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diff --git a/R/WP_internal.R b/R/WP_internal.R new file mode 100644 index 0000000..54744b9 --- /dev/null +++ b/R/WP_internal.R @@ -0,0 +1,106 @@ +#' 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. +#' +#' @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 +WP_known <- function(NT, p) { + 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) + } + + 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. +#' +#' @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). +#' +#' @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] + + 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 + } + } + + 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. +#' +#' @param NT Vector of case counts. +#' @param p Discretized version of the serial distribution. +#' @param R0 Basic reproductive ratio. +#' +#' @return This function returns the log-likelihood at the input variables and parameters. +#' +#' @keywords internal +computeLL <- function(p, NT, R0) { + 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) + } + + mu_t <- R0 * mu_t + LL <- sum(NT[-1] * log(mu_t)) - sum(mu_t) + + return(LL) +} |