metafor (version 3.8-1)

influence.rma.mv: Model Diagnostics for 'rma.mv' Objects

Description

The functions can be used to compute various outlier and influential case diagnostics (some of which indicate the influence of deleting one case at a time on the model fit or 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, ...)
# S3 method for rma.mv
dfbetas(model, progbar=FALSE, cluster,
        reestimate=TRUE, parallel="no", ncpus=1, cl, ...)
# S3 method for rma.mv
hatvalues(model, type="diagonal", ...)

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.

Arguments

model

an object of class "rma.mv".

progbar

logical to specify whether a progress bar should be shown (the default is FALSE).

cluster

optional vector to specify a clustering variable to use for computing the Cook's distances or DFBETAS values. If not specified, these measures are computed for the individual observed effect sizes or outcomes.

reestimate

logical to specify whether variance/correlation components should be re-estimated after deletion of the ithith case (the default is TRUE).

parallel

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

ncpus

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

cl

optional cluster to use if parallel="snow". If unspecified, a cluster on the local machine is created for the duration of the call.

type

character string to specify whether only the diagonal of the hat matrix ("diagonal") or the entire hat matrix ("matrix") should be returned.

...

other arguments.

Author

Wolfgang Viechtbauer https://www.metafor-project.org

Details

The term ‘case’ below refers to a particular row from the dataset used in the model fitting (when argument cluster is not specified) or each level of the variable specified via cluster.

Cook's distance for the ithith case can be interpreted as the Mahalanobis distance between the entire set of predicted values once with the ithith case included and once with the ithith case 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 ithith case 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. https://doi.org/10.18637/jss.v036.i03

Viechtbauer, W. (2021). Model checking in meta-analysis. In C. H. Schmid, T. Stijnen, & I. R. White (Eds.), Handbook of meta-analysis (pp. 219--254). Boca Raton, FL: CRC Press. https://doi.org/10.1201/9781315119403

Viechtbauer, W., & Cheung, M. W.-L. (2010). Outlier and influence diagnostics for meta-analysis. Research Synthesis Methods, 1(2), 112--125. https://doi.org/10.1002/jrsm.11

See Also

rstudent.rma.mv for externally standardized residuals and weights.rma.mv for model fitting weights.

Examples

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

### Cook's distance for each district
x <- cooks.distance(res, cluster=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)