*! version 1.0.0 23Aug2020

Title

metapred -- Outlier and influence diagnostics for meta-analysis

Syntax

metapred newvar [if] [in] [, statistic]

Before using metapred, a model must first be estimated using meta regress

statistic

Main
rstandard Standardized residuals

* rstudent Studentized (jackknifed) residuals

* dfits DFITS

cooksd Cook's distance

* welsch Welsch distance

* covratio COVRATIO

* dfbeta(varname) DFBETA for varname

Unstarred statistics are available both in and out of sample;
type predict ... if e(sample) ... if wanted only for the estimation
sample. Starred statistics are calculated only for the estimation sample,
even when if e(sample) is not specified.

Description

metapred extends the currently available post-estimation predictions for meta regress
to include standardized residuals, studentized residuals, DFITS, Cook's distance, Welsch distance, and covariate ratio (see Viechtbauer
and Cheung [2010] for a comprehensive discussion of post-estimation statistics following meta-regression).

Standardized residuals and studentized residuals produced by metapred
correspond to those produced by the R package
METAFOR (http://www.metafor-project.org/doku.php).

DFITS produced by metapred are identical to those produced by METAFOR when using fixed-effects regression (metapred
currently does not implement the adjustment for random-effects models as suggested in Viechtbauer and Cheung [2010]).

metapred computes the Cook's distance statistic, covariate ratio and DFBETA according to the formulas used for post estimation following regress
(see Methods and formulas). As such, the resulting estimates are consistent
with those produced by "predict" following regress, but are not consistent with estimates computed in METAFOR.

metapred offers the Welsch distance metric which is not offered in METAFOR.

See the Stata Manual entry under regression post-estimation predictions for how to interpret these statistics following
regression. The interpretation following meta regression is the same.

Options

Main

rstandard calculates the standardized residuals.

rstudent calculates the Studentized (jackknifed) residuals.

dfits calculates DFITS (Welsch and Kuh 1977)
and attempts to summarize the information in the leverage versus
residual-squared plot into one statistic. The calculation is
automatically restricted to the estimation
subsample.

cooksd calculates the Cook's D influence statistic (Cook 1977).

welsch calculates Welsch distance (Welsch 1982) and is a variation on
dfits. The calculation is automatically restricted to the estimation
subsample.

covratio covratio calculates COVRATIO (Belsley, Kuh, and Welsch 1980), a measure of the influence
of the jth observation based on considering the effect on the variance-covariance matrix of the estimates.
The calculation is automatically restricted to the estimation subsample.

dfbeta(varname) calculates the DFBETA for varname, the difference
between the regression coefficient when the jth observation is included and
excluded, said difference being scaled by the estimated standard error of the
coefficient. varname must have been included among the regressors in the
previously fitted model. The calculation is automatically restricted to the
estimation subsample.

Examples

Load example data

. webuse bcgset, clear

Use meta esize to compute effect sizes for the log risk-ratio using a random effects(REML) model

. meta esize npost nnegt nposc nnegc, esize(lnrratio) studylabel(studylbl)

Use meta regress to estimate the effect of latitute on the effect estimates

. meta regress latitude

Standardized residuals

. metapred esta, rstandard

Studentized residuals

. metapred estu, rstudent

DFITS influence measure

. metapred dfits, dfits

Cook's distance

. metapred cooksd, cooksd

Welsch distance

. metapred wd, welsch

COVRATIO influence measure

. metapred covr, covratio

DFBETAs influence measure

. metapred dfor, dfbeta(latitude)

Acknowledgments

I thank John Moran for advocating that I write this package.

References

Belsley, D. A., E. Kuh, and R. E. Welsch. 1980. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: Wiley.

Cook, R. D. 1977. Detection of influential observations in linear regression. Technometrics 19: 15-18.

Viechtbauer, W. and M. W. L. Cheung. 2010. Outlier and influence diagnostics for meta‐analysis. Research synthesis methods 1(2): 112-125.

Welsch, R. E. 1982. Influence functions and regression diagnostics. In Modern Data Analysis, ed. R. L. Launer and A. F. Siegel, 149-169. New York: Academic Press.

Welsch, R. E., and E. Kuh. 1977. Linear Regression Diagnostics. Technical Report 923-77, Massachusetts Institute of Technology, Cambridge, MA.

Citation of metapred

metapred is not an official Stata command. It is a free contribution
to the research community, like a paper. Please cite it as such:

Linden A. (2020). METAPRED: Stata module for computing outlier and influence diagnostics for meta-analysis.

Authors

Ariel Linden

President, Linden Consulting Group, LLC

alinden@lindenconsulting.org

Also see

Online: meta, meta regress, regress postestimation, metafrag (if installed)