+WP <- function(NT, mu = NA,
+ search = list(B = 100, shape.max = 10, scale.max = 10),
+ tol = 0.999) {
+ if (is.na(mu)) {
+ print("You have assumed that the serial distribution is unknown.")
+ res <- WP_unknown(NT, B = search$B, shape.max = search$shape.max,
+ scale.max = search$scale.max, tol = tol)
+ Rhat <- res$Rhat
+ p <- res$p
+ range.max <- res$range.max
+ JJ <- res$JJ
+ } else {
+ print("You have assumed that the serial distribution is known.")
+ range.max <- ceiling(qexp(tol, rate = 1 / mu))
+ p <- diff(pexp(0:range.max, 1 / mu))
+ p <- p / sum(p)
+ res <- WP_known(NT = NT, p = p)
+ Rhat <- res
+ JJ <- NA
+ }
+
+ return(list(Rhat = Rhat,
+ check = length(JJ),
+ SD = list(supp = 1:range.max, pmf = p)))
+}
+
+#' WP method background function WP_known
+#'
+#' This is a background/internal function called by \code{WP}. It computes the
+#' maximum likelihood estimator of R0 assuming that the serial distribution is
+#' known and finite discrete.
+#'
+#' @param NT Vector of case counts.
+#' @param p Discretized version of the serial distribution.
+#'
+#' @return The function returns the maximum likelihood estimator of R0.
+#'
+#' @noRd
+WP_known <- function(NT, p) {
+ k <- length(p)
+ TT <- length(NT) - 1
+ mu_t <- rep(0, TT)
+
+ for (i in 1:TT) {
+ Nt <- NT[i:max(1, i - k + 1)]
+ mu_t[i] <- sum(p[1:min(k, i)] * Nt)
+ }
+
+ Rhat <- sum(NT[-1]) / sum(mu_t)
+ return(Rhat)
+}
+
+#' WP method background function WP_unknown
+#'
+#' This is a background/internal function called by \code{WP}. It computes the
+#' maximum likelihood estimator of R0 assuming that the serial distribution is
+#' unknown but comes from a discretized gamma distribution. The function then
+#' implements a simple grid search algorithm to obtain the maximum likelihood
+#' estimator of R0 as well as the gamma parameters.
+#'
+#' @param NT Vector of case counts.
+#' @param B Length of grid for shape and scale (grid search parameter).
+#' @param shape.max Maximum shape value (grid \code{search} parameter).
+#' @param scale.max Maximum scale value (grid \code{search} parameter).
+#' @param tol cutoff value for cumulative distribution function of the serial
+#' distribution (defaults to 0.999).
+#'
+#' @return The function returns \code{Rhat}, the maximum likelihood estimator of
+#' R0, as well as the maximum likelihood estimator of the discretized
+#' serial distribution given by \code{p} (the probability mass function)
+#' and \code{range.max} (the distribution has support on the integers
+#' one to \code{range.max}). The function also returns \code{resLL} (all
+#' values of the log-likelihood) at \code{shape} (grid for shape
+#' parameter) and at \code{scale} (grid for scale parameter), as well as
+#' \code{resR0} (the full vector of maximum likelihood estimators),
+#' \code{JJ} (the locations for the likelihood for these), and \code{J0}
+#' (the location for the maximum likelihood estimator \code{Rhat}). If
+#' \code{JJ} and \code{J0} are not the same, this means that the maximum
+#' likelihood estimator is not unique.
+#'
+#' @importFrom stats pgamma qgamma
+#'
+#' @noRd
+WP_unknown <- function(NT, B = 100, shape.max = 10, scale.max = 10,
+ tol = 0.999) {
+ shape <- seq(0, shape.max, length.out = B + 1)
+ scale <- seq(0, scale.max, length.out = B + 1)
+ shape <- shape[-1]
+ scale <- scale[-1]
+
+ resLL <- matrix(0, B, B)
+ resR0 <- matrix(0, B, B)
+
+ for (i in 1:B)
+ for (j in 1:B) {
+ range.max <- ceiling(qgamma(tol, shape = shape[i], scale = scale[j]))
+ p <- diff(pgamma(0:range.max, shape = shape[i], scale = scale[j]))
+ p <- p / sum(p)
+ mle <- WP_known(NT, p)
+ resLL[i, j] <- computeLL(p, NT, mle)
+ resR0[i, j] <- mle
git.nmode.ca / Rnaught / blobdiff
