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#' Compute Support Intervals
#'
#' A support interval contains only the values of the parameter that predict the observed data better
#' than average, by some degree *k*; these are values of the parameter that are associated with an
#' updating factor greater or equal than *k*. From the perspective of the Savage-Dickey Bayes factor, testing
#' against a point null hypothesis for any value within the support interval will yield a Bayes factor smaller
#' than *1/k*.
#'
#' **For more info, in particular on specifying correct priors for factors with more than 2 levels,
#' see [the Bayes factors vignette](https://easystats.github.io/bayestestR/articles/bayes_factors.html).**
#'
#' @param BF The amount of support required to be included in the support interval.
#' @inheritParams bayesfactor_parameters
#' @inheritParams hdi
#' @inherit hdi seealso
#' @family ci
#'
#' @details This method is used to compute support intervals based on prior and posterior distributions.
#' For the computation of support intervals, the model priors must be proper priors (at the very least
#' they should be *not flat*, and it is preferable that they be *informative* - note
#' that by default, `brms::brm()` uses flat priors for fixed-effects; see example below).
#'
#' @section Choosing a value of `BF`:
#' The choice of `BF` (the level of support) depends on what we want our interval
#' to represent:
#'
#' - A `BF` = 1 contains values whose credibility is not decreased by observing the data.
#' - A `BF` > 1 contains values who received more impressive support from the data.
#' - A `BF` < 1 contains values whose credibility has *not* been impressively
#' decreased by observing the data. Testing against values outside this interval
#' will produce a Bayes factor larger than 1/`BF` in support of the alternative.
#' E.g., if an SI (BF = 1/3) excludes 0, the Bayes factor against the point-null
#' will be larger than 3.
#'
#' @inheritSection bayesfactor_parameters Setting the correct `prior`
#'
#' @note There is also a [`plot()`-method](https://easystats.github.io/see/articles/bayestestR.html) implemented in the \href{https://easystats.github.io/see/}{\pkg{see}-package}.
#'
#' @return
#' A data frame containing the lower and upper bounds of the SI.
#'
#' Note that if the level of requested support is higher than observed in the data, the
#' interval will be `[NA,NA]`.
#'
#' @examplesIf require("logspline") && require("rstanarm") && require("brms") && require("emmeans")
#' library(bayestestR)
#'
#' prior <- distribution_normal(1000, mean = 0, sd = 1)
#' posterior <- distribution_normal(1000, mean = 0.5, sd = 0.3)
#'
#' si(posterior, prior, verbose = FALSE)
#' \donttest{
#' # rstanarm models
#' # ---------------
#' library(rstanarm)
#' contrasts(sleep$group) <- contr.equalprior_pairs # see vignette
#' stan_model <- stan_lmer(extra ~ group + (1 | ID), data = sleep)
#' si(stan_model, verbose = FALSE)
#' si(stan_model, BF = 3, verbose = FALSE)
#'
#' # emmGrid objects
#' # ---------------
#' library(emmeans)
#' group_diff <- pairs(emmeans(stan_model, ~group))
#' si(group_diff, prior = stan_model, verbose = FALSE)
#'
#' # brms models
#' # -----------
#' library(brms)
#' contrasts(sleep$group) <- contr.equalprior_pairs # see vingette
#' my_custom_priors <-
#' set_prior("student_t(3, 0, 1)", class = "b") +
#' set_prior("student_t(3, 0, 1)", class = "sd", group = "ID")
#'
#' brms_model <- suppressWarnings(brm(extra ~ group + (1 | ID),
#' data = sleep,
#' prior = my_custom_priors,
#' refresh = 0
#' ))
#' si(brms_model, verbose = FALSE)
#' }
#' @references
#' Wagenmakers, E., Gronau, Q. F., Dablander, F., & Etz, A. (2018, November 22).
#' The Support Interval. \doi{10.31234/osf.io/zwnxb}
#'
#' @export
si <- function(posterior, ...) {
UseMethod("si")
}
#' @rdname si
#' @export
si.numeric <- function(posterior, prior = NULL, BF = 1, verbose = TRUE, ...) {
if (is.null(prior)) {
prior <- posterior
if (verbose) {
insight::format_warning(
"Prior not specified!",
"Support intervals ('si') can only be computed for Bayesian models with proper priors.",
"Please specify priors (with column order matching 'posterior')."
)
}
}
prior <- data.frame(X = prior)
posterior <- data.frame(X = posterior)
# Get SIs
out <- si.data.frame(
posterior = posterior, prior = prior,
BF = BF, verbose = verbose, ...
)
out$Parameter <- NULL
out
}
#' @rdname si
#' @export
si.stanreg <- function(posterior, prior = NULL,
BF = 1, verbose = TRUE,
effects = c("fixed", "random", "all"),
component = c("location", "conditional", "all", "smooth_terms", "sigma", "auxiliary", "distributional"),
parameters = NULL,
...) {
cleaned_parameters <- insight::clean_parameters(posterior)
effects <- match.arg(effects)
component <- match.arg(component)
samps <- .clean_priors_and_posteriors(posterior, prior,
effects = effects, component = component,
parameters = parameters, verbose = verbose
)
# Get SIs
temp <- si.data.frame(
posterior = samps$posterior, prior = samps$prior,
BF = BF, verbose = verbose, ...
)
out <- .prepare_output(temp, cleaned_parameters, inherits(posterior, "stanmvreg"))
attr(out, "ci_method") <- "SI"
attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(posterior))
class(out) <- class(temp)
attr(out, "plot_data") <- attr(temp, "plot_data")
out
}
#' @rdname si
#' @export
si.brmsfit <- si.stanreg
#' @rdname si
#' @export
si.blavaan <- si.stanreg
#' @rdname si
#' @export
si.emmGrid <- function(posterior, prior = NULL,
BF = 1, verbose = TRUE, ...) {
samps <- .clean_priors_and_posteriors(posterior, prior, verbose = verbose)
# Get SIs
out <- si.data.frame(
posterior = samps$posterior, prior = samps$prior,
BF = BF, verbose = verbose, ...
)
attr(out, "ci_method") <- "SI"
attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(posterior))
out
}
#' @export
si.emm_list <- si.emmGrid
#' @export
si.stanfit <- function(posterior, prior = NULL, BF = 1, verbose = TRUE, effects = c("fixed", "random", "all"), ...) {
out <- si(insight::get_parameters(posterior, effects = effects),
prior = prior, BF = BF, verbose = verbose
)
attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(posterior))
out
}
#' @rdname si
#' @export
si.get_predicted <- function(posterior, prior = NULL, BF = 1, use_iterations = FALSE, verbose = TRUE, ...) {
if (isTRUE(use_iterations)) {
if ("iterations" %in% names(attributes(posterior))) {
out <- si(
as.data.frame(t(attributes(posterior)$iterations)),
prior = prior,
BF = BF,
verbose = verbose,
...
)
} else {
insight::format_error("No iterations present in the output.")
}
attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(posterior))
} else {
out <- si(insight::get_parameters(posterior), prior = prior, BF = BF, verbose = verbose, ...)
}
out
}
#' @rdname si
#' @export
si.data.frame <- function(posterior, prior = NULL, BF = 1, verbose = TRUE, ...) {
if (is.null(prior)) {
prior <- posterior
insight::format_warning(
"Prior not specified!",
"Support intervals ('si') can only be computed for Bayesian models with proper priors.",
"Please specify priors (with column order matching 'posterior')."
)
}
if (verbose && (nrow(posterior) < 4e4 || nrow(prior) < 4e4)) {
insight::format_warning(
"Support intervals might not be precise.",
"For precise support intervals, sampling at least 40,000 posterior samples is recommended."
)
}
out <- lapply(BF, function(BFi) {
.si.data.frame(posterior, prior, BFi, verbose = verbose)
})
out <- do.call(rbind, out)
attr(out, "ci_method") <- "SI"
attr(out, "ci") <- BF
attr(out, "plot_data") <- .make_BF_plot_data(posterior, prior, 0, 0, ...)$plot_data
class(out) <- unique(c("bayestestR_si", "see_si", "bayestestR_ci", "see_ci", class(out)))
out
}
#' @export
si.draws <- function(posterior, prior = NULL, BF = 1, verbose = TRUE, ...) {
si(.posterior_draws_to_df(posterior), prior = prior, BF = BF, verbose = verbose, ...)
}
#' @export
si.rvar <- si.draws
# Helper ------------------------------------------------------------------
.si.data.frame <- function(posterior, prior, BF, verbose = TRUE, ...) {
sis <- matrix(NA, nrow = ncol(posterior), ncol = 2)
for (par in seq_along(posterior)) {
sis[par, ] <- .si(posterior[[par]],
prior[[par]],
BF = BF,
verbose = verbose,
...
)
}
out <- data.frame(
Parameter = colnames(posterior),
CI = BF,
CI_low = sis[, 1],
CI_high = sis[, 2],
stringsAsFactors = FALSE
)
}
#' @keywords internal
.si <- function(posterior, prior, BF = 1, extend_scale = 0.05, precision = 2^8, verbose = TRUE, ...) {
insight::check_if_installed("logspline")
if (isTRUE(all.equal(prior, posterior))) {
return(c(NA, NA))
}
x <- c(prior, posterior)
x_range <- range(x)
x_rangex <- stats::median(x) + 7 * stats::mad(x) * c(-1, 1)
x_range <- c(
max(c(x_range[1], x_rangex[1])),
min(c(x_range[2], x_rangex[2]))
)
extension_scale <- diff(x_range) * extend_scale
x_range <- x_range + c(-1, 1) * extension_scale
x_axis <- seq(x_range[1], x_range[2], length.out = precision)
f_prior <- .logspline(prior, ...)
f_posterior <- .logspline(posterior, ...)
d_prior <- logspline::dlogspline(x_axis, f_prior)
d_posterior <- logspline::dlogspline(x_axis, f_posterior)
relative_d <- d_posterior / d_prior
crit <- relative_d >= BF
cp <- rle(stats::na.omit(crit))
if (length(cp$lengths) > 3 && verbose) {
insight::format_warning("More than 1 SI detected. Plot the result to investigate.")
}
x_supported <- stats::na.omit(x_axis[crit])
if (length(x_supported) < 2) {
return(c(NA, NA))
}
range(x_supported)
}
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