#' 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.
+#' 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.
#'
-#' @keywords internal
+#' @noRd
WP_known <- function(NT, p) {
- k <- length(p)
- TT <- length(NT) - 1
- mu_t <- rep(0, TT)
+ 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)
- }
+ 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)
+ 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.
+#' 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).
+#' @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.
+#' @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
#'
-#' @keywords internal
-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]
+#' @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)
+ 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
- }
+ 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))
+
+ 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.
+#' This is a background/internal function called by \code{WP}. It computes the
+#' log-likelihood.
#'
-#' @param NT Vector of case counts.
#' @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.
+#' @return This function returns the log-likelihood at the input variables and
+#' parameters.
#'
-#' @keywords internal
+#' @noRd
computeLL <- function(p, NT, R0) {
- k <- length(p)
- TT <- length(NT) - 1
- mu_t <- rep(0, TT)
+ 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)
- }
+ 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)
+ mu_t <- R0 * mu_t
+ LL <- sum(NT[-1] * log(mu_t)) - sum(mu_t)
- return(LL)
+ return(LL)
}
git.nmode.ca / Rnaught / blobdiff
