# Calculate p-values with cluster wild bootstrapping for meta-regression models.

Source:`R/Wald_test_wildmeta.R`

`Wald_test_cwb.Rd`

Calculate p-values for single coefficient and multiple contrast hypothesis tests using cluster wild bootstrapping.

## Usage

```
Wald_test_cwb(
full_model,
constraints,
R,
cluster = NULL,
auxiliary_dist = "Rademacher",
adjust = "CR0",
type = "CR0",
test = "Naive-F",
seed = NULL,
future_args = NULL
)
```

## Arguments

- full_model
Model fit using

`robumeta::robu()`

,`metafor::rma.mv()`

, or`metafor::rma.uni()`

that includes the full set of moderators in the meta-regression model.- constraints
A q X p constraint matrix be tested. Alternately, a function to create such a matrix, specified using

`clubSandwich::constrain_equal()`

or`clubSandwich::constrain_zero()`

.- R
Number of bootstrap replications.

- cluster
Vector of identifiers indicating which observations belong to the same cluster. If

`NULL`

(the default), then the clustering variable will be inferred based on the structure of`full_mod`

.- auxiliary_dist
Character string indicating the auxiliary distribution to be used for cluster wild bootstrapping, with available options: "Rademacher", "Mammen", "Webb six", "uniform", "standard normal". The default is set to "Rademacher." We recommend the Rademacher distribution for models that have at least 10 clusters. For models with less than 10 clusters, we recommend the use of "Webb six" distribution.

- adjust
Character string specifying which small-sample adjustment should be used to multiply the residuals by. The available options are

`"CRO"`

,`"CR1"`

,`"CR2"`

,`"CR3"`

, or`"CR4"`

, with a default of`"CRO"`

.- type
Character string specifying which small-sample adjustment is used to calculate the Wald test statistic. The available options are

`"CRO"`

,`"CR1"`

,`"CR2"`

,`"CR3"`

, or`"CR4"`

, with a default of`"CRO"`

.- test
Character string specifying which (if any) small-sample adjustment is used in calculating the test statistic. Default is

`"Naive-F"`

, which does not make any small-sample adjustment.- seed
Optional seed value to ensure reproducibility.

- future_args
Optional list of additional arguments passed to the

`future_*()`

functions used in calculating results across bootstrap replications. Ignored if the future.apply package is not available.

## Value

A `data.frame`

containing the name of the test, the adjustment
used for the bootstrap process, the type of variance-covariance matrix
used, the type of test statistic, the number of bootstrap replicates, and
the bootstrapped p-value.

## Examples

```
library(clubSandwich)
library(robumeta)
model <- robu(d ~ 0 + study_type + hrs + test,
studynum = study,
var.eff.size = V,
small = FALSE,
data = SATcoaching)
C_mat <- constrain_equal(1:3, coefs = coef(model))
Wald_test_cwb(full_model = model,
constraints = C_mat,
R = 12)
#> Test Adjustment CR_type Statistic R p_val
#> 1 CWB CR0 CR0 Naive-F 12 0.3333333
# Equivalent, using constrain_equal()
Wald_test_cwb(full_model = model,
constraints = constrain_equal(1:3),
R = 12)
#> Test Adjustment CR_type Statistic R p_val
#> 1 CWB CR0 CR0 Naive-F 12 0.3333333
```