# R/ci_cramersv.R In confintr: Confidence Intervals

#### Documented in ci_cramersv

#' Confidence Interval for the Population Cramer's V
#'
#' This function calculates confidence intervals for the population Cramer's V. By default, a parametric approach based on the non-centrality parameter (ncp) of the chi-squared distribution is utilized. Alternatively, bootstrap confidence intervals are available, also by boostrapping confidence intervals for the ncp.
#'
#' A positive lower (1-alpha)*100%-confidence limit for the ncp goes hand-in-hand with a significant association test at level alpha. In order to allow such test approach also with Cramer's V, if the lower bound for the ncp is 0, we round down to 0 also the lower bound for Cramer's V. Without this slightly conservative adjustment, the lower limit for V would always be positive since ci for V = sqrt((ci for ncp + df)/(n (k - 1))), where k is the smaller number of levels in the two variables (see Smithson for this formula). Use \code{test_adjustment = FALSE} to switch off this behaviour. Note that this is also a reason to bootstrap V via ncp instead of directly bootstrapping V.
#' Bootstrap confidence intervals are calculated by the package "boot", see references. The default bootstrap type is "bca" (bias-corrected accelerated) as it enjoys the property of being second order accurate as well as transformation respecting (see Efron, p. 188).
#' Note that no continuity correction is applied for 2x2 tables. Further note that large chi-squared test statistics might provide unreliable results with method "chi-squared" (see \code{?pchisq}).
#' @importFrom stats chisq.test
#' @param x The result of \code{stats::chisq.test}, a matrix/table of counts or a \code{data.frame} with exactly two columns representing the two variables.
#' @param probs Error probabilites. The default c(0.025, 0.975) gives a symmetric 95% confidence interval.
#' @param type Type of confidence interval. One of "chi-squared" (default) or "bootstrap".
#' @param boot_type Type of bootstrap confidence interval ("bca", "perc", "norm", "basic"). Only used for \code{type = "bootstrap"}.
#' @param R The number of bootstrap resamples. Only used for \code{type = "bootstrap"}.
#' @param seed An integer random seed. Only used for \code{type = "bootstrap"}.
#' @param test_adjustment Adjustment to allow for test of association, see Details. The default is \code{TRUE}.
#' @param ... Further arguments passed to \code{resample::CI.boot_type}.
#' @return A list with class \code{cint} containing these components:
#' \itemize{
#'   \item \code{parameter}: The parameter in question.
#'   \item \code{interval}: The confidence interval for the parameter.
#'   \item \code{estimate}: The estimate for the parameter.
#'   \item \code{probs}: A vector of error probabilities.
#'   \item \code{type}: The type of the interval.
#'   \item \code{info}: An additional description text for the interval.
#' }
#' @export
#' @examples
#' ir <- iris
#' ir$PL <- ir$Petal.Width > 1
#' ci_cramersv(ir[, c("Species", "PL")])
#' ci_cramersv(ir[, c("Species", "PL")], type = "bootstrap", R = 999)
#' ci_cramersv(ir[, c("Species", "PL")], probs = c(0.05, 1))
#' ci_cramersv(mtcars[c("am", "vs")])
#' ci_cramersv(mtcars[c("am", "vs")], test_adjustment = FALSE)
#' @references
#' \enumerate{
#'   \item Smithson, M. (2003). Confidence intervals. Series: Quantitative Applications in the Social Sciences. New York, NY: Sage Publications.
#'   \item Efron, B. and Tibshirani R. J. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC.
#'   \item Canty, A and Ripley B. (2019). boot: Bootstrap R (S-Plus) Functions.
#' }
ci_cramersv <- function(x, probs = c(0.025, 0.975), type = c("chi-squared", "bootstrap"),
boot_type = c("bca", "perc", "norm", "basic"),
R = 9999, seed = NULL, test_adjustment = TRUE, ...) {
# Input check and initialization
check_probs(probs)
stopifnot(inherits(x, "htest") || is.matrix(x) || is.data.frame(x))
if (inherits(x, "htest")) {
stopifnot("X-squared" %in% names(x[["statistic"]]))
} else {
if (is.data.frame(x)) {
stopifnot(ncol(x) == 2L)
x <- table(x[, 1], x[, 2])
}
stopifnot(all(x >= 0))
x <- chisq.test(x, correct = FALSE)
}
stat <- as.numeric(x[["statistic"]])
n <- sum(x[["observed"]])
k <- min(dim(x[["observed"]]))
df <- x[["parameter"]]

# ci for ncp -> ci for V
out <- ci_chisq_ncp(x, probs = probs, type = type, boot_type = boot_type,
R = R, seed = seed, correct = FALSE, ...)
ci <- sqrt((out$interval + df) / (n * (k - 1))) # Modification to allow hypothesis test of association if (test_adjustment && out$interval == 0) {
ci <- 0
}

# Replace ncp by Cramer's V
out$estimate <- cramersv(x) out$interval <- check_output(ci, probs, 0:1)
out\$parameter <- "population Cramer's V"
out
}


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confintr documentation built on Jan. 29, 2022, 1:08 a.m.