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.

## Value

A data frame summarizing the bootstrapped parameters.

## 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.

bootstrap_model(), simulate_parameters(), simulate_model()

## 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%
# }