residuals
, rstandard
, and rstudent
functions can be used to compute residuals, corresponding standard errors, and standardized residuals for models fitted with the rma.uni
, rma.mh
, rma.peto
, and rma.mv
functions.
"residuals"(object, ...)
"rstandard"(model, digits, ...)
"rstandard"(model, digits, ...)
"rstandard"(model, digits, ...)
"rstandard"(model, digits, ...)
"rstudent"(model, digits, ...)
"rstudent"(model, digits, ...)
"rstudent"(model, digits, ...)
"rma"
(for residuals
)."rma.uni"
, "rma.mh"
, "rma.peto"
, or "rma.mv"
(for rstandard
and rstudent
).residuals
) or an object of class "list.rma"
, which is a list containing the following components:The "list.rma"
object is formated and printed with print.list.rma
.
residuals
) are simply equal to the observed - fitted values. Dividing the observed residuals by their corresponding standard errors yields (internally) standardized residuals. These can be obtained with rstandard
.
The rstudent
function calculates externally standardized residuals (studentized deleted 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 (the deleted residual), and then standardizing the deleted residual. The standard error of the deleted residual is equal to the square root of the sampling variance of the $i$th case plus the variance of the predicted value plus the amount of (residual) heterogeneity from the fitted model (for fixed-effects models, this last part is always equal to zero).
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).
See also influence.rma.uni
for other leave-one-out diagnostics that are useful for detecting influential cases in models fitted with the rma.uni
function.
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.
rma.uni
, rma.mh
, rma.peto
, rma.glmm
, rma.mv
, influence.rma.uni
### meta-analysis of the log relative risks 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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