/
jfa-methods.R
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jfa-methods.R
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# Copyright (C) 2020-2023 Koen Derks
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#' Methods for jfa objects
#'
#' Methods defined for objects returned from the \code{\link{auditPrior}}, \code{\link{planning}}, \code{\link{selection}}, and \code{\link{evaluation}} functions.
#'
#' @param object,x an object of class \code{jfaPrior}, \code{jfaPosterior}, \code{jfaPlanning}, \code{jfaSelection}, \code{jfaEvaluation}, \code{jfaDistr}, \code{jfaRv}, or \code{jfaFairness}.
#' @param digits an integer specifying the number of digits to which output should be rounded. Used in \code{summary}.
#' @param type used in \code{plot}. Specifies the type of plot to produce.
#' @param n used in \code{predict}. Specifies the sample size for which predictions should be made.
#' @param cumulative used in \code{predict}. Specifies whether cumulative probabilities should be shown.
#' @param ... further arguments, currently ignored.
#'
#' @return
#' The \code{summary} methods return a \code{data.frame} which contains the input and output.
#'
#' The \code{print} methods simply print and return nothing.
#'
#' @name jfa-methods
NULL
# Methods for class: jfaPrior #####################################################
#' @rdname jfa-methods
#' @method print jfaPrior
#' @export
print.jfaPrior <- function(x, ...) {
cat("\n")
cat(strwrap("Prior Distribution for Audit Sampling", prefix = "\t"), sep = "\n")
cat("\n")
cat("functional form:", x[["prior"]], "\nparameters obtained via method", paste0("'", x[["method"]], "'\n"))
}
#' @rdname jfa-methods
#' @method print summary.jfaPrior
#' @export
print.summary.jfaPrior <- function(x, digits = getOption("digits"), ...) {
cat("\n")
cat(strwrap("Prior Distribution Summary", prefix = "\t"), sep = "\n")
cat("\nOptions:\n")
cat(paste(" Likelihood: ", x[["likelihood"]]), "\n")
cat(paste(" Specifics: ", switch(x[["method"]],
"default" = "default prior",
"strict" = "improper prior",
"impartial" = paste0("p(\u0398 < ", x[["materiality"]], ") = p(\u0398 > ", x[["materiality"]], ") = 0.5"),
"hyp" = paste0("p(\u0398 < ", x[["materiality"]], ") = ", x[["p.h1"]], "; p(\u0398 > ", x[["materiality"]], ") = ", x[["p.h0"]]),
"arm" = paste0("ir = ", x[["ir"]], "; cr = ", x[["icr"]], "; dr = ", x[["dr"]]),
"bram" = paste0("mode = ", x[["mode.prior"]], "; upper bound = ", x[["ub.prior"]]),
"sample" = paste0("earlier sample of ", x[["n.prior"]], " items with ", x[["x.prior"]], " errors"),
"factor" = paste0("earlier sample of ", x[["n.prior"]], " items with ", x[["x.prior"]], " errors weighted by ", x[["factor"]]),
"param" = paste0("\u03B1 = ", x[["alpha"]], "; \u03B2 = ", x[["beta"]]),
"nonparam" = "nonparametric prior",
"mcmc" = "nonparametric prior"
)), "\n")
cat("\nResults:\n")
cat(paste(" Functional form: ", x[["prior"]]), "\n")
if (!is.null(x[["implicit.n"]]) && x[["method"]] %in% c("poisson", "binomial", "hypergeometric")) {
cat(paste(" Equivalent sample size: ", format(x[["implicit.n"]], digits = max(1L, digits - 2L))), "\n")
}
if (!is.null(x[["implicit.x"]]) && x[["method"]] %in% c("poisson", "binomial", "hypergeometric")) {
cat(paste(" Equivalent errors: ", format(x[["implicit.x"]], digits = max(1L, digits - 2L))), "\n")
}
cat(paste(" Mode: ", format(x[["mode"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Mean: ", format(x[["mean"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Median: ", format(x[["median"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Variance: ", format(x[["var"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Skewness: ", format(x[["skewness"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Information entropy (nat): ", format(x[["entropy"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" ", format(x[["conf.level"]] * 100), "percent upper bound: ", format(x[["ub"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Precision: ", format(x[["precision"]], digits = max(1L, digits - 2L))), "\n")
}
#' @rdname jfa-methods
#' @method summary jfaPrior
#' @export
summary.jfaPrior <- function(object, digits = getOption("digits"), ...) {
out <- data.frame(
"conf.level" = round(object[["conf.level"]], digits),
"likelihood" = object[["likelihood"]],
"method" = object[["method"]],
"prior" = object[["prior"]],
"ub" = round(object[["statistics"]]$ub, digits),
"precision" = round(object[["statistics"]]$precision, digits),
"mode" = round(object[["statistics"]]$mode, digits),
"mean" = round(object[["statistics"]]$mean, digits),
"median" = round(object[["statistics"]]$median, digits),
"var" = round(object[["statistics"]]$var, digits),
"skewness" = round(object[["statistics"]]$skewness, digits),
"entropy" = round(object[["statistics"]]$entropy, digits),
stringsAsFactors = FALSE
)
if (!is.null(object[["expected"]])) {
out[["x"]] <- round(object[["expected"]], digits)
}
if (!is.null(object[["description"]]$implicit.n)) {
out[["implicit.n"]] <- round(object[["description"]]$implicit.n, digits)
}
if (!is.null(object[["description"]]$implicit.x)) {
out[["implicit.x"]] <- round(object[["description"]]$implicit.x, digits)
}
if (object[["method"]] == "impartial") {
out[["materiality"]] <- round(object[["materiality"]], digits)
} else if (object[["method"]] == "arm") {
out[["ir"]] <- round(object[["specifics"]]$ir, digits)
out[["icr"]] <- round(object[["specifics"]]$cr, digits)
out[["dr"]] <- round((1 - object[["conf.level"]]) / (object[["specifics"]]$ir * object[["specifics"]]$cr), digits)
} else if (object[["method"]] == "bram") {
out[["mode.prior"]] <- round(object[["specifics"]]$mode, digits)
out[["ub.prior"]] <- round(object[["specifics"]]$ub, digits)
} else if (object[["method"]] == "hyp") {
out[["materiality"]] <- round(object[["materiality"]], digits)
out[["p.h1"]] <- round(object[["specifics"]]$p.h1, digits)
out[["p.h0"]] <- round(object[["specifics"]]$p.h0, digits)
} else if (object[["method"]] == "sample" || object[["method"]] == "factor") {
out[["n.prior"]] <- object[["specifics"]]$n
out[["x.prior"]] <- object[["specifics"]]$x
if (object[["method"]] == "factor") {
out[["factor"]] <- round(object[["specifics"]]$factor, digits)
}
} else if (object[["method"]] == "param") {
out[["alpha"]] <- round(object[["specifics"]]$alpha, digits)
out[["beta"]] <- round(object[["specifics"]]$beta, digits)
}
class(out) <- c("summary.jfaPrior", "data.frame")
return(out)
}
#' @rdname jfa-methods
#' @method predict jfaPrior
#' @export
predict.jfaPrior <- function(object, n, cumulative = FALSE, ...) {
nobs <- 5e5
if (object[["description"]]$density == "gamma") {
p <- stats::dnbinom(0:n, object[["description"]]$alpha, 1 / (1 + object[["description"]]$beta))
names(p) <- 0:n
} else if (object[["description"]]$density %in% c("beta", "beta-binomial")) {
p <- extraDistr::dbbinom(0:n, n, object[["description"]]$alpha, object[["description"]]$beta)
names(p) <- 0:n
} else if (object[["description"]]$density == "normal") {
p <- prop.table(table(stats::rbinom(nobs, n, truncdist::rtrunc(nobs, "norm", 0, 1, mean = object[["description"]]$alpha, sd = object[["description"]]$beta))))
} else if (object[["description"]]$density == "uniform") {
p <- prop.table(table(stats::rbinom(nobs, n, truncdist::rtrunc(nobs, "unif", 0, 1, min = object[["description"]]$alpha, max = object[["description"]]$beta))))
} else if (object[["description"]]$density == "Cauchy") {
p <- prop.table(table(stats::rbinom(nobs, n, truncdist::rtrunc(nobs, "cauchy", 0, 1, location = object[["description"]]$alpha, scale = object[["description"]]$beta))))
} else if (object[["description"]]$density == "Student-t") {
p <- prop.table(table(stats::rbinom(nobs, n, truncdist::rtrunc(nobs, "t", 0, 1, df = object[["description"]]$alpha))))
} else if (object[["description"]]$density == "chi-squared") {
p <- prop.table(table(stats::rbinom(nobs, n, truncdist::rtrunc(nobs, "chisq", 0, 1, df = object[["description"]]$alpha))))
} else if (object[["description"]]$density == "exponential") {
p <- prop.table(table(stats::rbinom(nobs, n, truncdist::rtrunc(nobs, "exp", 0, 1, rate = object[["description"]]$alpha))))
} else if (object[["description"]]$density == "MCMC") {
p <- prop.table(table(stats::rbinom(nobs, n, .rsample(object[["fitted.density"]], n = nobs))))
}
if (cumulative) {
p <- cumsum(p)
names(p) <- if (object[["description"]]$density == "gamma") paste0("n<=", names(p)) else paste0("x<=", names(p))
} else {
names(p) <- if (object[["description"]]$density == "gamma") paste0("n=", names(p)) else paste0("x=", names(p))
}
class(p) <- c("jfaPredict", "table")
return(p)
}
#' @rdname jfa-methods
#' @method print jfaPredict
#' @export
print.jfaPredict <- function(x, ...) {
print.table(x, ...)
}
#' @rdname jfa-methods
#' @method plot jfaPrior
#' @export
plot.jfaPrior <- function(x, ...) {
y <- NULL
xs <- seq(0, 1, length.out = 1001)
if (x[["description"]]$density == "gamma") {
y <- stats::dgamma(xs, x[["description"]]$alpha, x[["description"]]$beta)
} else if (x[["description"]]$density == "beta") {
y <- stats::dbeta(xs, x[["description"]]$alpha, x[["description"]]$beta)
} else if (x[["description"]]$density == "beta-binomial") {
xs <- seq(0, x[["N.units"]], by = 1)
if (inherits(x, "jfaPrior")) {
y <- extraDistr::dbbinom(xs, x[["N.units"]], x[["description"]]$alpha, x[["description"]]$beta)
} else {
y <- extraDistr::dbbinom(xs - x[["description"]]$x, x[["N.units"]] - x[["description"]]$n, x[["description"]]$alpha, x[["description"]]$beta)
}
} else if (x[["description"]]$density == "normal") {
y <- truncdist::dtrunc(xs, spec = "norm", a = 0, b = 1, mean = x[["description"]]$alpha, sd = x[["description"]]$beta)
} else if (x[["description"]]$density == "uniform") {
y <- truncdist::dtrunc(xs, spec = "unif", a = 0, b = 1, min = x[["description"]]$alpha, max = x[["description"]]$beta)
} else if (x[["description"]]$density == "Cauchy") {
y <- truncdist::dtrunc(xs, spec = "cauchy", a = 0, b = 1, location = x[["description"]]$alpha, scale = x[["description"]]$beta)
} else if (x[["description"]]$density == "Student-t") {
y <- truncdist::dtrunc(xs, spec = "t", a = 0, b = 1, df = x[["description"]]$alpha)
} else if (x[["description"]]$density == "chi-squared") {
y <- truncdist::dtrunc(xs, spec = "chisq", a = 0, b = 1, df = x[["description"]]$alpha)
} else if (x[["description"]]$density == "exponential") {
y <- truncdist::dtrunc(xs, spec = "exp", a = 0, b = 1, rate = x[["description"]]$alpha)
} else if (x[["description"]]$density == "MCMC") {
y <- x[["fitted.density"]]$y
}
yMax <- if (is.infinite(max(y))) 10 else max(y)
yBreaks <- pretty(c(0, yMax), min.n = 4)
xBreaks <- pretty(xs, min.n = 4)
df <- data.frame(x = xs, y = y)
p <- ggplot2::ggplot(data = df, mapping = ggplot2::aes(x = x, y = y))
if (x[["description"]]$density != "beta-binomial") {
if (inherits(x, "jfaPrior")) {
p <- p + ggplot2::geom_line(linetype = "dashed")
} else if (inherits(x, "jfaPosterior")) {
p <- p + ggplot2::geom_line(linetype = "solid")
}
p <- p + ggplot2::scale_x_continuous(name = "Population misstatement", breaks = xBreaks, limits = range(xBreaks)) +
ggplot2::scale_y_continuous(name = "Density", breaks = yBreaks, limits = c(0, max(yBreaks)))
} else {
if (inherits(x, "jfaPrior")) {
p <- p + ggplot2::geom_col(colour = "black", fill = "lightgray")
} else if (inherits(x, "jfaPosterior")) {
p <- p + ggplot2::geom_col(colour = "black", fill = "darkgray")
}
p <- p + ggplot2::scale_x_continuous(name = "Population misstatements", breaks = xBreaks, limits = c(xBreaks[1] - 1, max(xBreaks) + 1)) +
ggplot2::scale_y_continuous(name = "Probability", breaks = yBreaks, limits = c(0, max(yBreaks)))
}
p <- p + ggplot2::geom_segment(x = -Inf, xend = -Inf, y = 0, yend = max(yBreaks)) +
ggplot2::geom_segment(x = min(xBreaks), xend = max(xBreaks), y = -Inf, yend = -Inf)
p <- .theme_jfa(p)
return(p)
}
#' @rdname jfa-methods
#' @method plot jfaPredict
#' @export
plot.jfaPredict <- function(x, ...) {
y <- NULL
df <- data.frame(x = seq_len(length(x)) - 1, y = as.numeric(x), lab = names(x))
yBreaks <- pretty(c(0, df$y), min.n = 4)
xBreaks <- pretty(df$x, min.n = 4)
p <- ggplot2::ggplot(data = df, mapping = ggplot2::aes(x = x, y = y)) +
ggplot2::geom_col(position = "identity", colour = "black", fill = "lightgray") +
ggplot2::scale_x_continuous(name = "Misstatements", breaks = xBreaks, limits = c(min(xBreaks) - 0.5, max(xBreaks) + 0.5)) +
ggplot2::scale_y_continuous(name = "Probability", breaks = yBreaks, limits = c(0, max(yBreaks))) +
ggplot2::geom_segment(x = -Inf, xend = -Inf, y = 0, yend = max(yBreaks)) +
ggplot2::geom_segment(x = min(xBreaks), xend = max(xBreaks), y = -Inf, yend = -Inf)
p <- .theme_jfa(p)
return(p)
}
# Methods for class: jfaPosterior #####################################################
#' @rdname jfa-methods
#' @method print jfaPosterior
#' @export
print.jfaPosterior <- function(x, ...) {
cat("\n")
cat(strwrap("Posterior Distribution from Audit Sampling", prefix = "\t"), sep = "\n")
cat("\n")
cat("functional form:", x[["posterior"]], "\nparameters obtained via method", paste0("'", x[["method"]], "'\n"))
}
#' @rdname jfa-methods
#' @method print summary.jfaPosterior
#' @export
print.summary.jfaPosterior <- function(x, digits = getOption("digits"), ...) {
cat("\n")
cat(strwrap("Posterior Distribution Summary", prefix = "\t"), sep = "\n")
cat("\nResults:\n")
cat(paste(" Functional form: ", x[["posterior"]]), "\n")
cat(paste(" Mode: ", format(x[["mode"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Mean: ", format(x[["mean"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Median: ", format(x[["median"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Variance: ", format(x[["var"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Skewness: ", format(x[["skewness"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Information entropy (nat): ", format(x[["entropy"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" ", format(x[["conf.level"]] * 100), "percent upper bound: ", format(x[["ub"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Precision: ", format(x[["precision"]], digits = max(1L, digits - 2L))), "\n")
}
#' @rdname jfa-methods
#' @method summary jfaPosterior
#' @export
summary.jfaPosterior <- function(object, digits = getOption("digits"), ...) {
out <- data.frame(
"posterior" = object[["posterior"]],
"ub" = round(object[["statistics"]]$ub, digits),
"precision" = round(object[["statistics"]]$precision, digits),
"mode" = round(object[["statistics"]]$mode, digits),
"mean" = round(object[["statistics"]]$mean, digits),
"median" = round(object[["statistics"]]$median, digits),
"var" = round(object[["statistics"]]$var, digits),
"skewness" = round(object[["statistics"]]$skewness, digits),
"entropy" = round(object[["statistics"]]$entropy, digits),
"conf.level" = object[["conf.level"]],
stringsAsFactors = FALSE
)
class(out) <- c("summary.jfaPosterior", "data.frame")
return(out)
}
#' @rdname jfa-methods
#' @method predict jfaPosterior
#' @export
predict.jfaPosterior <- function(object, n, cumulative = FALSE, ...) {
predict.jfaPrior(object, n, cumulative, ...)
}
#' @rdname jfa-methods
#' @method plot jfaPosterior
#' @export
plot.jfaPosterior <- function(x, ...) {
plot.jfaPrior(x, ...)
}
# Methods for class: jfaPlanning #####################################################
#' @rdname jfa-methods
#' @method print jfaPlanning
#' @export
print.jfaPlanning <- function(x, ...) {
cat("\n")
if (is.null(x[["prior"]])) cat(strwrap("Classical Audit Sample Planning", prefix = "\t"), sep = "\n") else cat(strwrap("Bayesian Audit Sample Planning", prefix = "\t"), sep = "\n")
cat("\n")
cat("minimum sample size =", x[["n"]], if (x[["sequential"]] && is.null(x[["prior"]])) paste0("(", x[["n_staged"]], " per stage)"), "\nsample size obtained in", x[["iterations"]], "iterations via method", if (is.null(x[["prior"]])) paste0("'", x[["likelihood"]], if (x[["sequential"]]) "' + 'sequential", "'\n") else paste0("'", x[["likelihood"]], "' + 'prior'\n"))
}
#' @rdname jfa-methods
#' @method print summary.jfaPlanning
#' @export
print.summary.jfaPlanning <- function(x, digits = getOption("digits"), ...) {
cat("\n")
cat(strwrap(paste(x[["type"]], "Audit Sample Planning Summary"), prefix = "\t"), sep = "\n")
cat("\nOptions:\n")
cat(paste(" Confidence level: ", format(x[["conf.level"]], digits = max(1L, digits - 2L))), "\n")
if (!is.null(x[["N.units"]])) {
cat(paste(" Population size: ", format(x[["N.units"]], digits = max(1L, digits - 2L))), "\n")
}
if (x[["materiality"]] < 1) {
cat(paste(" Materiality: ", format(x[["materiality"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Hypotheses: ", paste0("H\u2080: \u0398 ", if (x[["type"]] == "Bayesian") ">" else ">=", " ", format(x[["materiality"]], digits = max(1L, digits - 2L)), " vs. H\u2081: \u0398 < ", format(x[["materiality"]], digits = max(1L, digits - 2L)))), "\n")
}
if (x[["min.precision"]] < 1) {
cat(paste(" Min. precision: ", format(x[["min.precision"]], digits = max(1L, digits - 2L))), "\n")
}
cat(paste(" Expected: ", format(x[["expected"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Likelihood: ", x[["likelihood"]]), "\n")
if (x[["type"]] == "Bayesian") {
cat(paste(" Prior distribution: ", x[["prior"]]), "\n")
}
cat("\nResults:\n")
cat(paste(" Minimum sample size: ", x[["n"]]), "\n")
cat(paste(" Tolerable errors: ", format(x[["x"]], digits = max(1L, digits - 2L))), "\n")
if (x[["type"]] == "Bayesian") {
cat(paste(" Posterior distribution: ", x[["posterior"]]), "\n")
}
cat(paste(" Expected most likely error: ", format(x[["mle"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Expected upper bound: ", format(x[["ub"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Expected precision: ", format(x[["precision"]], digits = max(1L, digits - 2L))), "\n")
if (x[["materiality"]] < 1 && x[["type"]] == "Bayesian") {
cat(paste(" Expected BF\u2081\u2080: ", format(x[["bf.h1"]], digits = max(1L, digits - 2L))), "\n")
}
if (x[["materiality"]] < 1 && x[["type"]] == "Classical") {
cat(paste(" Expected p-value: ", format.pval(x[["p.value"]], digits = max(1L, digits - 2L), eps = 0.001)), "\n")
}
}
#' @rdname jfa-methods
#' @method summary jfaPlanning
#' @export
summary.jfaPlanning <- function(object, digits = getOption("digits"), ...) {
out <- data.frame(
"conf.level" = round(object[["conf.level"]], digits),
"expected" = round(object[["expected"]], digits),
"materiality" = round(object[["materiality"]], digits),
"min.precision" = round(object[["min.precision"]], digits),
"likelihood" = object[["likelihood"]],
"x" = round(object[["x"]], digits),
"n" = object[["n"]],
"ub" = round(object[["ub"]], digits),
"precision" = round(object[["precision"]], digits),
"sequential" = object[["sequential"]],
stringsAsFactors = FALSE
)
if (!is.null(object[["p.value"]])) {
out[["p.value"]] <- object[["p.value"]]
}
if (!is.null(object[["N.units"]])) {
out[["N.units"]] <- object[["N.units"]]
}
if (inherits(object[["prior"]], "jfaPrior")) {
out[["prior"]] <- object[["prior"]]$prior
out[["posterior"]] <- object[["posterior"]]$posterior
out[["mle"]] <- round(object[["posterior"]][["statistics"]]$mode, digits)
if (object[["materiality"]] != 1) {
out[["bf.h1"]] <- round(object[["posterior"]][["hypotheses"]]$bf.h1, digits)
}
} else {
out[["mle"]] <- round(object[["x"]] / object[["n"]], digits)
}
out[["type"]] <- if (inherits(object[["prior"]], "jfaPrior")) "Bayesian" else "Classical"
class(out) <- c("summary.jfaPlanning", "data.frame")
return(out)
}
#' @rdname jfa-methods
#' @method plot jfaPlanning
#' @export
plot.jfaPlanning <- function(x, ...) {
if (is.null(x[["sequential"]]) || isFALSE(x[["sequential"]])) {
if (is.null(x[["prior"]])) {
if (inherits(x, "jfaPlanning")) {
likelihood <- x[["likelihood"]]
} else if (inherits(x, "jfaEvaluation")) {
likelihood <- x[["method"]]
}
xs <- 0:max(10, x[["x"]])
if (likelihood == "hypergeometric") {
ys <- stats::dhyper(x = xs, m = x[["K"]], n = x[["N.units"]] - x[["K"]], k = x[["n"]])
} else if (likelihood == "binomial") {
ys <- stats::dbinom(x = xs, size = x[["n"]], prob = x[["materiality"]])
} else if (likelihood == "poisson") {
ys <- stats::dpois(x = xs, lambda = x[["n"]] * x[["materiality"]])
}
ncolored <- 1 + ceiling(x[["x"]])
fill <- c(rep("firebrick", ncolored), rep("darkgray", length(xs) - ncolored))
df <- data.frame(x = xs, y = ys)
y_breaks <- pretty(c(0, df$y), min.n = 4)
p <- ggplot2::ggplot(data = df, mapping = ggplot2::aes(x = x, y = y)) +
ggplot2::geom_col(position = "identity", fill = fill, colour = "black") +
ggplot2::annotate(geom = "text", x = df$x, y = df$y, label = round(df$y, 3), vjust = -0.5, size = 3) +
ggplot2::scale_x_continuous(name = "Misstatements", breaks = xs) +
ggplot2::scale_y_continuous(name = "Probability", breaks = y_breaks, limits = c(0, max(y_breaks))) +
ggplot2::geom_segment(x = -Inf, xend = -Inf, y = 0, yend = max(y_breaks)) +
ggplot2::geom_segment(x = 0, xend = max(xs), y = -Inf, yend = -Inf)
p <- .theme_jfa(p)
} else {
y <- type <- NULL
x1 <- x2 <- seq(0, 1, length.out = 1001)
if (x[["prior"]][["description"]]$density == "gamma") {
y1 <- stats::dgamma(x1, x[["prior"]][["description"]]$alpha, x[["prior"]][["description"]]$beta)
} else if (x[["prior"]][["description"]]$density == "beta") {
y1 <- stats::dbeta(x1, x[["prior"]][["description"]]$alpha, x[["prior"]][["description"]]$beta)
} else if (x[["prior"]][["description"]]$density == "beta-binomial") {
x1 <- x2 <- seq(0, x[["N.units"]], by = 1)
y1 <- extraDistr::dbbinom(x1, x[["prior"]][["N.units"]], x[["prior"]][["description"]]$alpha, x[["prior"]][["description"]]$beta)
} else if (x[["prior"]][["description"]]$density == "normal") {
y1 <- truncdist::dtrunc(x1, spec = "norm", a = 0, b = 1, mean = x[["prior"]][["description"]]$alpha, sd = x[["prior"]][["description"]]$beta)
} else if (x[["prior"]][["description"]]$density == "uniform") {
y1 <- truncdist::dtrunc(x1, spec = "unif", a = 0, b = 1, min = x[["prior"]][["description"]]$alpha, max = x[["prior"]][["description"]]$beta)
} else if (x[["prior"]][["description"]]$density == "Cauchy") {
y1 <- truncdist::dtrunc(x1, spec = "cauchy", a = 0, b = 1, location = x[["prior"]][["description"]]$alpha, scale = x[["prior"]][["description"]]$beta)
} else if (x[["prior"]][["description"]]$density == "Student-t") {
y1 <- truncdist::dtrunc(x1, spec = "t", a = 0, b = 1, df = x[["prior"]][["description"]]$alpha)
} else if (x[["prior"]][["description"]]$density == "chi-squared") {
y1 <- truncdist::dtrunc(x1, spec = "chisq", a = 0, b = 1, df = x[["prior"]][["description"]]$alpha)
} else if (x[["prior"]][["description"]]$density == "exponential") {
y1 <- truncdist::dtrunc(x1, spec = "exp", a = 0, b = 1, rate = x[["prior"]][["description"]]$alpha)
} else if (x[["prior"]][["description"]]$density == "MCMC") {
y1 <- x[["prior"]][["fitted.density"]]$y
}
if (x[["posterior"]][["description"]]$density == "gamma") {
y2 <- stats::dgamma(x2, x[["posterior"]][["description"]]$alpha, x[["posterior"]][["description"]]$beta)
} else if (x[["posterior"]][["description"]]$density == "beta") {
y2 <- stats::dbeta(x2, x[["posterior"]][["description"]]$alpha, x[["posterior"]][["description"]]$beta)
} else if (x[["posterior"]][["description"]]$density == "beta-binomial") {
y2 <- extraDistr::dbbinom(x2 - x[["x"]], x[["posterior"]][["N.units"]] - x[["n"]], x[["posterior"]][["description"]]$alpha, x[["posterior"]][["description"]]$beta)
} else if (x[["posterior"]][["description"]]$density == "MCMC") {
y2 <- x[["posterior"]][["fitted.density"]]$y
}
df <- data.frame(x = c(x1, x2), y = c(y1, y2), type = c(rep("Prior", length(y1)), rep("Posterior", length(y2))))
yMax <- if (is.infinite(max(df$y))) max(y2) else max(df$y)
yBreaks <- pretty(c(0, yMax * 1.05), min.n = 4)
xBreaks <- pretty(df$x, min.n = 4)
p <- ggplot2::ggplot(data = df, mapping = ggplot2::aes(x = x, y = y))
if (x[["prior"]][["description"]]$density != "beta-binomial") {
p <- p + ggplot2::geom_line(mapping = ggplot2::aes(linetype = type)) +
ggplot2::scale_linetype_manual(name = NULL, values = c("solid", "dashed")) +
ggplot2::scale_x_continuous(name = "Population misstatement", breaks = xBreaks, limits = c(0, 1)) +
ggplot2::scale_y_continuous(name = "Density", breaks = yBreaks, limits = c(0, max(yBreaks)))
} else {
p <- p + ggplot2::geom_col(mapping = ggplot2::aes(fill = type), alpha = 0.75, colour = "black", position = "identity") +
ggplot2::scale_fill_manual(name = NULL, values = c("darkgray", "lightgray")) +
ggplot2::scale_x_continuous(name = "Population misstatements", breaks = xBreaks, limits = c(xBreaks[1] - 1, max(xBreaks) + 1)) +
ggplot2::scale_y_continuous(name = "Probability", breaks = yBreaks, limits = c(0, max(yBreaks)))
}
if (inherits(x, "jfaEvaluation")) {
if (x[["prior"]][["description"]]$density != "beta-binomial") {
p <- p + ggplot2::geom_segment(x = x[["lb"]], xend = x[["ub"]], y = max(yBreaks), yend = max(yBreaks)) +
ggplot2::geom_segment(x = x[["lb"]], xend = x[["lb"]], y = max(yBreaks) - ((yBreaks[2] - yBreaks[1]) / 10), yend = max(yBreaks) + ((yBreaks[2] - yBreaks[1]) / 10)) +
ggplot2::geom_segment(x = x[["ub"]], xend = x[["ub"]], y = max(yBreaks) - ((yBreaks[2] - yBreaks[1]) / 10), yend = max(yBreaks) + ((yBreaks[2] - yBreaks[1]) / 10)) +
ggplot2::geom_point(x = x[["mle"]], y = max(yBreaks), size = 2, fill = "darkgray", colour = "black", shape = 21)
} else {
p <- p + ggplot2::geom_segment(x = ceiling(x[["lb"]] * x[["N.units"]]), xend = ceiling(x[["ub"]] * x[["N.units"]]), y = max(yBreaks), yend = max(yBreaks)) +
ggplot2::geom_segment(x = ceiling(x[["lb"]] * x[["N.units"]]), xend = ceiling(x[["lb"]] * x[["N.units"]]), y = max(yBreaks) - ((yBreaks[2] - yBreaks[1]) / 10), yend = max(yBreaks) + ((yBreaks[2] - yBreaks[1]) / 10)) +
ggplot2::geom_segment(x = ceiling(x[["ub"]] * x[["N.units"]]), xend = ceiling(x[["ub"]] * x[["N.units"]]), y = max(yBreaks) - ((yBreaks[2] - yBreaks[1]) / 10), yend = max(yBreaks) + ((yBreaks[2] - yBreaks[1]) / 10)) +
ggplot2::geom_point(x = ceiling(x[["mle"]] * x[["N.units"]]), y = max(yBreaks), size = 2, fill = "darkgray", colour = "black", shape = 21)
}
}
p <- p + ggplot2::geom_segment(x = -Inf, xend = -Inf, y = 0, yend = max(yBreaks)) +
ggplot2::geom_segment(x = min(xBreaks), xend = max(xBreaks), y = -Inf, yend = -Inf)
p <- .theme_jfa(p, legend.position = "inside", legend.position.inside = c(0.8, 0.8))
}
} else {
stopifnot("plot(...) not supported for multi-stage sampling plans with > 2 stages" = length(x[["k_staged"]]) == 2)
k_1_approve <- x[["k_staged"]][1] - 1
k_1_disapprove <- x[["k_staged"]][1]
k_2_approve <- x[["k_staged"]][2]
n_min <- jfa::planning(materiality = x[["materiality"]], expected = k_1_approve, likelihood = x[["likelihood"]], N.units = x[["N.units"]], conf.level = x[["conf.level"]])$n
n_max <- jfa::planning(materiality = x[["materiality"]], expected = sum(k_1_disapprove + k_2_approve), likelihood = x[["likelihood"]], N.units = x[["N.units"]], conf.level = x[["conf.level"]])$n
n1 <- seq(n_min, n_max, 1)
n2 <- rep(-1, length(n1))
for (i in seq_along(n1)) {
p <- 1
while (p > 1 - x[["conf.level"]]) {
n2[i] <- n2[i] + 1
p <- switch(x[["likelihood"]],
"poisson" = stats::ppois(k_1_approve, lambda = n1[i] * x[["materiality"]]) + stats::dpois(k_1_disapprove, lambda = n1[i] * x[["materiality"]]) * stats::ppois(k_2_approve, lambda = n2[i] * x[["materiality"]]),
"binomial" = stats::pbinom(k_1_approve, size = n1[i], prob = x[["materiality"]]) + stats::dbinom(k_1_disapprove, size = n1[i], prob = x[["materiality"]]) * stats::pbinom(k_2_approve, size = n2[i], prob = x[["materiality"]]),
"hypergeometric" = stats::phyper(k_1_approve, m = x[["K"]], n = x[["N.units"]] - x[["K"]], k = n1[i]) + stats::dhyper(k_1_disapprove, m = x[["K"]], n = x[["N.units"]] - x[["K"]], k = n1[i]) * stats::phyper(k_2_approve, m = x[["K"]], n = x[["N.units"]] - x[["K"]], k = n2[i])
)
}
}
lines <- seq(1, length(n1), length.out = 5)
xBreaks <- pretty(c(n1, x[["n_staged"]]), min.n = 4)
yBreaks <- pretty(c(n2, x[["n_staged"]]), min.n = 4)
n1_lines <- n1[lines]
n2_lines <- n2[lines]
p <- ggplot2::ggplot(data.frame(x = n1, y = n2), ggplot2::aes(x = x, y = y)) +
ggplot2::scale_x_continuous(name = parse(text = "Initial~sample~size~n[1]"), breaks = xBreaks, limits = range(xBreaks)) +
ggplot2::scale_y_continuous(name = parse(text = "Follow*'-'*up~sample~size~n[2]"), breaks = yBreaks, limits = range(yBreaks))
for (i in seq_along(n1_lines)) {
p <- p + ggplot2::geom_segment(x = n1_lines[i], xend = n1_lines[i], y = -Inf, yend = n2_lines[i], color = "lightgray", linewidth = 0.25) +
ggplot2::geom_segment(x = -Inf, xend = n1_lines[i], y = n2_lines[i], yend = n2_lines[i], color = "lightgray", linewidth = 0.25) +
ggplot2::annotate(geom = "text", x = n1_lines[i], y = n2_lines[i], label = sum(n1_lines[i] + n2_lines[i]), hjust = -0.25, vjust = 0, size = 3)
}
p <- p + ggplot2::geom_segment(x = x[["n_staged"]], xend = x[["n_staged"]], y = -Inf, yend = x[["n_staged"]], color = "red", linewidth = 0.25) +
ggplot2::geom_segment(x = -Inf, xend = x[["n_staged"]], y = x[["n_staged"]], yend = x[["n_staged"]], color = "red", linewidth = 0.25) +
ggplot2::annotate(geom = "text", x = x[["n_staged"]], y = x[["n_staged"]], label = paste0(x[["n"]], "~(n[1] == n[2])"), hjust = -0.05, vjust = 0, size = 3, col = "red", parse = TRUE) +
ggplot2::geom_line() +
ggplot2::geom_point(data = data.frame(x = x[["n_staged"]], y = x[["n_staged"]]), fill = "red", shape = 21) +
ggplot2::geom_point(data = data.frame(x = n1_lines, y = n2_lines), ggplot2::aes(x = x, y = y), fill = "lightgray", shape = 21) +
ggplot2::geom_segment(x = -Inf, xend = -Inf, y = min(yBreaks), yend = max(yBreaks)) +
ggplot2::geom_segment(x = min(xBreaks), xend = max(xBreaks), y = -Inf, yend = -Inf)
p <- .theme_jfa(p)
}
return(p)
}
# Methods for class: jfaSelection #####################################################
#' @rdname jfa-methods
#' @method print jfaSelection
#' @export
print.jfaSelection <- function(x, ...) {
cat("\n")
cat(strwrap("Audit Sample Selection", prefix = "\t"), sep = "\n")
cat("\n")
cat(paste("data: ", x[["data.name"]]), sep = "\n")
cat(paste0("number of sampling units = ", x[["n.units"]], ", number of items = ", x[["n.items"]], "\nsample selected via method ", paste0("'", x[["units"]], "' + '", x[["method"]], "'\n")))
}
#' @rdname jfa-methods
#' @method print summary.jfaSelection
#' @export
print.summary.jfaSelection <- function(x, digits = getOption("digits"), ...) {
cat("\n")
cat(strwrap(paste(x[["type"]], "Audit Sample Selection Summary"), prefix = "\t"), sep = "\n")
cat("\nOptions:\n")
cat(paste(" Requested sample size: ", x[["n.req"]]), "\n")
cat(paste(" Sampling units: ", switch(x[["units"]],
"values" = "monetary units",
"items" = "items"
)), "\n")
cat(paste(" Method: ", switch(x[["method"]],
"random" = "random sampling",
"interval" = "fixed interval sampling",
"cell" = "cell sampling",
"sieve" = "modified sieve sampling"
)), "\n")
if (x[["method"]] == "interval") {
cat(paste(" Starting point: ", x[["start"]]), "\n")
}
cat("\nData:\n")
cat(paste(" Population size: ", x[["N.items"]]), "\n")
if (x[["units"]] == "values") {
cat(paste(" Population value: ", format(x[["N.units"]], digits = max(1L, digits - 2L))), "\n")
}
if (x[["method"]] == "interval" || x[["method"]] == "cell") {
cat(paste(" Selection interval: ", format(x[["interval"]], digits = max(1L, digits - 2L))), "\n")
}
cat("\nResults:\n")
cat(paste(" Selected sampling units: ", x[["n.units"]]), "\n")
if (x[["units"]] == "values") {
cat(paste(" Proportion of value: ", format(x[["prop.val"]], digits = max(1L, digits - 2L))), "\n")
}
cat(paste(" Selected items: ", x[["n.items"]]), "\n")
cat(paste(" Proportion of size: ", format(x[["prop.n"]], digits = max(1L, digits - 2L))), "\n")
}
#' @rdname jfa-methods
#' @method summary jfaSelection
#' @export
summary.jfaSelection <- function(object, digits = getOption("digits"), ...) {
out <- data.frame(
"N.items" = object[["N.items"]],
"N.units" = round(object[["N.units"]], digits),
"n.req" = object[["n.req"]],
"units" = object[["units"]],
"method" = object[["method"]],
"n.units" = object[["n.units"]],
"n.items" = object[["n.items"]],
"prop.n" = round(object[["n.items"]] / object[["N.items"]], digits),
stringsAsFactors = FALSE
)
if (object[["method"]] == "interval" || object[["method"]] == "cell") {
out[["interval"]] <- round(object[["interval"]], digits)
if (object[["method"]] == "interval") {
out[["start"]] <- object[["start"]]
}
}
if (object[["units"]] == "values") {
out[["prop.val"]] <- round(sum(abs(object[["sample"]][, object[["values.name"]]])) / object[["N.units"]], digits)
}
class(out) <- c("summary.jfaSelection", "data.frame")
return(out)
}
# Methods for class: jfaEvaluation #####################################################
#' @rdname jfa-methods
#' @method print jfaEvaluation
#' @export
print.jfaEvaluation <- function(x, digits = getOption("digits"), ...) {
cat("\n")
if (is.null(x[["prior"]])) cat(strwrap(paste0("Classical Audit Sample Evaluation"), prefix = "\t"), sep = "\n") else cat(strwrap(paste0("Bayesian Audit Sample Evaluation"), prefix = "\t"), sep = "\n")
cat("\n")
lab <- if (!is.null(x[["data"]])) x[["data.name"]] else paste0(x[["x"]], " and ", x[["n"]])
cat(paste("data: ", lab), sep = "\n")
out <- character()
out <- c(out, paste("number of errors =", format(x[["x"]], digits = max(1L, digits - 2L))))
out <- c(out, paste("number of samples =", format(x[["n"]], digits = max(1L, digits - 2L))))
out <- c(out, paste("taint =", format(x[["t"]], digits = max(1L, digits - 2L))))
if (is.null(x[["prior"]]) && x[["materiality"]] < 1 && x[["method"]] %in% c("binomial", "poisson", "hypergeometric")) {
out <- c(out, paste("p-value =", format.pval(x[["p.value"]], digits = max(1L, digits - 2L))))
}
if (!is.null(x[["prior"]]) && x[["materiality"]] < 1) {
out <- c(out, paste("BF\u2081\u2080 =", format(x[["posterior"]][["hypotheses"]]$bf.h1, digits = max(1L, digits - 2L))))
}
cat(strwrap(paste(out, collapse = ", ")), sep = "\n")
if (!is.null(x[["p.value"]]) || !is.null(x[["posterior"]]$hypotheses)) {
if (x[["alternative"]] == "less") {
cat(paste0("alternative hypothesis: true misstatement rate is less than ", format(x[["materiality"]], digits = max(1L, digits - 2L))), sep = "\n")
}
if (x[["alternative"]] == "two.sided") {
cat(paste0("alternative hypothesis: true misstatement rate is not equal to ", format(x[["materiality"]], digits = max(1L, digits - 2L))), sep = "\n")
}
if (x[["alternative"]] == "greater") {
cat(paste0("alternative hypothesis: true misstatement rate is greater than ", format(x[["materiality"]], digits = max(1L, digits - 2L))), sep = "\n")
}
}
if (!is.null(x[["ub"]])) {
cat(format(100 * x$conf.level), " percent ", if (is.null(x[["prior"]])) "confidence" else "credible", " interval:\n", " ", paste(format(c(x[["lb"]], x[["ub"]]), digits = digits), collapse = " "), "\n", sep = "")
}
if (!is.null(x[["mle"]])) {
cat("most likely estimate:\n", format(x[["mle"]], digits = max(1L, digits - 2L)), "\n")
}
method_string <- paste0("'", x[["method"]], "'")
if (!is.null(x[["strata"]]) && x[["pooling"]] == "complete") {
method_string <- paste0(method_string, " + 'complete-pooling'")
} else if (!is.null(x[["strata"]]) && x[["pooling"]] == "none") {
method_string <- paste0(method_string, " + 'no-pooling'")
} else if (!is.null(x[["strata"]]) && x[["pooling"]] == "partial") {
method_string <- paste0(method_string, " + 'partial-pooling'")
}
if (!is.null(x[["prior"]])) {
method_string <- paste0(method_string, " + 'prior'")
}
cat("results obtained via method", method_string, "\n")
}
#' @rdname jfa-methods
#' @method print summary.jfaEvaluation
#' @export
print.summary.jfaEvaluation <- function(x, digits = getOption("digits"), ...) {
cat("\n")
cat(strwrap(paste(x[["type"]], "Audit Sample Evaluation Summary"), prefix = "\t"), sep = "\n")
cat("\nOptions:\n")
cat(paste(" Confidence level: ", format(x[["conf.level"]], digits = max(1L, digits - 2L))), "\n")
if (!is.null(x[["N.units"]])) {
cat(paste(" Population size: ", format(x[["N.units"]], digits = max(1L, digits - 2L))), "\n")
}
if (x[["materiality"]] < 1) {
cat(paste(" Materiality: ", format(x[["materiality"]], digits = max(1L, digits - 2L))), "\n")
if (x[["method"]] %in% c("poisson", "binomial", "hypergeometric")) {
cat(paste(" Hypotheses: ", switch(x[["alternative"]],
"two.sided" = paste0("H\u2080: \u0398 = ", format(x[["materiality"]], digits = max(1L, digits - 2L)), " vs. H\u2081: \u0398 \u2260 ", format(x[["materiality"]], digits = max(1L, digits - 2L))),
"less" = paste0("H\u2080: \u0398 ", if (x[["type"]] == "Bayesian") ">" else ">=", " ", format(x[["materiality"]], digits = max(1L, digits - 2L)), " vs. H\u2081: \u0398 < ", format(x[["materiality"]], digits = max(1L, digits - 2L))),
"greater" = paste0("H\u2080: \u0398 ", if (x[["type"]] == "Bayesian") "<" else "<=", " ", format(x[["materiality"]], digits = max(1L, digits - 2L)), " vs. H\u2081: \u0398 > ", format(x[["materiality"]], digits = max(1L, digits - 2L)))
)), "\n")
}
}
cat(paste(" Method: ", x[["method"]]), "\n")
if (x[["type"]] == "Bayesian") {
cat(paste(" Prior distribution: ", x[["prior"]]), "\n")
}
cat("\nData:\n")
cat(paste(" Sample size: ", x[["n"]]), "\n")
cat(paste(" Number of errors: ", x[["x"]]), "\n")
cat(paste(" Sum of taints: ", x[["t"]]), "\n")
cat("\nResults:\n")
if (x[["type"]] == "Bayesian") {
cat(" Posterior distribution: ", x[["posterior"]], "\n")
}
cat(paste(" Most likely error: ", format(x[["mle"]], digits = max(1L, digits - 2L))), "\n")
if (x[["type"]] == "Bayesian") {
cat(paste(" ", paste0(format(x[["conf.level"]] * 100), " percent credible interval: ", paste0("[", format(x[["lb"]], digits = max(1L, digits - 2L)), ", ", format(x[["ub"]], digits = max(1L, digits - 2L)), "]"))), "\n")
} else if (x[["type"]] == "Classical") {
cat(paste(" ", paste0(format(x[["conf.level"]] * 100), " percent confidence interval: ", paste0("[", format(x[["lb"]], digits = max(1L, digits - 2L)), ", ", format(x[["ub"]], digits = max(1L, digits - 2L)), "]"))), "\n")
}
cat(paste(" Precision: ", format(x[["precision"]], digits = max(1L, digits - 2L))), "\n")
if (x[["materiality"]] < 1 && x[["type"]] == "Bayesian") {
cat(paste(" BF\u2081\u2080:\t ", format(x[["bf.h1"]], digits = max(1L, digits - 2L))), "\n")
}
if (x[["materiality"]] < 1 && x[["type"]] == "Classical" && x[["method"]] %in% c("poisson", "binomial", "hypergeometric")) {
cat(paste(" p-value: ", format.pval(x[["p.value"]], digits = max(1L, digits - 2L))), "\n")
}
if (!is.null(x[["strata"]])) {
cat(paste0("\nStrata (", nrow(x[["strata"]]), "):\n"))
rownames(x[["strata"]]) <- paste0(" ", rownames(x[["strata"]]))
print(round(x[["strata"]], digits = max(1L, digits - 2L)), quote = FALSE)
}
}
#' @rdname jfa-methods
#' @method summary jfaEvaluation
#' @export
summary.jfaEvaluation <- function(object, digits = getOption("digits"), ...) {
out <- list(
"conf.level" = round(object[["conf.level"]], digits),
"materiality" = round(object[["materiality"]], digits),
"x" = object[["x"]],
"n" = object[["n"]],
"method" = object[["method"]],
"mle" = round(object[["mle"]], digits),
"precision" = round(object[["precision"]], digits),
"alternative" = object[["alternative"]],
"pooling" = object[["pooling"]],
stringsAsFactors = FALSE
)
if (!is.null(object[["p.value"]])) {
out[["p.value"]] <- object[["p.value"]]
}
if (!is.null(object[["N.units"]])) {
out[["N.units"]] <- object[["N.units"]]
}
if (object[["method"]] %in% c("direct", "difference", "quotient", "regression")) {
out[["type"]] <- "Classical"
out[["lb"]] <- round(object[["lb"]], digits)
out[["ub"]] <- round(object[["ub"]], digits)
} else {
out[["t"]] <- round(object[["t"]], digits)
out[["ub"]] <- round(object[["ub"]], digits)
out[["lb"]] <- round(object[["lb"]], digits)
if (!is.null(object[["prior"]])) {
out[["type"]] <- "Bayesian"
out[["prior"]] <- object[["prior"]][["prior"]]
out[["posterior"]] <- object[["posterior"]][["posterior"]]
if (object[["materiality"]] != 1) {
out[["bf.h1"]] <- round(object[["posterior"]][["hypotheses"]]$bf.h1, digits)
}
} else {
out[["type"]] <- "Classical"
}
}
if (!is.null(object[["strata"]])) {
out[["strata"]] <- object[["strata"]]
}
class(out) <- c("summary.jfaEvaluation", "list")
return(out)
}
#' @rdname jfa-methods
#' @method plot jfaEvaluation
#' @export
plot.jfaEvaluation <- function(x, type = c("estimates", "posterior"), ...) {
y <- lb <- ub <- NULL
type <- match.arg(type)
if (type == "posterior") {
if (!(x[["method"]] %in% c("binomial", "poisson", "hypergeometric", "inflated.poisson", "hurdle.beta"))) {
stop(paste0('plot(..., type = "posterior") not supported for method = "', x[["method"]], '"'))
} else if (x[["method"]] %in% c("inflated.poisson", "hurdle.beta") && is.null(x[["prior"]])) {
stop(paste0('plot(..., type = "posterior") not supported for method = "', x[["method"]], '" without "prior = TRUE"'))
}
p <- plot.jfaPlanning(x, ...)
} else {
xs <- 0
labels <- "Population"
mles <- x[["mle"]]
lbs <- x[["lb"]]
ubs <- x[["ub"]]
if (!is.null(x[["strata"]])) {
xs <- c(xs, seq_len(nrow(x[["strata"]])))
labels <- c(labels, rownames(x[["strata"]]))
mles <- c(mles, x[["strata"]]$mle)
lbs <- c(lbs, x[["strata"]]$lb)
ubs <- c(ubs, x[["strata"]]$ub)
}
df <- data.frame(x = xs, y = mles, lb = lbs, ub = ubs, lab = labels)
xBreaks <- df$x
xLimits <- c(min(df$x) - 0.25, max(df$x) + 0.25)
p <- ggplot2::ggplot(data = df, mapping = ggplot2::aes(x = x, y = y, ymin = lb, ymax = ub))
if (x[["materiality"]] < 1) {
p <- p + ggplot2::geom_segment(
x = -Inf,
xend = Inf,
y = x[["materiality"]],
yend = x[["materiality"]],
colour = "darkred",
linetype = "dashed"
)
}
p <- p + ggplot2::geom_errorbar(linewidth = 0.5, width = 0.25) +
ggplot2::geom_point(size = 2.5, fill = "darkgray", colour = "black", shape = 21) +
ggplot2::scale_x_continuous(name = NULL, breaks = xBreaks, limits = xLimits, labels = df$lab) +
ggplot2::scale_y_continuous(name = "Misstatement", limits = c(0, 1), breaks = seq(0, 1, 0.2)) +
ggplot2::geom_segment(x = -Inf, xend = -Inf, y = 0, yend = 1) +
ggplot2::geom_segment(x = 0, xend = max(xBreaks), y = -Inf, yend = -Inf)
p <- .theme_jfa(p)
}
return(p)
}
# Methods for class: jfaDistr #####################################################
#' @rdname jfa-methods
#' @method print jfaDistr
#' @export
print.jfaDistr <- function(x, digits = getOption("digits"), ...) {
type <- if (!is.null(x$p.value)) "Classical" else "Bayesian"
cat(paste0("\n\t", type, " Digit Distribution Test\n\n"))
cat("data: ", x$data.name, "\n", sep = "")
out <- character()
if (!is.null(x$n)) {
out <- c(out, paste(names(x$n), "=", format(x$n, digits = max(1L, digits - 2L))))
}
if (!is.null(x$mad)) {
out <- c(out, paste(names(x$mad), "=", format(x$mad, digits = max(1L, digits - 2L))))
}
if (!is.null(x$statistic)) {
out <- c(out, paste(names(x$statistic), "=", format(x$statistic, digits = max(1L, digits - 2L))))
}
if (!is.null(x$parameter)) {
out <- c(out, paste(names(x$parameter), "=", format(x$parameter, digits = max(1L, digits - 2L))))
}
if (!is.null(x$bf)) {
out <- c(out, paste("BF\u2081\u2080", "=", format(x$bf, digits = max(1L, digits - 2L))))
}
if (!is.null(x$p.value)) {
fp <- format.pval(x$p.value, digits = max(1L, digits - 3L))
out <- c(out, paste("p-value", if (startsWith(fp, "<")) fp else paste("=", fp)))
}
cat(strwrap(paste(out, collapse = ", ")), sep = "\n")
digitLabel <- switch(x$check,
"first" = "leading",
"last" = "last",
"firsttwo" = "first two"
)
distLabel <- if (is.numeric(x$reference)) "reference" else x$reference
cat(paste0("alternative hypothesis: ", digitLabel, " digit(s) are not distributed according to the ", distLabel, " distribution."))
cat("\n")
invisible(x)
}
#' @rdname jfa-methods
#' @method print summary.jfaDistr
#' @export
print.summary.jfaDistr <- function(x, digits = getOption("digits"), ...) {
type <- if (!is.null(x$p.value)) "Classical" else "Bayesian"
cat(paste0("\n\t", type, " Digit Distribution Test Summary\n"))
cat("\nOptions:\n")
cat(paste(" Confidence level: ", format(x[["conf.level"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Digits: ", switch(x[["check"]],
"first" = "Leading",
"firsttwo" = "First and second",
"last" = "Last"
)), "\n")
cat(paste(" Reference: ", if (x[["reference"]] == "benford") {
"Benford's law"
} else if (x[["reference"]] == "uniform") {
"Uniform distribution"
} else {
"Custom distribution"
}), "\n")
if (x[["type"]] == "Bayesian") {
cat(paste(" Prior distribution: ", "Dirichlet(1, ..., 1)"), "\n")
}
cat("\nData:\n")
cat(paste(" Sample size: ", format(x[["n"]], digits = max(1L, digits - 2L))), "\n")
cat("\nResults:\n")
if (x[["type"]] == "Bayesian") {
cat(paste(" BF\u2081\u2080:\t ", format(x[["bf"]], digits = max(1L, digits - 2L))), "\n")
} else {
cat(paste(" X-squared:\t ", format(x[["statistic"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" Degrees of freedom:\t ", format(x[["parameter"]], digits = max(1L, digits - 2L))), "\n")
cat(paste(" p-value: ", format.pval(x[["p.value"]], digits = max(1L, digits - 2L))), "\n")
}
cat(paste(" Mean absolute difference (MAD):", format(x[["mad"]], digits = max(1L, digits - 2L))), "\n")
cat(paste0("\nDigits (", length(x[["digits"]]), "):\n"))
x[["estimates"]] <- round(x[["estimates"]], digits = max(1L, digits - 2L))
x[["estimates"]][["d"]] <- paste0(" ", x[["estimates"]][["d"]])
print(x[["estimates"]], quote = FALSE, row.names = FALSE)
}
#' @rdname jfa-methods
#' @method summary jfaDistr
#' @export
summary.jfaDistr <- function(object, digits = getOption("digits"), ...) {
out <- list(
"conf.level" = round(object[["conf.level"]], digits),
"n" = object[["n"]],
"check" = object[["check"]],
"digits" = object[["digits"]],
"reference" = object[["reference"]],
"mad" = object[["mad"]],
stringsAsFactors = FALSE
)
if (!is.null(object[["p.value"]])) {
out[["statistic"]] <- object[["statistic"]]
out[["parameter"]] <- object[["parameter"]]
out[["p.value"]] <- object[["p.value"]]
out[["type"]] <- "Classical"
} else if (!is.null(object[["bf"]])) {
out[["bf"]] <- object[["bf"]]
out[["type"]] <- "Bayesian"
}
out[["estimates"]] <- object[["estimates"]]
class(out) <- c("summary.jfaDistr", "list")
return(out)
}
#' @rdname jfa-methods
#' @method plot jfaDistr
#' @export
plot.jfaDistr <- function(x, type = c("estimates", "robustness", "sequential"), ...) {
type <- match.arg(type)
if (type == "estimates") {
y <- type <- d <- lb <- ub <- NULL
df <- data.frame(
x = c(x[["digits"]], x[["digits"]]),
y = c(x$observed / x$n, x$expected / x$n),
type = c(rep("Observed", length(x[["digits"]])), rep("Expected", length(x[["digits"]])))
)
yBreaks <- pretty(c(0, df$y, x[["estimates"]]$ub), min.n = 4)
if (x[["check"]] == "first" || x[["check"]] == "last") {
xBreaks <- x[["digits"]]
xLabels <- x[["digits"]]
pointSize <- 5
lineSize <- 1.5
} else {
xBreaks <- x[["digits"]]
xLabels <- c(
10, rep("", 9),
20, rep("", 9),
30, rep("", 9),
40, rep("", 9),
50, rep("", 9),
60, rep("", 9),
70, rep("", 9),
80, rep("", 9),
90, rep("", 8),
99
)
pointSize <- 2
lineSize <- 1.2
}
axisName <- switch(x[["check"]],
"first" = "Leading digit",
"firsttwo" = "Leading digits",
"last" = "Last digit"
)
xs <- rep(xBreaks[1], 2)
ys <- rep(yBreaks[1], 2)
types <- c("Observed", "Expected")
sizes <- c(7, 10)
shapes <- c(21, 22)
fills <- c("dodgerblue", "darkgray")
if (any(x[["deviation"]])) {
xs <- c(xs, xBreaks[1])