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 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.
   4 #'
   5 #' @param NT vector of case counts
   6 #' @param B length of grid for shape and scale (grid search parameter)
   7 #' @param shape.max maximum shape value (grid search parameter)
   8 #' @param scale.max maximum scale value (grid search parameter)
   9 #' @param tol cutoff value for cumulative distribution function of the serial distribution, defaults to 0.999
  10 #' @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.
  11 #'
  12 #' @export
  13
  14 WP_unknown              <-      function(NT, B=100, shape.max=10, scale.max=10, tol=0.999){
  15
  16         shape           <-      seq(0, shape.max, length.out=B+1)
  17         scale           <-      seq(0, scale.max, length.out=B+1)
  18         shape           <-      shape[-1]
  19         scale           <-      scale[-1]
  20
  21         resLL           <-      matrix(0,B,B)
  22         resR0           <-      matrix(0,B,B)
  23
  24         for(i in 1:B){
  25         for(j in 1:B){
  26                 range.max       <-      ceiling(qgamma(tol, shape=shape[i], scale=scale[j]))
  27                 p                       <-      diff(pgamma(0:range.max, shape=shape[i], scale=scale[j]))
  28                 p                       <-      p/sum(p)
  29                 mle                     <-      WP_known(NT, p)
  30                 resLL[i,j]      <-      computeLL(p, NT, mle$R)
  31                 resR0[i,j]      <-      mle$R
  32         }
  33 #               print(i)
  34         }
  35
  36         J0                      <-      which.max(resLL)
  37         R0hat           <-      resR0[J0]
  38         JJ                      <-      which(resLL==resLL[J0], arr.ind=TRUE)
  39 #       JJ                      <-      which(resLL==max(resLL), arr.ind=TRUE)
  40         range.max       <-      ceiling(qgamma(tol, shape=shape[JJ[1]], scale=scale[JJ[2]]))
  41         p                       <-      diff(pgamma(0:range.max, shape=shape[JJ[1]], scale=scale[JJ[2]]))
  42         p                       <-      p/sum(p)
  43
  44         return(list(Rhat=R0hat, J0=J0, ll=resLL, Rs=resR0, scale=scale, shape=shape, JJ=JJ, p=p, range.max=range.max))
  45 }
  46
  47