impute_covariance_matrix {clubSandwich} R Documentation

## Impute a block-diagonal covariance matrix

### Description

impute_covariance_matrix calculates a block-diagonal covariance matrix, given the marginal variances, the block structure, and an assumed correlation structure. Can be used to create compound-symmetric structures, AR(1) auto-correlated structures, or combinations thereof.

### Usage

impute_covariance_matrix(
vi,
cluster,
r,
ti,
ar1,
smooth_vi = FALSE,
subgroup = NULL,
return_list = identical(as.factor(cluster), sort(as.factor(cluster))),
check_PD = TRUE
)

### Arguments

 vi Vector of variances cluster Vector indicating which effects belong to the same cluster. Effects with the same value of 'cluster' will be treated as correlated. r Vector or numeric value of assumed constant correlation(s) between effect size estimates from each study. ti Vector of time-points describing temporal spacing of effects, for use with auto-regressive correlation structures. ar1 Vector or numeric value of assumed AR(1) auto-correlation(s) between effect size estimates from each study. If specified, then ti argument must be specified. smooth_vi Logical indicating whether to smooth the marginal variances by taking the average vi within each cluster. Defaults to FALSE. subgroup Vector of category labels describing sub-groups of effects. If non-null, effects that share the same category label and the same cluster will be treated as correlated, but effects with different category labels will be treated as uncorrelated, even if they come from the same cluster. return_list Optional logical indicating whether to return a list of matrices (with one entry per block) or the full variance-covariance matrix. check_PD Optional logical indicating whether to check whether each covariance matrix is positive definite. If TRUE (the default), the function will display a warning if any covariance matrix is not positive definite.

### Details

A block-diagonal variance-covariance matrix (possibly represented as a list of matrices) with a specified structure. The structure depends on whether the r argument, ar1 argument, or both arguments are specified. Let v_{ij} denote the specified variance for effect i in cluster j and C_{hij} be the covariance between effects h and i in cluster j.

• If only r is specified, each block of the variance-covariance matrix will have a constant (compound symmetric) correlation, so that

C_{hij} = r_j \sqrt{v_{hj} v_{ij},}

where r_j is the specified correlation for cluster j. If only a single value is given in r, then it will be used for every cluster.

• If only ar1 is specified, each block of the variance-covariance matrix will have an AR(1) auto-correlation structure, so that

C_{hij} = \phi_j^{|t_{hj} - t_{ij}|} \sqrt{v_{hj} v_{ij},}

where \phi_j is the specified auto-correlation for cluster j and t_{hj} and t_{ij} are specified time-points corresponding to effects h and i in cluster j. If only a single value is given in ar1, then it will be used for every cluster.

• If both r and ar1 are specified, each block of the variance-covariance matrix will have combination of compound symmetric and an AR(1) auto-correlation structures, so that

C_{hij} = \left[r_j + (1 - r_j)\phi_j^{|t_{hj} - t_{ij}|}\right] \sqrt{v_{hj} v_{ij},}

where r_j is the specified constant correlation for cluster j, \phi_j is the specified auto-correlation for cluster j and t_{hj} and t_{ij} are specified time-points corresponding to effects h and i in cluster j. If only single values are given in r or ar1, they will be used for every cluster.

If smooth_vi = TRUE, then all of the variances within cluster j will be set equal to the average variance of cluster j, i.e.,

v'_{ij} = \frac{1}{n_j} \sum_{i=1}^{n_j} v_{ij}

for i=1,...,n_j and j=1,...,k.

### Value

If cluster is appropriately sorted, then a list of matrices, with one entry per cluster, will be returned by default. If cluster is out of order, then the full variance-covariance matrix will be returned by default. The output structure can be controlled with the optional return_list argument.

### Examples

library(metafor)

# Constant correlation
data(SATcoaching)
V_list <- impute_covariance_matrix(vi = SATcoaching$V, cluster = SATcoaching$study, r = 0.66)
MVFE <- rma.mv(d ~ 0 + test, V = V_list, data = SATcoaching)
conf_int(MVFE, vcov = "CR2", cluster = SATcoaching\$study)

[Package clubSandwich version 0.5.6 Index]