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 fixed-effects models) and \(v_i\) is the sampling variance of the \(i\)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.

Author

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

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

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 vcov(res, type="obs")
#> 1 2 3 4 5 6 7 #> 1 0.4363721 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 #> 2 0.0000000 0.3053685 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 #> 3 0.0000000 0.0000000 0.5261553 0.0000000 0.0000000 0.000000 0.0000000 #> 4 0.0000000 0.0000000 0.0000000 0.1307974 0.0000000 0.000000 0.0000000 #> 5 0.0000000 0.0000000 0.0000000 0.0000000 0.1619975 0.000000 0.0000000 #> 6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.117693 0.0000000 #> 7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.3338046 #> 8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 #> 9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 #> 10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 #> 11 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 #> 12 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 #> 13 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 0.0000000 #> 8 9 10 11 12 13 #> 1 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 #> 2 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 #> 3 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 #> 4 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 #> 5 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 #> 6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 #> 7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 #> 8 0.1147489 0.0000000 0.0000000 0.0000000 0.0000000 0.000000 #> 9 0.0000000 0.1672216 0.0000000 0.0000000 0.0000000 0.000000 #> 10 0.0000000 0.0000000 0.1838121 0.0000000 0.0000000 0.000000 #> 11 0.0000000 0.0000000 0.0000000 0.1231996 0.0000000 0.000000 #> 12 0.0000000 0.0000000 0.0000000 0.0000000 0.6432932 0.000000 #> 13 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.182192
### var-cov matrix of the fitted values vcov(res, type="fitted")
#> 1 2 3 4 5 #> 1 0.075274494 0.066352321 0.036850236 -2.415804e-02 0.008969395 #> 2 0.066352321 0.072275443 0.039773414 1.147263e-02 -0.008575967 #> 3 0.036850236 0.039773414 0.025624295 1.415547e-02 0.004190524 #> 4 -0.024158035 0.011472626 0.014155473 1.057123e-01 -0.022285939 #> 5 0.008969395 -0.008575967 0.004190524 -2.228594e-02 0.040217694 #> 6 0.058837510 0.055885092 0.032460721 -5.773337e-03 0.005698563 #> 7 0.005895881 -0.004203294 0.006263841 -4.856637e-03 0.031004314 #> 8 -0.014042383 -0.023230087 -0.001954797 3.452639e-03 0.035638528 #> 9 0.018234846 0.012094166 0.013417779 -2.265090e-06 0.021990641 #> 10 0.033562839 0.037679969 0.024746392 1.783241e-02 0.003536357 #> 11 0.003120737 -0.007025518 0.005040385 -4.084581e-03 0.031885711 #> 12 0.011873935 0.014373393 0.014613193 2.110398e-02 0.012123095 #> 13 -0.011137843 -0.000280727 0.008467872 4.684255e-02 0.007543929 #> 6 7 8 9 10 #> 1 0.058837510 0.005895881 -0.014042383 1.823485e-02 0.033562839 #> 2 0.055885092 -0.004203294 -0.023230087 1.209417e-02 0.037679969 #> 3 0.032460721 0.006263841 -0.001954797 1.341778e-02 0.024746392 #> 4 -0.005773337 -0.004856637 0.003452639 -2.265090e-06 0.017832413 #> 5 0.005698563 0.031004314 0.035638528 2.199064e-02 0.003536357 #> 6 0.047790886 0.005293240 -0.009766710 1.579943e-02 0.030251397 #> 7 0.005293240 0.025561416 0.030160616 1.890686e-02 0.006143313 #> 8 -0.009766710 0.030160616 0.041624471 1.858106e-02 -0.001099662 #> 9 0.015799432 0.018906860 0.018581060 1.723057e-02 0.012930696 #> 10 0.030251397 0.006143313 -0.001099662 1.293070e-02 0.024084104 #> 11 0.003151469 0.026348037 0.031928736 1.893374e-02 0.005046532 #> 12 0.013184784 0.013343434 0.013958283 1.365970e-02 0.014875363 #> 13 -0.002280489 0.012499736 0.019944225 1.025012e-02 0.010239343 #> 11 12 13 #> 1 0.003120737 0.01187394 -0.011137843 #> 2 -0.007025518 0.01437339 -0.000280727 #> 3 0.005040385 0.01461319 0.008467872 #> 4 -0.004084581 0.02110398 0.046842555 #> 5 0.031885711 0.01212309 0.007543929 #> 6 0.003151469 0.01318478 -0.002280489 #> 7 0.026348037 0.01334343 0.012499736 #> 8 0.031928736 0.01395828 0.019944225 #> 9 0.018933741 0.01365970 0.010250123 #> 10 0.005046532 0.01487536 0.010239343 #> 11 0.027277130 0.01340221 0.013445239 #> 12 0.013402214 0.01514221 0.016977401 #> 13 0.013445239 0.01697740 0.029377697
### var-cov matrix of the residuals vcov(res, type="resid")
#> 1 2 3 4 5 #> 1 0.361097623 -0.066352321 -0.036850236 2.415804e-02 -0.008969395 #> 2 -0.066352321 0.233093030 -0.039773414 -1.147263e-02 0.008575967 #> 3 -0.036850236 -0.039773414 0.500531022 -1.415547e-02 -0.004190524 #> 4 0.024158035 -0.011472626 -0.014155473 2.508510e-02 0.022285939 #> 5 -0.008969395 0.008575967 -0.004190524 2.228594e-02 0.121779830 #> 6 -0.058837510 -0.055885092 -0.032460721 5.773337e-03 -0.005698563 #> 7 -0.005895881 0.004203294 -0.006263841 4.856637e-03 -0.031004314 #> 8 0.014042383 0.023230087 0.001954797 -3.452639e-03 -0.035638528 #> 9 -0.018234846 -0.012094166 -0.013417779 2.265091e-06 -0.021990641 #> 10 -0.033562839 -0.037679969 -0.024746392 -1.783241e-02 -0.003536357 #> 11 -0.003120737 0.007025518 -0.005040385 4.084581e-03 -0.031885711 #> 12 -0.011873935 -0.014373393 -0.014613193 -2.110398e-02 -0.012123095 #> 13 0.011137843 0.000280727 -0.008467872 -4.684255e-02 -0.007543929 #> 6 7 8 9 10 #> 1 -0.058837510 -0.005895881 0.014042383 -1.823485e-02 -0.033562839 #> 2 -0.055885092 0.004203294 0.023230087 -1.209417e-02 -0.037679969 #> 3 -0.032460721 -0.006263841 0.001954797 -1.341778e-02 -0.024746392 #> 4 0.005773337 0.004856637 -0.003452639 2.265091e-06 -0.017832413 #> 5 -0.005698563 -0.031004314 -0.035638528 -2.199064e-02 -0.003536357 #> 6 0.069902084 -0.005293240 0.009766710 -1.579943e-02 -0.030251397 #> 7 -0.005293240 0.308243183 -0.030160616 -1.890686e-02 -0.006143313 #> 8 0.009766710 -0.030160616 0.073124460 -1.858106e-02 0.001099662 #> 9 -0.015799432 -0.018906860 -0.018581060 1.499910e-01 -0.012930696 #> 10 -0.030251397 -0.006143313 0.001099662 -1.293070e-02 0.159728042 #> 11 -0.003151469 -0.026348037 -0.031928736 -1.893374e-02 -0.005046532 #> 12 -0.013184784 -0.013343434 -0.013958283 -1.365970e-02 -0.014875363 #> 13 0.002280489 -0.012499736 -0.019944225 -1.025012e-02 -0.010239343 #> 11 12 13 #> 1 -0.003120737 -0.01187394 0.011137843 #> 2 0.007025518 -0.01437339 0.000280727 #> 3 -0.005040385 -0.01461319 -0.008467872 #> 4 0.004084581 -0.02110398 -0.046842555 #> 5 -0.031885711 -0.01212309 -0.007543929 #> 6 -0.003151469 -0.01318478 0.002280489 #> 7 -0.026348037 -0.01334343 -0.012499736 #> 8 -0.031928736 -0.01395828 -0.019944225 #> 9 -0.018933741 -0.01365970 -0.010250123 #> 10 -0.005046532 -0.01487536 -0.010239343 #> 11 0.095922436 -0.01340221 -0.013445239 #> 12 -0.013402214 0.62815098 -0.016977401 #> 13 -0.013445239 -0.01697740 0.152814314