:

resid

observed residuals (for rstandard) or deleted residuals (for rstudent).

se

corresponding standard errors.

z

standardized residuals (internally standardized for rstandard or externally standardized for rstudent).

When a clustering variable is specified for "rma.mv" objects, the returned object is a list with the first element (named obs) as described above and a second element (named cluster of class "list.rma" with:

X2

cluster-level multivariate standardized residuals.

k

number of outcomes within the clusters.

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

Details

The observed residuals (obtained with residuals) are simply equal to the ‘observed - fitted’ values. These can be obtained with residuals(object) (using the default type="response").

Dividing the observed residuals by the model-implied standard errors of the observed effect sizes or outcomes yields Pearson (or semi-standardized) residuals. These can be obtained with residuals(object, type="pearson").

Dividing the observed residuals by their corresponding standard errors yields (internally) standardized residuals. These can be obtained with rstandard or residuals(object, type="rstandard").

The rstudent function (or residuals(object, type="rstudent")) calculates externally standardized residuals (also called standardized deleted residuals or (externally) studentized residuals). The externally standardized residual for the \(i\)th case is obtained by deleting the \(i\)th case from the dataset, fitting the model based on the remaining cases, calculating the predicted value for the \(i\)th case based on the fitted model, taking the difference between the observed and the predicted value for the \(i\)th case (which yields the deleted residual), and then standardizing the deleted residual based on its standard error.

If a particular study fits the model, its standardized residual follows (asymptotically) a standard normal distribution. A large standardized residual for a study therefore may suggest that the study does not fit the assumed model (i.e., it may be an outlier).

For "rma.uni" objects, rstandard.rma.uni also can compute conditional residuals (when type="conditional"), which are the deviations of the observed outcomes from the best linear unbiased predictions (BLUPs) of the study-specific true outcomes (see blup.rma.uni).

For "rma.mv" objects, one can specify a clustering variable (via the cluster argument). If specified, rstandard and rstudent also compute cluster-level multivariate (internally or externally) standardized residuals. If all outcomes within a cluster fit the model, then the multivariate standardized residual for the cluster follows (asymptotically) a chi-square distribution with \(k<U+1D62>\) degrees of freedom (where \(k<U+1D62>\) denotes the number of outcomes within the cluster).

See also influence.rma.uni and influence.rma.mv for other leave-one-out diagnostics that are useful for detecting influential cases in models fitted with the rma.uni and rma.mv functions.

References

Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. San Diego, CA: Academic Press.

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.

Viechtbauer, W., & Cheung, M. W.-L. (2010). Outlier and influence diagnostics for meta-analysis. Research Synthesis Methods, 1, 112--125.

See Also

rma.uni, rma.mh, rma.peto, rma.glmm, rma.mv, influence.rma.uni, influence.rma.mv

Examples

Run this code
# NOT RUN {
### meta-analysis of the log risk ratios using a random-effects model
res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)
rstudent(res)

### mixed-effects model with absolute latitude as a moderator
res <- rma(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, mods = ~ ablat,
           data=dat.bcg)
rstudent(res)
# }

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