impute_covariance_matrix {clubSandwich} | R Documentation |

`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.

```
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
)
```

`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 |

`smooth_vi` |
Logical indicating whether to smooth the marginal variances
by taking the average |

`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 |

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`

.

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.

```
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]