Cluster-robust variance-covariance matrix for a rma.mv object.

vcovCR returns a sandwich estimate of the variance-covariance matrix of a set of regression coefficient estimates from a rma.mv object.

Usage

# S3 method for class 'rma.mv'
vcovCR(obj, cluster, type, target, inverse_var, form = "sandwich", ...)

Arguments

obj

Fitted model for which to calculate the variance-covariance matrix

cluster

Optional expression or vector indicating which observations belong to the same cluster. If not specified, will be set to the factor in the random-effects structure with the fewest distinct levels. Caveat emptor: the function does not check that the random effects are nested.

type

Character string specifying which small-sample adjustment should be used, with available options "CR0", "CR1", "CR1p", "CR1S", "CR2", or "CR3". See "Details" section of vcovCR for further information.

target

Optional matrix or vector describing the working variance-covariance model used to calculate the CR2 and CR4 adjustment matrices. If not specified, the target is taken to be the estimated variance-covariance structure of the rma.mv object.

inverse_var

Optional logical indicating whether the weights used in fitting the model are inverse-variance. If not specified, vcovCR will attempt to infer a value.

form

Controls the form of the returned matrix. The default "sandwich" will return the sandwich variance-covariance matrix. Alternately, setting form = "meat" will return only the meat of the sandwich and setting form = B, where B is a matrix of appropriate dimension, will return the sandwich variance-covariance matrix calculated using B as the bread. form = "estfun" will return the (appropriately scaled) estimating function, the transposed crossproduct of which is equal to the sandwich variance-covariance matrix.

...

Additional arguments available for some classes of objects.

Value

An object of class c("vcovCR","clubSandwich"), which consists of a matrix of the estimated variance of and covariances between the regression coefficient estimates.

See also

vcovCR

Examples

pkgs_available <- 
  requireNamespace("metafor", quietly = TRUE) & 
  requireNamespace("metadat", quietly = TRUE)

if (pkgs_available) withAutoprint({

library(metafor)
data(dat.assink2016, package = "metadat")

mfor_fit <- rma.mv(yi ~ year + deltype, 
                 V = vi, random = ~ 1 | study / esid,
                 data = dat.assink2016)
mfor_fit

mfor_CR2 <- vcovCR(mfor_fit, type = "CR2")
mfor_CR2

coef_test(mfor_fit, vcov = mfor_CR2, test = c("Satterthwaite", "saddlepoint"))
Wald_test(mfor_fit, constraints = constrain_zero(3:4), vcov = mfor_CR2)

})
#> > library(metafor)
#> > data(dat.assink2016, package = "metadat")
#> > mfor_fit <- rma.mv(yi ~ year + deltype, 
#> +                  V = vi, random = ~ 1 | study / esid,
#> +                  data = dat.assink2016)
#> > mfor_fit
#> 
#> Multivariate Meta-Analysis Model (k = 100; method: REML)
#> 
#> Variance Components:
#> 
#>             estim    sqrt  nlvls  fixed      factor 
#> sigma^2.1  0.1493  0.3863     17     no       study 
#> sigma^2.2  0.0853  0.2920    100     no  study/esid 
#> 
#> Test for Residual Heterogeneity:
#> QE(df = 96) = 610.2644, p-val < .0001
#> 
#> Test of Moderators (coefficients 2:4):
#> QM(df = 3) = 19.2399, p-val = 0.0002
#> 
#> Model Results:
#> 
#>                 estimate      se     zval    pval    ci.lb    ci.ub      
#> intrcpt          -0.2438  0.2101  -1.1605  0.2458  -0.6556   0.1680      
#> year             -0.0380  0.0183  -2.0773  0.0378  -0.0738  -0.0021    * 
#> deltypegeneral    0.7094  0.1914   3.7069  0.0002   0.3343   1.0845  *** 
#> deltypeovert      0.5054  0.2099   2.4078  0.0160   0.0940   0.9168    * 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> > mfor_CR2 <- vcovCR(mfor_fit, type = "CR2")
#> > mfor_CR2
#>                     intrcpt          year deltypegeneral deltypeovert
#> intrcpt         0.015081059 -0.0020131555  -0.0036579995 -0.007130740
#> year           -0.002013156  0.0007603265  -0.0002607379  0.000218784
#> deltypegeneral -0.003658000 -0.0002607379   0.0042972555  0.004769307
#> deltypeovert   -0.007130740  0.0002187840   0.0047693066  0.010075586
#> > coef_test(mfor_fit, vcov = mfor_CR2, test = c("Satterthwaite", "saddlepoint"))
#>           Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.  s.p.
#>         intrcpt   -0.244 0.1228  -1.99        5.35      0.10015      0.327
#>            year   -0.038 0.0276  -1.38        7.22      0.20977      0.209
#>  deltypegeneral    0.709 0.0656  10.82        2.25      0.00555   ** 0.437
#>    deltypeovert    0.505 0.1004   5.03        2.03      0.03614    * 0.344
#>  p-val (Saddle) Sig.
#>          0.0915    .
#>          0.2103     
#>          <0.001  ***
#>          0.0278    *
#> > Wald_test(mfor_fit, constraints = constrain_zero(3:4), vcov = mfor_CR2)
#>  test Fstat df_num df_denom p_val sig
#>   HTZ  30.6      2    0.842 0.164