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
   4 #' maximum likelihood estimator of R0 assuming that the serial distribution is
   5 #' known and finite discrete.
   6 #'
   7 #' @param NT Vector of case counts.
   8 #' @param p Discretized version of the serial distribution.
   9 #'
  10 #' @return The function returns the maximum likelihood estimator of R0.
  11 #'
  12 #' @noRd
  13 WP_known <- function(NT, p) {
  14   k <- length(p)
  15   TT <- length(NT) - 1
  16   mu_t <- rep(0, TT)
  17
  18   for (i in 1:TT) {
  19     Nt <- NT[i:max(1, i - k + 1)]
  20     mu_t[i] <- sum(p[1:min(k, i)] * Nt)
  21   }
  22
  23   Rhat <- sum(NT[-1]) / sum(mu_t)
  24   return(Rhat)
  25 }
  26
  27 #' WP method background function WP_unknown
  28 #'
  29 #' This is a background/internal function called by \code{WP}. It computes the
  30 #' maximum likelihood estimator of R0 assuming that the serial distribution is
  31 #' unknown but comes from a discretized gamma distribution. The function then
  32 #' implements a simple grid search algorithm to obtain the maximum likelihood
  33 #' estimator of R0 as well as the gamma parameters.
  34 #'
  35 #' @param NT Vector of case counts.
  36 #' @param B Length of grid for shape and scale (grid search parameter).
  37 #' @param shape.max Maximum shape value (grid \code{search} parameter).
  38 #' @param scale.max Maximum scale value (grid \code{search} parameter).
  39 #' @param tol cutoff value for cumulative distribution function of the serial
  40 #'            distribution (defaults to 0.999).
  41 #'
  42 #' @return The function returns \code{Rhat}, the maximum likelihood estimator of
  43 #'         R0, as well as the maximum likelihood estimator of the discretized
  44 #'         serial distribution given by \code{p} (the probability mass function)
  45 #'         and \code{range.max} (the distribution has support on the integers
  46 #'         one to \code{range.max}). The function also returns \code{resLL} (all
  47 #'         values of the log-likelihood) at \code{shape} (grid for shape
  48 #'         parameter) and at \code{scale} (grid for scale parameter), as well as
  49 #'         \code{resR0} (the full vector of maximum likelihood estimators),
  50 #'         \code{JJ} (the locations for the likelihood for these), and \code{J0}
  51 #'         (the location for the maximum likelihood estimator \code{Rhat}). If
  52 #'         \code{JJ} and \code{J0} are not the same, this means that the maximum
  53 #'         likelihood estimator is not unique.
  54 #'
  55 #' @importFrom stats pgamma qgamma
  56 #'
  57 #' @noRd
  58 WP_unknown <- function(NT, B = 100, shape.max = 10, scale.max = 10,
  59                        tol = 0.999) {
  60   shape <- seq(0, shape.max, length.out = B + 1)
  61   scale <- seq(0, scale.max, length.out = B + 1)
  62   shape <- shape[-1]
  63   scale <- scale[-1]
  64
  65   resLL <- matrix(0, B, B)
  66   resR0 <- matrix(0, B, B)
  67
  68   for (i in 1:B)
  69     for (j in 1:B) {
  70       range.max <- ceiling(qgamma(tol, shape = shape[i], scale = scale[j]))
  71       p <- diff(pgamma(0:range.max, shape = shape[i], scale = scale[j]))
  72       p <- p / sum(p)
  73       mle <- WP_known(NT, p)
  74       resLL[i, j] <- computeLL(p, NT, mle)
  75       resR0[i, j] <- mle
  76     }
  77
  78   J0 <- which.max(resLL)
  79   R0hat <- resR0[J0]
  80   JJ <- which(resLL == resLL[J0], arr.ind = TRUE)
  81   range.max <- ceiling(qgamma(tol, shape = shape[JJ[1]], scale = scale[JJ[2]]))
  82   p <- diff(pgamma(0:range.max, shape = shape[JJ[1]], scale = scale[JJ[2]]))
  83   p <- p / sum(p)
  84
  85   return(list(Rhat = R0hat, J0 = J0, ll = resLL, Rs = resR0, scale = scale,
  86               shape = shape, JJ = JJ, p = p, range.max = range.max))
  87 }
  88
  89 #' WP method background function computeLL
  90 #'
  91 #' This is a background/internal function called by \code{WP}. It computes the
  92 #' log-likelihood.
  93 #'
  94 #' @param p Discretized version of the serial distribution.
  95 #' @param NT Vector of case counts.
  96 #' @param R0 Basic reproductive ratio.
  97 #'
  98 #' @return This function returns the log-likelihood at the input variables and
  99 #'         parameters.
 100 #'
 101 #' @noRd
 102 computeLL <- function(p, NT, R0) {
 103   k <- length(p)
 104   TT <- length(NT) - 1
 105   mu_t <- rep(0, TT)
 106
 107   for (i in 1:TT) {
 108     Nt <- NT[i:max(1, i - k + 1)]
 109     mu_t[i] <- sum(p[1:min(k, i)] * Nt)
 110   }
 111
 112   mu_t <- R0 * mu_t
 113   LL <- sum(NT[-1] * log(mu_t)) - sum(mu_t)
 114
 115   return(LL)
 116 }