metafor (version 2.1-0)

influence.rma.mv: Outlier and Influential Case Diagnostics for 'rma.mv' Objects

Description

The functions compute various outlier and influential case diagnostics (some of which indicate the influence of deleting one case/study at a time on the model fit and the fitted/residual values) for objects of class "rma.mv".

Usage

# S3 method for rma.mv
cooks.distance(model, progbar=FALSE, cluster,
               reestimate=TRUE, parallel="no", ncpus=1, cl=NULL, …)
# S3 method for rma.mv
dfbetas(model, progbar=FALSE, cluster,
        reestimate=TRUE, parallel="no", ncpus=1, cl=NULL, …)
# S3 method for rma.mv
hatvalues(model, type="diagonal", …)

Arguments

model

an object of class "rma.mv".

progbar

logical indicating whether a progress bar should be shown (the default is FALSE). Ignored when using parallel processing.

cluster

optional vector specifying a clustering variable to use for computing the Cook's distances. If not specified, Cook's distances are computed for all individual observed outcomes.

reestimate

logical indicating whether variance/correlation components should be re-estimated after deletion of the \(i\)th study/cluster (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.

type

character string indicating whether to return only the diagonal of the hat matrix ("diagonal") or the entire hat matrix ("matrix").

…

other arguments.

Value

The cooks.distance function returns a vector. The dfbetas function returns a data frame. The hatvalues function returns either a vector with the diagonal elements of the hat matrix or the entire hat matrix.

Details

Cook's distance for the \(i\)th study/cluster can be interpreted as the Mahalanobis distance between the entire set of predicted values once with the \(i\)th study/cluster included and once with the \(i\)th study/cluster excluded from the model fitting.

The DFBETAS value(s) essentially indicate(s) how many standard deviations the estimated coefficient(s) change(s) after excluding the \(i\)th study/cluster from the model fitting.

References

Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics. New York: Wiley.

Cook, R. D., & Weisberg, S. (1982). Residuals and influence in regression. London: Chapman and Hall.

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/.

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

See Also

rstudent.rma.mv, weights.rma.mv

Examples

# NOT RUN {
### copy data from Konstantopoulos (2011) into 'dat'
dat <- dat.konstantopoulos2011

### multilevel random-effects model
res <- rma.mv(yi, vi, random = ~ 1 | district/school, data=dat)
print(res, digits=3)

### Cook's distances for each observed outcome
x <- cooks.distance(res)
x
plot(x, type="o", pch=19, xlab="Observed Outcome", ylab="Cook's Distance")

### Cook's distances for each district
x <- cooks.distance(res, cluster=dat$district)
x
plot(x, type="o", pch=19, xlab="District", ylab="Cook's Distance", xaxt="n")
axis(side=1, at=seq_along(x), labels=as.numeric(names(x)))

### hat values
hatvalues(res)
# }

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