Group WP-related functions

1 files changed, 117 insertions, 0 deletions

diff --git a/R/WP.R b/R/WP.R
index 5440e35..04791e2 100644
--- a/R/WP.R
+++ b/R/WP.R
@@ -110,3 +110,120 @@ WP <- function(NT, mu = NA,
               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
+    }
+
+  J0 <- which.max(resLL)
+  R0hat <- resR0[J0]
+  JJ <- which(resLL == resLL[J0], arr.ind = TRUE)
+  range.max <- ceiling(qgamma(tol, shape = shape[JJ[1]], scale = scale[JJ[2]]))
+  p <- diff(pgamma(0:range.max, shape = shape[JJ[1]], scale = scale[JJ[2]]))
+  p <- p / sum(p)
+
+  return(list(Rhat = R0hat, J0 = J0, ll = resLL, Rs = resR0, scale = scale,
+              shape = shape, JJ = JJ, p = p, range.max = range.max))
+}
+
+#' WP method background function computeLL
+#'
+#' This is a background/internal function called by \code{WP}. It computes the
+#' log-likelihood.
+#'
+#' @param p Discretized version of the serial distribution.
+#' @param NT Vector of case counts.
+#' @param R0 Basic reproductive ratio.
+#'
+#' @return This function returns the log-likelihood at the input variables and
+#'         parameters.
+#'
+#' @noRd
+computeLL <- function(p, NT, R0) {
+  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)
+  }
+
+  mu_t <- R0 * mu_t
+  LL <- sum(NT[-1] * log(mu_t)) - sum(mu_t)
+
+  return(LL)
+}