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

   1 #' WP method background function WP_known
   2 #'
   3 #' This is a background/internal function called by \code{WP}. It computes the maximum
   4 #' likelihood estimator of R0 assuming that the serial distribution is known and finite discrete.
   5 #'
   6 #' @param NT Vector of case counts.
   7 #' @param p Discretized version of the serial distribution.
   8 #'
   9 #' @return The function returns the maximum likelihood estimator of R0.
  10 #'
  11 #' @keywords internal
  12 WP_known <- function(NT, p) {
  13     k <- length(p)
  14     TT <- length(NT) - 1
  15         mu_t <- rep(0, TT)
  16
  17     for (i in 1:TT) {
  18         Nt <- NT[i:max(1, i-k+1)]
  19         mu_t[i] <- sum(p[1:min(k, i)] * Nt)
  20     }
  21
  22     Rhat <- sum(NT[-1]) / sum(mu_t)
  23         return(Rhat)
  24 }
  25
  26 #' WP method background function WP_unknown
  27 #'
  28 #' This is a background/internal function called by \code{WP}. It computes the maximum likelihood estimator
  29 #' of R0 assuming that the serial distribution is unknown but comes from a discretized gamma distribution.
  30 #' The function then implements a simple grid search algorithm to obtain the maximum likelihood estimator
  31 #' of R0 as well as the gamma parameters.
  32 #'
  33 #' @param NT Vector of case counts.
  34 #' @param B Length of grid for shape and scale (grid search parameter).
  35 #' @param shape.max Maximum shape value (grid \code{search} parameter).
  36 #' @param scale.max Maximum scale value (grid \code{search} parameter).
  37 #' @param tol cutoff value for cumulative distribution function of the serial distribution (defaults to 0.999).
  38 #'
  39 #' @return The function returns \code{Rhat}, the maximum likelihood estimator of R0, as well as the maximum
  40 #'         likelihood estimator of the discretized serial distribution given by \code{p} (the probability mass
  41 #'         function) and \code{range.max} (the distribution has support on the integers one to \code{range.max}).
  42 #'         The function also returns \code{resLL} (all values of the log-likelihood) at \code{shape} (grid for
  43 #'         shape parameter) and at \code{scale} (grid for scale parameter), as well as \code{resR0} (the full
  44 #'         vector of maximum likelihood estimators), \code{JJ} (the locations for the likelihood for these), and
  45 #'         \code{J0} (the location for the maximum likelihood estimator \code{Rhat}). If \code{JJ} and \code{J0}
  46 #'         are not the same, this means that the maximum likelihood estimator is not unique.
  47 #'
  48 #' @importFrom stats pgamma qgamma
  49 #'
  50 #' @keywords internal
  51 WP_unknown <- function(NT, B=100, shape.max=10, scale.max=10, tol=0.999) {
  52         shape <- seq(0, shape.max, length.out=B+1)
  53         scale <- seq(0, scale.max, length.out=B+1)
  54         shape <- shape[-1]
  55         scale <- scale[-1]
  56
  57         resLL <- matrix(0,B,B)
  58         resR0 <- matrix(0,B,B)
  59
  60     for (i in 1:B) {
  61         for (j in 1:B) {
  62             range.max <- ceiling(qgamma(tol, shape=shape[i], scale=scale[j]))
  63             p <- diff(pgamma(0:range.max, shape=shape[i], scale=scale[j]))
  64             p <- p / sum(p)
  65             mle <- WP_known(NT, p)
  66             resLL[i,j] <- computeLL(p, NT, mle)
  67             resR0[i,j] <- mle
  68         }
  69     }
  70
  71     J0 <- which.max(resLL)
  72     R0hat <- resR0[J0]
  73     JJ <- which(resLL == resLL[J0], arr.ind=TRUE)
  74     range.max <- ceiling(qgamma(tol, shape=shape[JJ[1]], scale=scale[JJ[2]]))
  75     p <- diff(pgamma(0:range.max, shape=shape[JJ[1]], scale=scale[JJ[2]]))
  76     p <- p / sum(p)
  77
  78     return(list(Rhat=R0hat, J0=J0, ll=resLL, Rs=resR0, scale=scale, shape=shape, JJ=JJ, p=p, range.max=range.max))
  79 }
  80
  81 #' WP method background function computeLL
  82 #'
  83 #' This is a background/internal function called by \code{WP}.  It computes the log-likelihood.
  84 #'
  85 #' @param NT Vector of case counts.
  86 #' @param p Discretized version of the serial distribution.
  87 #' @param R0 Basic reproductive ratio.
  88 #'
  89 #' @return This function returns the log-likelihood at the input variables and parameters.
  90 #'
  91 #' @keywords internal
  92 computeLL <- function(p, NT, R0) {
  93     k <- length(p)
  94     TT <- length(NT) - 1
  95     mu_t <- rep(0, TT)
  96
  97     for (i in 1:TT) {
  98         Nt <- NT[i:max(1, i-k+1)]
  99         mu_t[i] <- sum(p[1:min(k, i)] * Nt)
 100     }
 101
 102     mu_t <- R0 * mu_t
 103     LL <- sum(NT[-1] * log(mu_t)) - sum(mu_t)
 104
 105         return(LL)
 106 }