nmode's Git Repositories - Rnaught/blob - R/WP_unknown.R

   1 #' WP method background function WP_unknown
   2 #'
   3 #' This is a background/internal function called by \code{WP}. It computes the maximum likelihood estimator
   4 #' of R0 assuming that the serial distribution is unknown but comes from a discretized gamma distribution.
   5 #' The function then implements a simple grid search algorithm to obtain the maximum likelihood estimator
   6 #' of R0 as well as the gamma parameters.
   7 #'
   8 #' @param NT Vector of case counts.
   9 #' @param B Length of grid for shape and scale (grid search parameter).
  10 #' @param shape.max Maximum shape value (grid \code{search} parameter).
  11 #' @param scale.max Maximum scale value (grid \code{search} parameter).
  12 #' @param tol cutoff value for cumulative distribution function of the serial distribution (defaults to 0.999).
  13 #'
  14 #' @return The function returns \code{Rhat}, the maximum likelihood estimator of R0, as well as the maximum
  15 #'         likelihood estimator of the discretized serial distribution given by \code{p} (the probability mass
  16 #'         function) and \code{range.max} (the distribution has support on the integers one to \code{range.max}).
  17 #'         The function also returns \code{resLL} (all values of the log-likelihood) at \code{shape} (grid for
  18 #'         shape parameter) and at \code{scale} (grid for scale parameter), as well as \code{resR0} (the full
  19 #'         vector of maximum likelihood estimators), \code{JJ} (the locations for the likelihood for these), and
  20 #'         \code{J0} (the location for the maximum likelihood estimator \code{Rhat}). If \code{JJ} and \code{J0}
  21 #'         are not the same, this means that the maximum likelihood estimator is not unique.
  22 #'
  23 #' @importFrom stats pgamma qgamma
  24 #'
  25 #' @keywords internal
  26 WP_unknown <- function(NT, B=100, shape.max=10, scale.max=10, tol=0.999) {
  27         shape <- seq(0, shape.max, length.out=B+1)
  28         scale <- seq(0, scale.max, length.out=B+1)
  29         shape <- shape[-1]
  30         scale <- scale[-1]
  31
  32         resLL <- matrix(0,B,B)
  33         resR0 <- matrix(0,B,B)
  34
  35     for (i in 1:B) {
  36         for (j in 1:B) {
  37             range.max <- ceiling(qgamma(tol, shape=shape[i], scale=scale[j]))
  38             p <- diff(pgamma(0:range.max, shape=shape[i], scale=scale[j]))
  39             p <- p / sum(p)
  40             mle <- WP_known(NT, p)
  41             resLL[i,j] <- computeLL(p, NT, mle)
  42             resR0[i,j] <- mle
  43         }
  44     }
  45
  46     J0 <- which.max(resLL)
  47     R0hat <- resR0[J0]
  48     JJ <- which(resLL == resLL[J0], arr.ind=TRUE)
  49     range.max <- ceiling(qgamma(tol, shape=shape[JJ[1]], scale=scale[JJ[2]]))
  50     p <- diff(pgamma(0:range.max, shape=shape[JJ[1]], scale=scale[JJ[2]]))
  51     p <- p / sum(p)
  52
  53     return(list(Rhat=R0hat, J0=J0, ll=resLL, Rs=resR0, scale=scale, shape=shape, JJ=JJ, p=p, range.max=range.max))
  54 }