influence.rma.uni {metafor}R Documentation

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, ...)

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.

Details

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

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.

For the meta-analytic models underlying the rma.uni function, the DFFITS value for the ith case is here defined as the difference between the predicted value based on the fitted model using the complete dataset and the predicted value based on the fitted model using the dataset with the ith case removed, divided by the standard error of the predicted value based on the fitted model using the dataset with the ith case removed.

Cook's distance is here defined as (b-b(i))' Sigma^(-1) (b-b(i)) , where b is the vector of parameter estimates based on the complete dataset, b(i) is the vector of parameter estimates based on the dataset with the ith case removed, and Sigma is the variance-covariance matrix of the parameter estimates based on the full dataset.

The covariance ratio is defined as the determinant of the variance-covariance matrix of the parameter estimates based on the dataset with the ith case removed divided by the determinant of the variance-covariance matrix of the parameter estimates based on the complete dataset.

The leave-one-out amount of (residual) heterogeneity is the estimated value of tau^2 based on the dataset with the ith case removed. 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 ith case removed.

Finally, the DFBETAS values for the ith case are defined as the difference between the parameter estimates based on the complete dataset and the parameter estimates based on the dataset with the ith case removed, divided by the standard error of the parameter estimates based on the dataset with the ith case removed.

Value

An object of class "infl.rma.uni". The object is a list containing the following components:

inf A 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.
dfb A 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.

Note

Right now, the leave-one-out diagnostics are calculated by refitting the model k times. Depending on how large k is, it may take a few moments to finish the calculations. There are shortcuts for calculating at least some of these values without refitting the model each time, but these are currently not implemented (and may not exist for all of the leave-one-out diagnostics calculated by the present function).

It may not be possible to fit the model after deletion of the ith case from the dataset. This will result in NA values for that case.

Certain relationships between the leave-one-out diagnostics and the (internally or externally) standardized residuals (Belsley, Kuh, & Welsch, 1980; Cook & Weisberg, 1982) no longer hold for the meta-analytic models. Maybe there are other relationships. These remain to be determined.

Author(s)

Wolfgang Viechtbauer; wvb@www.wvbauer.com; http://www.wvbauer.com/

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.

See Also

print.infl.rma.uni, plot.infl.rma.uni, rstudent.rma.uni, hatvalues.rma.uni

Examples

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

### meta-analysis of the log risk ratios 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)

[Package metafor version 0.5-5 Index]