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

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

## Arguments

model Statistical model. The number of draws to simulate/bootstrap. The point-estimates (centrality indices) to compute. Character (vector) or list with one or more of these options: "median", "mean", "MAP" or "all". Value or vector of probability of the CI (between 0 and 1) to be estimated. Default to .95 (95%). The type of index used for Credible Interval. Can be "HDI" (default, see hdi), "ETI" (see eti), "BCI" (see bci) or "SI" (see si). 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. rope or p_direction) and its results included in the summary output. Arguments passed to or from other methods.

## 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 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

if (FALSE) {
if (require("boot", quietly = TRUE)) {
set.seed(2)
model <- lm(Sepal.Length ~ Species * Petal.Width, data = iris)
b <- bootstrap_parameters(model)
print(b)

if (require("emmeans")) {
est <- emmeans(b, trt.vs.ctrl ~ Species)
print(model_parameters(est))
}
}
}