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#' @importFrom bayestestR p_direction
#' @export
bayestestR::p_direction
#' @title Probability of Direction (pd)
#' @name p_direction.lm
#'
#' @description Compute the **Probability of Direction** (*pd*, also known as
#' the Maximum Probability of Effect - *MPE*). This can be interpreted as the
#' probability that a parameter (described by its full confidence, or
#' "compatibility" interval) is strictly positive or negative (whichever is the
#' most probable). Although differently expressed, this index is fairly similar
#' (i.e., is strongly correlated) to the frequentist *p-value* (see 'Details').
#'
#' @param x A statistical model.
#' @inheritParams bayestestR::p_direction
#' @inheritParams model_parameters.default
#' @param ... Arguments passed to other methods, e.g. `ci()`. Arguments like
#' `vcov` or `vcov_args` can be used to compute confidence intervals using a
#' specific variance-covariance matrix for the standard errors.
#'
#' @seealso See also [`equivalence_test()`], [`p_function()`] and
#' [`p_significance()`] for functions related to checking effect existence and
#' significance.
#'
#' @inheritSection bayestestR::p_direction What is the *pd*?
#'
#' @inheritSection bayestestR::p_direction Relationship with the p-value
#'
#' @inheritSection bayestestR::p_direction Possible Range of Values
#'
#' @inheritSection model_parameters Statistical inference - how to quantify evidence
#'
#' @references
#'
#' - Amrhein, V., Korner-Nievergelt, F., and Roth, T. (2017). The earth is
#' flat (p > 0.05): Significance thresholds and the crisis of unreplicable
#' research. PeerJ, 5, e3544. \doi{10.7717/peerj.3544}
#'
#' - Greenland S, Rafi Z, Matthews R, Higgs M. To Aid Scientific Inference,
#' Emphasize Unconditional Compatibility Descriptions of Statistics. (2022)
#' https://arxiv.org/abs/1909.08583v7 (Accessed November 10, 2022)
#'
#' - Lakens, D. (2024). Improving Your Statistical Inferences (Version v1.5.1).
#' Retrieved from https://lakens.github.io/statistical_inferences/.
#' \doi{10.5281/ZENODO.6409077}
#'
#' - Lakens, D., Scheel, A. M., and Isager, P. M. (2018). Equivalence Testing
#' for Psychological Research: A Tutorial. Advances in Methods and Practices
#' in Psychological Science, 1(2), 259–269. \doi{10.1177/2515245918770963}
#'
#' - Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., and Lüdecke, D. (2019).
#' Indices of Effect Existence and Significance in the Bayesian Framework.
#' Frontiers in Psychology, 10, 2767. \doi{10.3389/fpsyg.2019.02767}
#'
#' - Rafi Z, Greenland S. Semantic and cognitive tools to aid statistical
#' science: replace confidence and significance by compatibility and surprise.
#' BMC Medical Research Methodology (2020) 20:244.
#'
#' - Schweder T. Confidence is epistemic probability for empirical science.
#' Journal of Statistical Planning and Inference (2018) 195:116–125.
#' \doi{10.1016/j.jspi.2017.09.016}
#'
#' - Schweder T, Hjort NL. Frequentist analogues of priors and posteriors.
#' In Stigum, B. (ed.), Econometrics and the Philosophy of Economics: Theory
#' Data Confrontation in Economics, pp. 285-217. Princeton University Press,
#' Princeton, NJ, 2003
#'
#' - Vos P, Holbert D. Frequentist statistical inference without repeated sampling.
#' Synthese 200, 89 (2022). \doi{10.1007/s11229-022-03560-x}
#'
#' @return A data frame.
#'
#' @examplesIf requireNamespace("bayestestR") && require("see", quietly = TRUE) && requireNamespace("sandwich")
#' data(qol_cancer)
#' model <- lm(QoL ~ time + age + education, data = qol_cancer)
#' p_direction(model)
#'
#' # based on heteroscedasticity-robust standard errors
#' p_direction(model, vcov = "HC3")
#'
#' result <- p_direction(model)
#' plot(result)
#' @export
p_direction.lm <- function(x,
ci = 0.95,
method = "direct",
null = 0,
vcov = NULL,
vcov_args = NULL,
...) {
# generate normal distribution based on CI range
result <- .posterior_ci(x, ci, vcov = vcov, vcov_args = vcov_args, ...)
# copy
out <- result$out
posterior <- result$posterior
# add pd
out$pd <- as.numeric(bayestestR::p_direction(
posterior,
method = method,
null = null,
...
))
# reorder
out <- out[intersect(c("Parameter", "CI", "CI_low", "CI_high", "pd", "Effects", "Component"), colnames(out))]
attr(out, "data") <- posterior
attr(out, "null") <- null
class(out) <- c("p_direction_lm", "p_direction", "see_p_direction", "data.frame")
out
}
# methods ---------------------------------------------------------------------
#' @export
print.p_direction_lm <- function(x, digits = 2, p_digits = 3, ...) {
null <- attributes(x)$null
caption <- sprintf(
"Probability of Direction (null: %s)",
insight::format_value(null, digits = digits, protect_integer = TRUE)
)
x <- insight::format_table(x, digits = digits, p_digits = p_digits)
cat(insight::export_table(x, title = caption, ...))
}
# other classes --------------------------------------------------------------
#' @export
p_direction.glm <- p_direction.lm
#' @export
p_direction.coxph <- p_direction.lm
#' @export
p_direction.svyglm <- p_direction.lm
#' @export
p_direction.glmmTMB <- p_direction.lm
#' @export
p_direction.merMod <- p_direction.lm
#' @export
p_direction.wbm <- p_direction.lm
#' @export
p_direction.lme <- p_direction.lm
#' @export
p_direction.gee <- p_direction.lm
#' @export
p_direction.gls <- p_direction.lm
#' @export
p_direction.feis <- p_direction.lm
#' @export
p_direction.felm <- p_direction.lm
#' @export
p_direction.mixed <- p_direction.lm
#' @export
p_direction.hurdle <- p_direction.lm
#' @export
p_direction.zeroinfl <- p_direction.lm
#' @export
p_direction.rma <- p_direction.lm
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