print.rma {metafor}R Documentation

Print and Summary Methods for 'rma' Objects

Description

Functions to print objects of class "rma.uni", "rma.mh", "rma.peto", "rma.glmm", "rma.glmm", and "rma.mv".

Usage

## S3 method for class 'rma.uni'
print(x, digits, showfit=FALSE, signif.stars=getOption("show.signif.stars"),
      signif.legend=signif.stars, ...)

## S3 method for class 'rma.mh'
print(x, digits, showfit=FALSE, ...)

## S3 method for class 'rma.peto'
print(x, digits, showfit=FALSE, ...)

## S3 method for class 'rma.glmm'
print(x, digits, showfit=FALSE, signif.stars=getOption("show.signif.stars"),
      signif.legend=signif.stars, ...)

## S3 method for class 'rma.mv'
print(x, digits, showfit=FALSE, signif.stars=getOption("show.signif.stars"),
      signif.legend=signif.stars, ...)

## S3 method for class 'rma'
summary(object, digits, ...)

## S3 method for class 'summary.rma'
print(x, digits, showfit=TRUE, signif.stars=getOption("show.signif.stars"),
      signif.legend=signif.stars, ...)

Arguments

x

an object of class "rma.uni", "rma.mh", "rma.peto", "rma.glmm", "rma.mv", or "summary.rma" (for print).

object

an object of class "rma" (for summary).

digits

integer to specify the number of decimal places to which the printed results should be rounded. If unspecified, the default is to take the value from the object. See also here for further details on how to control the number of digits in the output.

showfit

logical to specify whether the fit statistics and information criteria should be printed (the default is FALSE for print and TRUE for summary).

signif.stars

logical to specify whether p-values should be encoded visually with ‘significance stars’. Defaults to the show.signif.stars slot of options.

signif.legend

logical to specify whether the legend for the ‘significance stars’ should be printed. Defaults to the value for signif.stars.

...

other arguments.

Details

The output includes:

See also here for details on the option to create styled/colored output with the help of the crayon package.

Value

The print functions do not return an object. The summary function returns the object passed to it (with additional class "summary.rma").

Note

For random-effects models, the \(I^2\) statistic is computed with \[I^2 = 100\% \times \frac{\hat{\tau}^2}{\hat{\tau}^2 + \tilde{v}},\] where \(\hat{\tau}^2\) is the estimated value of \(\tau^2\) and \[\tilde{v} = \frac{(k-1) \sum w_i}{(\sum w_i)^2 - \sum w_i^2},\] where \(w_i = 1 / v_i\) is the inverse of the sampling variance of the \(i\textrm{th}\) study (\(\tilde{v}\) is equation 9 in Higgins & Thompson, 2002, and can be regarded as the ‘typical’ within-study variance of the observed effect sizes or outcomes). The \(H^2\) statistic is computed with \[H^2 = \frac{\hat{\tau}^2 + \tilde{v}}{\tilde{v}}.\] Analogous equations are used for mixed-effects models.

Therefore, depending on the estimator of \(\tau^2\) used, the values of \(I^2\) and \(H^2\) will change. For random-effects models, \(I^2\) and \(H^2\) are often computed with \(I^2 = (Q-(k-1))/Q\) and \(H^2 = Q/(k-1)\), where \(Q\) denotes the statistic of the test for heterogeneity and \(k\) the number of studies (i.e., observed effect sizes or outcomes) included in the meta-analysis. The equations used in the metafor package to compute these statistics are more general and have the advantage that the values of \(I^2\) and \(H^2\) will be consistent with the estimated value of \(\tau^2\) (i.e., if \(\hat{\tau}^2 = 0\), then \(I^2 = 0\) and \(H^2 = 1\) and if \(\hat{\tau}^2 > 0\), then \(I^2 > 0\) and \(H^2 > 1\)).

The two definitions of \(I^2\) and \(H^2\) actually coincide when using the DerSimonian-Laird estimator of \(\tau^2\) (i.e., the commonly used equations are actually special cases of the more general definitions given above). Therefore, if you prefer the more conventional definitions of these statistics, use method="DL" when fitting the random/mixed-effects model with the rma.uni function. The conventional definitions are also automatically used when fitting an equal-effects models.

For mixed-effects models, the pseudo \(R^2\) statistic (Raudenbush, 2009) is computed with \[R^2 = \frac{\hat{\tau}_{RE}^2 - \hat{\tau}_{ME}^2}{\hat{\tau}_{RE}^2},\] where \(\hat{\tau}_{RE}^2\) denotes the estimated value of \(\tau^2\) based on the random-effects model (i.e., the total amount of heterogeneity) and \(\hat{\tau}_{ME}^2\) denotes the estimated value of \(\tau^2\) based on the mixed-effects model (i.e., the residual amount of heterogeneity). It can happen that \(\hat{\tau}_{RE}^2 < \hat{\tau}_{ME}^2\), in which case \(R^2\) is set to zero (and also if \(\hat{\tau}_{RE}^2 = 0\)). Again, the value of \(R^2\) will change depending on the estimator of \(\tau^2\) used. This statistic is only computed when the mixed-effects model includes an intercept (so that the random-effects model is clearly nested within the mixed-effects model). You can also use the anova function to compute \(R^2\) for any two models that are known to be nested. Note that the pseudo \(R^2\) statistic may not be very accurate unless \(k\) is large (Lopez-Lopez et al., 2014).

For fixed-effects with moderators models, the \(R^2\) statistic is simply the standard \(R^2\) statistic (also known as the ‘coefficient of determination’) computed based on weighted least squares estimation. To be precise, the so-called ‘adjusted’ \(R^2\) statistic is provided, since \(k\) is often relatively small in meta-analyses, in which case the adjustment is relevant.

Author(s)

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

References

Higgins, J. P. T., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. Statistics in Medicine, 21(11), 1539–1558. ⁠https://doi.org/10.1002/sim.1186⁠

López-López, J. A., Marín-Martínez, F., Sánchez-Meca, J., Van den Noortgate, W., & Viechtbauer, W. (2014). Estimation of the predictive power of the model in mixed-effects meta-regression: A simulation study. British Journal of Mathematical and Statistical Psychology, 67(1), 30–48. ⁠https://doi.org/10.1111/bmsp.12002⁠

Raudenbush, S. W. (2009). Analyzing effect sizes: Random effects models. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis (2nd ed., pp. 295–315). New York: Russell Sage Foundation.

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

See Also

rma.uni, rma.mh, rma.peto, rma.glmm, and rma.mv for the corresponding model fitting functions.


[Package metafor version 4.6-0 Index]