influence.rma.uni: Case Diagnostics for rma.uni Objects

Description

The function calculates various case diagnostics that indicate the influence of deleting one case at a time on the model fit and the fitted/residual values for objects of class "rma.uni".

Usage

## S3 method for class 'rma.uni':
influence(model, digits=model$digits, \dots)

Arguments

model

an object of class "rma.uni".

digits

an integer specifying the number of decimal places to which the printed results should be rounded (the default is to take the value from the object).

...

other arguments.

Value

An object of class "infl.rma.uni". The object is a list containing the following components:
infA data frame with columns equal to the externally standardized residuals, DFFITS values, Cook's distances, covariance ratios, leave-one-out $\tau^2$ estimates, leave-one-out (residual) heterogeneity test statistics, hat values, and weights.
dfbA data frame with columns equal to the DFBETAS values.
...some additional elements/values.
The results are printed with print.infl.rma.uni and plotted with plot.infl.rma.uni.

Details

The following leave-one-out diagnostics are calculated for each study:

externally standardized residual,
DFFITS value,
Cook's distance,
covariance ratio,
the leave-one-out amount of (residual) heterogeneity,
the leave-one-out test statistic for the test of (residual) heterogeneity, and
DFBETAS value(s).

The diagonal elements of the hat matrix and the weights (in %) given to the observed effects or outcomes during the model fitting are also provided (the hat values and weights are the same for models without moderators, but will differ once moderators are included). For details on externally standardized residuals, see rstudent.rma.uni. The DFFITS value essentially indicates how many standard deviations the predicted average effect for the $i^{th}$ study changes after excluding the $i^{th}$ study from the model fitting. Cook's distance can be interpreted as the Mahalanobis distance between the entire set of predicted values once with the $i^{th}$ study included and once with the $i^{th}$ study excluded from the model fitting. The covariance ratio is defined as the determinant of the variance-covariance matrix of the parameter estimates based on the dataset with the $i^{th}$ study removed divided by the determinant of the variance-covariance matrix of the parameter estimates based on the complete dataset. A value below 1 therefore indicates that removal of the $i^{th}$ study yields more precise estimates of the model coefficients. The leave-one-out amount of (residual) heterogeneity is the estimated value of $\tau^2$ based on the dataset with the $i^{th}$ study removed. Note that this is always equal to 0 for fixed-effects models. Similarly, the leave-one-out test statistic for the test of (residual) heterogeneity is the value of the test statistic of the test for (residual) heterogeneity calculated based on the dataset with the $i^{th}$ study removed. Finally, the DFBETAS value(s) essentially indicate(s) how many standard deviations the estimated coefficient(s) change(s) after excluding the $i^{th}$ study 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. 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. http://www.jstatsoft.org/v36/i03/. Viechtbauer, W. & Cheung, M. W.-L. (in press). Outlier and influence diagnostics for meta-analysis. Research Synthesis Methods.

Examples

Run this code

### load BCG vaccine data
data(dat.bcg)

### meta-analysis of the log relative risks using a mixed-effects model
### with two moderators (absolute latitude and publication year)
res <- rma(ai=tpos, bi=tneg, ci=cpos, di=cneg, mods=cbind(ablat, year),
           data=dat.bcg, measure="RR", method="REML")
influence(res)

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