R/bf_binom.R

In multinomineq: Bayesian Inference for Multinomial Models with Inequality Constraints

#' Bayes Factor for Linear Inequality Constraints
#'
#' Computes the Bayes factor for product-binomial/-multinomial models with
#' linear order-constraints (specified via: \code{A*x <= b} or the convex hull \code{V}).
#'
#' @param ... further arguments passed to \code{\link{count_binom}} or
#'   \code{\link{count_multinom}} (e.g., \code{M}, \code{steps}).
#' @inheritParams count_binom
#' @inheritParams count_to_bf
#'
#' @details
#' For more control, use \code{\link{count_binom}} to specifiy how many samples
#' should be drawn from the prior and posterior, respectively. This is especially
#' recommended if the same prior distribution (and thus the same prior probability/integral)
#' is used for computing BFs for multiple data sets that differ only in the
#' observed frequencies \code{k} and the sample size \code{n}.
#' In this case, the prior probability/proportion of the parameter space in line
#' with the inequality constraints can be computed once with high precision
#' (or even analytically), and only the posterior probability/proportion needs
#' to be estimated separately for each unique vector \code{k}.
#'
#' @template ref_karabatsos2005
#' @template ref_regenwetter2014
#' @template return_bf
#' @seealso \code{\link{count_binom}} and \code{\link{count_multinom}} for
#'     for more control on the number of prior/posterior samples and
#'     \code{\link{bf_nonlinear}} for nonlinear order constraints.
#'
#' @examples
#' k <- c(0, 3, 2, 5, 3, 7)
#' n <- rep(10, 6)
#'
#' # linear order constraints:
#' #             p1 <p2 <p3 <p4 <p5 <p6 <.50
#' A <- matrix(
#'   c(
#'     1, -1, 0, 0, 0, 0,
#'     0, 1, -1, 0, 0, 0,
#'     0, 0, 1, -1, 0, 0,
#'     0, 0, 0, 1, -1, 0,
#'     0, 0, 0, 0, 1, -1,
#'     0, 0, 0, 0, 0, 1
#'   ),
#'   ncol = 6, byrow = TRUE
#' )
#' b <- c(0, 0, 0, 0, 0, .50)
#'
#' # Bayes factor: unconstrained vs. constrained
#' bf_binom(k, n, A, b, prior = c(1, 1), M = 10000)
#' bf_binom(k, n, A, b, prior = c(1, 1), M = 2000, steps = c(2, 4, 5))
#' bf_binom(k, n, A, b, prior = c(1, 1), M = 1000, cmin = 200)
#'
#' @export
bf_binom <- function(k, n, A, b, V, map, prior = c(1, 1), log = FALSE, ...) {
  arg <- lapply(as.list(match.call())[-1], eval, envir = parent.frame())
  arg$log <- NULL
  po <- do.call("count_binom", arg)
  arg$k <- arg$n <- 0
  pr <- do.call("count_binom", arg)
  count_to_bf(po, pr, log = log)
}

#' @inheritParams count_multinom
#' @rdname bf_binom
#' @export
bf_multinom <- function(k, options, A, b, V, prior = rep(1, sum(options)),
                        log = FALSE, ...) {
  arg <- lapply(as.list(match.call())[-1], eval, envir = parent.frame())
  arg$log <- NULL
  po <- do.call("count_multinom", arg)
  arg$k <- 0
  pr <- do.call("count_multinom", arg)
  count_to_bf(po, pr, log = log)
}