Compute bootstrapped parameters and their related indices such as Confidence Intervals (CI) and p-values.

## Usage

```
bootstrap_parameters(model, ...)
# Default S3 method
bootstrap_parameters(
model,
iterations = 1000,
centrality = "median",
ci = 0.95,
ci_method = "quantile",
test = "p-value",
...
)
```

## Arguments

- model
Statistical model.

- ...
Arguments passed to or from other methods.

- iterations
The number of draws to simulate/bootstrap.

- centrality
The point-estimates (centrality indices) to compute. Character (vector) or list with one or more of these options:

`"median"`

,`"mean"`

,`"MAP"`

(see`map_estimate()`

),`"trimmed"`

(which is just`mean(x, trim = threshold)`

),`"mode"`

or`"all"`

.- ci
Value or vector of probability of the CI (between 0 and 1) to be estimated. Default to

`0.95`

(`95%`

).- ci_method
The type of index used for Credible Interval. Can be

`"ETI"`

(default, see`eti()`

),`"HDI"`

(see`hdi()`

),`"BCI"`

(see`bci()`

),`"SPI"`

(see`spi()`

), or`"SI"`

(see`si()`

).- test
The indices to compute. Character (vector) with one or more of these options:

`"p-value"`

(or`"p"`

),`"p_direction"`

(or`"pd"`

),`"rope"`

,`"p_map"`

,`"equivalence_test"`

(or`"equitest"`

),`"bayesfactor"`

(or`"bf"`

) or`"all"`

to compute all tests. For each "test", the corresponding**bayestestR**function is called (e.g.`bayestestR::rope()`

or`bayestestR::p_direction()`

) and its results included in the summary output.

## Details

This function first calls `bootstrap_model()`

to generate
bootstrapped coefficients. The resulting replicated for each coefficient
are treated as "distribution", and is passed to `bayestestR::describe_posterior()`

to calculate the related indices defined in the `"test"`

argument.

Note that that p-values returned here are estimated under the assumption of
*translation equivariance*: that shape of the sampling distribution is
unaffected by the null being true or not. If this assumption does not hold,
p-values can be biased, and it is suggested to use proper permutation tests
to obtain non-parametric p-values.

## Using with **emmeans**

The output can be passed directly to the various functions from the
**emmeans** package, to obtain bootstrapped estimates, contrasts, simple
slopes, etc. and their confidence intervals. These can then be passed to
`model_parameter()`

to obtain standard errors, p-values, etc. (see
example).

Note that that p-values returned here are estimated under the assumption of
*translation equivariance*: that shape of the sampling distribution is
unaffected by the null being true or not. If this assumption does not hold,
p-values can be biased, and it is suggested to use proper permutation tests
to obtain non-parametric p-values.

## References

Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application (Vol. 1). Cambridge university press.

## Examples

```
# \donttest{
set.seed(2)
model <- lm(Sepal.Length ~ Species * Petal.Width, data = iris)
b <- bootstrap_parameters(model)
print(b)
#> # Fixed Effects
#>
#> Parameter | Coefficient | 95% CI | p
#> --------------------------------------------------------------------
#> (Intercept) | 4.78 | [ 4.50, 5.00] | < .001
#> Speciesversicolor | -0.72 | [-1.62, 0.08] | 0.082
#> Speciesvirginica | 0.50 | [-0.67, 1.65] | 0.422
#> Petal.Width | 0.91 | [ 0.22, 1.97] | 0.016
#> Speciesversicolor:Petal.Width | 0.50 | [-0.66, 1.52] | 0.390
#> Speciesvirginica:Petal.Width | -0.27 | [-1.36, 0.67] | 0.558
est <- emmeans::emmeans(b, trt.vs.ctrl ~ Species)
#> NOTE: Results may be misleading due to involvement in interactions
print(model_parameters(est))
#> # Estimated Marginal Means
#>
#> Parameter | Median | 95% CI | pd
#> -----------------------------------------
#> setosa | 5.87 | [5.21, 6.87] | 100%
#> versicolor | 5.76 | [5.63, 5.89] | 100%
#> virginica | 6.04 | [5.55, 6.55] | 100%
#>
#> # Contrasts
#>
#> Parameter | Median | 95% CI | pd
#> -----------------------------------------------------
#> versicolor - setosa | -0.12 | [-1.09, 0.54] | 61.60%
#> virginica - setosa | 0.14 | [-0.91, 1.01] | 61.70%
# }
```