The function extracts various types of variance-covariance matrices from objects of class "rma". By default, the variance-covariance matrix of the parameter estimates (fixed effects) is returned.

# S3 method for rma
vcov(object, type="fixed", ...)

Arguments

object

an object of class "rma".

type

character string to specify the type of variance-covariance matrix to return: type="fixed" returns the variance-covariance matrix of the fixed effects (the default), type="obs" returns the marginal variance-covariance matrix of the observed effect sizes or outcomes, type="fitted" returns the variance-covariance matrix of the fitted values, type="resid" returns the variance-covariance matrix of the residuals.

...

other arguments.

Details

Note that type="obs" currently only works for object of class "rma.uni" and "rma.mv".

For objects of class "rma.uni", the marginal variance-covariance matrix of the observed effect sizes or outcomes is just a diagonal matrix with \(\hat{\tau}^2 + v_i\) along the diagonal, where \(\hat{\tau}^2\) is the estimated amount of (residual) heterogeneity (set to 0 in equal-effects models) and \(v_i\) is the sampling variance of the \(i\textrm{th}\) study.

For objects of class "rma.mv", the structure can be more complex and depends on the random effects included in the model.

Value

A matrix corresponding to the requested variance-covariance matrix.

References

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 functions to fit models for which the various types of variance-covariance matrices can be extracted.

Examples

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)

### fit mixed-effects model with absolute latitude and publication year as moderators
res <- rma(yi, vi, mods = ~ ablat + year, data=dat)

### var-cov matrix of the fixed effects (i.e., the model coefficients)
vcov(res)
#>             intrcpt         ablat          year
#> intrcpt 846.5702228 -0.1783751581 -0.4272176864
#> ablat    -0.1783752  0.0001047356  0.0000889397
#> year     -0.4272177  0.0000889397  0.0002156144

### marginal var-cov matrix of the observed log risk ratios
round(vcov(res, type="obs"), 3)
#>        1     2     3     4     5     6     7     8     9    10    11    12    13
#> 1  0.436 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
#> 2  0.000 0.305 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
#> 3  0.000 0.000 0.526 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
#> 4  0.000 0.000 0.000 0.131 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
#> 5  0.000 0.000 0.000 0.000 0.162 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
#> 6  0.000 0.000 0.000 0.000 0.000 0.118 0.000 0.000 0.000 0.000 0.000 0.000 0.000
#> 7  0.000 0.000 0.000 0.000 0.000 0.000 0.334 0.000 0.000 0.000 0.000 0.000 0.000
#> 8  0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.115 0.000 0.000 0.000 0.000 0.000
#> 9  0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.167 0.000 0.000 0.000 0.000
#> 10 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.184 0.000 0.000 0.000
#> 11 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.123 0.000 0.000
#> 12 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.643 0.000
#> 13 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.182

### var-cov matrix of the fitted values
round(vcov(res, type="fitted"), 3)
#>         1      2      3      4      5      6      7      8     9     10     11    12     13
#> 1   0.075  0.066  0.037 -0.024  0.009  0.059  0.006 -0.014 0.018  0.034  0.003 0.012 -0.011
#> 2   0.066  0.072  0.040  0.011 -0.009  0.056 -0.004 -0.023 0.012  0.038 -0.007 0.014  0.000
#> 3   0.037  0.040  0.026  0.014  0.004  0.032  0.006 -0.002 0.013  0.025  0.005 0.015  0.008
#> 4  -0.024  0.011  0.014  0.106 -0.022 -0.006 -0.005  0.003 0.000  0.018 -0.004 0.021  0.047
#> 5   0.009 -0.009  0.004 -0.022  0.040  0.006  0.031  0.036 0.022  0.004  0.032 0.012  0.008
#> 6   0.059  0.056  0.032 -0.006  0.006  0.048  0.005 -0.010 0.016  0.030  0.003 0.013 -0.002
#> 7   0.006 -0.004  0.006 -0.005  0.031  0.005  0.026  0.030 0.019  0.006  0.026 0.013  0.012
#> 8  -0.014 -0.023 -0.002  0.003  0.036 -0.010  0.030  0.042 0.019 -0.001  0.032 0.014  0.020
#> 9   0.018  0.012  0.013  0.000  0.022  0.016  0.019  0.019 0.017  0.013  0.019 0.014  0.010
#> 10  0.034  0.038  0.025  0.018  0.004  0.030  0.006 -0.001 0.013  0.024  0.005 0.015  0.010
#> 11  0.003 -0.007  0.005 -0.004  0.032  0.003  0.026  0.032 0.019  0.005  0.027 0.013  0.013
#> 12  0.012  0.014  0.015  0.021  0.012  0.013  0.013  0.014 0.014  0.015  0.013 0.015  0.017
#> 13 -0.011  0.000  0.008  0.047  0.008 -0.002  0.012  0.020 0.010  0.010  0.013 0.017  0.029

### var-cov matrix of the residuals
round(vcov(res, type="resid"), 3)
#>         1      2      3      4      5      6      7      8      9     10     11     12     13
#> 1   0.361 -0.066 -0.037  0.024 -0.009 -0.059 -0.006  0.014 -0.018 -0.034 -0.003 -0.012  0.011
#> 2  -0.066  0.233 -0.040 -0.011  0.009 -0.056  0.004  0.023 -0.012 -0.038  0.007 -0.014  0.000
#> 3  -0.037 -0.040  0.501 -0.014 -0.004 -0.032 -0.006  0.002 -0.013 -0.025 -0.005 -0.015 -0.008
#> 4   0.024 -0.011 -0.014  0.025  0.022  0.006  0.005 -0.003  0.000 -0.018  0.004 -0.021 -0.047
#> 5  -0.009  0.009 -0.004  0.022  0.122 -0.006 -0.031 -0.036 -0.022 -0.004 -0.032 -0.012 -0.008
#> 6  -0.059 -0.056 -0.032  0.006 -0.006  0.070 -0.005  0.010 -0.016 -0.030 -0.003 -0.013  0.002
#> 7  -0.006  0.004 -0.006  0.005 -0.031 -0.005  0.308 -0.030 -0.019 -0.006 -0.026 -0.013 -0.012
#> 8   0.014  0.023  0.002 -0.003 -0.036  0.010 -0.030  0.073 -0.019  0.001 -0.032 -0.014 -0.020
#> 9  -0.018 -0.012 -0.013  0.000 -0.022 -0.016 -0.019 -0.019  0.150 -0.013 -0.019 -0.014 -0.010
#> 10 -0.034 -0.038 -0.025 -0.018 -0.004 -0.030 -0.006  0.001 -0.013  0.160 -0.005 -0.015 -0.010
#> 11 -0.003  0.007 -0.005  0.004 -0.032 -0.003 -0.026 -0.032 -0.019 -0.005  0.096 -0.013 -0.013
#> 12 -0.012 -0.014 -0.015 -0.021 -0.012 -0.013 -0.013 -0.014 -0.014 -0.015 -0.013  0.628 -0.017
#> 13  0.011  0.000 -0.008 -0.047 -0.008  0.002 -0.012 -0.020 -0.010 -0.010 -0.013 -0.017  0.153