Nothing
R/step1_sample_mvt.R
In AccelStab: Accelerated Stability Kinetic Modelling
#' @title Sample the Multivariate t Distribution
#'
#' @description Take a selected number of samples from the multivariate t distribution (mvt).
#'
#' @details Using the provided data the function creates a fit of the
#' Šesták–Berggren kinetic model and then draws a selected number of
#' samples from the mvt of the model parameters.
#'
#' @param data Dataframe containing accelerated stability data (required).
#' @param y Name of decreasing variable (e.g. concentration) contained within data
#' (required).
#' @param .time Time variable contained within data (required).
#' @param K Kelvin variable (numeric or column name) (optional).
#' @param C Celsius variable (numeric or column name) (optional).
#' @param validation Validation dummy variable (column name) (optional).
#' @param draw Number of samples to draw from mvt (required).
#' @param parms Starting values for the parameters as a list - k1, k2, k3, and c0 (optional).
#' @param reparameterisation Use alternative parameterisation of the one-step
#' model which aims to reduce correlation between k1 and k2.
#' @param zero_order Set kinetic order, k3, to zero (straight lines).
#'
#' @return A matrix containing parameter draws from the mvt distribution.
#'
#' @examples #load antigenicity data.
#' data(antigenicity)
#'
#' #Basic use of the step1_sample_mvt function with C column defined and 1000 draws.
#' sample1 <- step1_sample_mvt(data = antigenicity, y = "conc", .time = "time",
#' C = "Celsius", draw = 1000)
#'
#' #Basic use of the step1_sample_mvt function with K column defined and 50000 draws
#' sample2 <- step1_sample_mvt(data = antigenicity, y = "conc", .time = "time",
#' K = "K", draw = 50000)
#'
#' #reparameterisation is TRUE and 10000 draws.
#' sample3 <- step1_sample_mvt(data = antigenicity, y = "conc", .time = "time",
#' C = "Celsius", reparameterisation = TRUE, draw = 10000)
#'
#' @importFrom stats vcov coef runif confint rnorm quantile qt complete.cases
#' @importFrom minpack.lm nls.lm
#' @importFrom mvtnorm rmvt
#'
#' @export step1_sample_mvt
step1_sample_mvt <- function (data, y, .time, K = NULL, C = NULL, validation = NULL,
draw, parms = NULL, reparameterisation = FALSE, zero_order = FALSE){
if (is.null(K) & is.null(C))
stop("Select the temperature variable in Kelvin or Celsius")
if (!is.null(parms) & !is.list(parms))
stop("The starting values for parameters must be a list, or keep as NULL")
if(!is.null(C) & !is.null(K)) {
data[, C] <- ifelse(is.na(data[, C]) & !is.na(data[, K]),
data$K - 273.15,
data[, C])
data[, K] <- ifelse(is.na(data[, K]) & !is.na(data[, C]),
data$C + 273.15,
data[, K])
}
data <- data[complete.cases(data[, c(C,K,y,.time)]), ]
dat = data
if (!is.null(validation))
if (!all(dat[,validation] %in% c(0,1)))
stop("Validation column must contain 1s and 0s only")
if (is.null(K))
dat$K = dat[, C] + 273.15
if (is.null(C)) {
dat$C = dat[, K] - 273.15
C = "C"}
Kref = mean(dat$K)
dat$Celsius = as.factor(dat[, C])
dat$time = dat[, .time]
dat$y = dat[, y]
if(!is.null(validation)){
dat$validation = ifelse(dat[,validation] == 0, "Fit", "Validation")
if(validation != "validation"){
dat <- dat[, !names(dat) %in% c(validation)]
}
}
if(.time != "time"){
dat <- dat[, !names(dat) %in% c(.time)]
}
if(y != "y"){
dat <- dat[, !names(dat) %in% c(y)]
}
dat_full <- dat
if(!is.null(validation)){
dat <- dat[dat$validation == "Fit",]
}
if(is.null(parms)){
sorted_data <- dat[order(dat$time), ]
min_time <- min(sorted_data$time)
if (sum(sorted_data$time == min_time) > 3) {
selected_rows <- sorted_data$time == min_time
} else {
selected_rows <- seq_len(min(3, nrow(sorted_data)))
}
c0_initial <- mean(sorted_data$y[selected_rows])
}
if(reparameterisation & zero_order){ # reparameterisation and k3 is 0
MyFctNL = function(parms) { # Make function
k1 = parms$k1
k2 = parms$k2
c0 = parms$c0
Model = c0 - c0 * dat$time * exp(k1 - k2/dat$K +
k2/Kref)
residual = dat$y - Model
return(residual)
}
# Fit model :
if (!is.null(parms)) {
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
else {
repeat {
parms = list(k1 = stats::runif(1, 0, 40), k2 = stats::runif(1,
1000, 20000), c0 = c0_initial)
fit = suppressWarnings(minpack.lm::nls.lm(par = parms,
fn = MyFctNL, lower = rep(0, length(parms))))
res = tryCatch({
summary(fit)
}, error = function(e) e, warning = function(w) w)
res2 = tryCatch({
stats::vcov(fit)
}, error = function(e) e)
if (any(stats::coef(fit) != parms) && !inherits(res, "error") &&
!inherits(res2, "error"))
(break)()
}
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
SIG = stats::vcov(fit)
pred_fct = function(coef.fit)
{
degrad = pred$time * exp(coef.fit[1] - coef.fit[2] / pred$K + coef.fit[2] / Kref)
conc = coef.fit[3] - coef.fit[3]*degrad
return(conc)
}
# Multi T bootstrap
rand.coef = rmvt(draw, sigma = SIG, df = nrow(dat) - 3) + matrix(nrow = draw, ncol = 3, byrow = TRUE, coef(fit))
}else if(!reparameterisation & zero_order){ # no reparameterisation and k3 is 0
MyFctNL = function(parms) { # make function
k1 = parms$k1
k2 = parms$k2
c0 = parms$c0
Model = c0 - c0 * dat$time * exp(k1 - k2 / dat$K)
residual = dat$y - Model
return(residual)
}
if (!is.null(parms)) { # fit model
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
else {
repeat {
parms = list(k1 = stats::runif(1, 0, 40), k2 = stats::runif(1,
1000, 20000), c0 = c0_initial)
fit = suppressWarnings(minpack.lm::nls.lm(par = parms,
fn = MyFctNL, lower = rep(0, length(parms))))
res = tryCatch({
summary(fit)
}, error = function(e) e, warning = function(w) w)
res2 = tryCatch({
stats::vcov(fit)
}, error = function(e) e)
if (any(stats::coef(fit) != parms) && !inherits(res, "error") &&
!inherits(res2, "error"))
(break)()
}
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
SIG = vcov(fit)
pred_fct = function(coef.fit)
{
degrad = pred$time * exp(coef.fit[1] - coef.fit[2] / pred$K)
conc = coef.fit[3] - coef.fit[3]*degrad
return(conc)
}
# Multi T bootstrap
rand.coef = rmvt(draw, sigma = SIG, df = nrow(dat) - 3) + matrix(nrow = draw, ncol = 3, byrow = TRUE, coef(fit))
}else if(reparameterisation & !zero_order){ #reparameterisation and k3 is not zero
MyFctNL = function(parms) {
k1 = parms$k1
k2 = parms$k2
k3 = parms$k3
c0 = parms$c0
Model = c0 - c0 * (1 - ((1 - k3) * (1/(1 - k3) - dat$time *
exp(k1 - k2/dat$K + k2/Kref)))^(1/(1 - k3)))
residual = dat$y - Model
return(residual)
}
if (!is.null(parms)) { # Fit the model
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
else {
repeat {
parms = list(k1 = stats::runif(1, 0, 60), k2 = stats::runif(1,
1000, 20000), k3 = stats::runif(1, 0, 11), c0 = c0_initial)
fit = suppressWarnings(minpack.lm::nls.lm(par = parms,
fn = MyFctNL, lower = rep(0, length(parms))))
res = tryCatch({
summary(fit)
}, error = function(e) e, warning = function(w) w)
res2 = tryCatch({
stats::vcov(fit)
}, error = function(e) e)
if (any(stats::coef(fit) != parms) && !inherits(res, "error") &&
!inherits(res2, "error"))
(break)()
}
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
k3 = coef(fit)[3]
if (k3 == 0){print("k3 is fitted to be exactly 0, we strongly suggest using option zero_order = TRUE")
}else if(confint(fit,'k3')[1] < 0 && confint(fit,'k3')[2] > 0){print(paste0("The 95% Wald Confidence Interval for k3 includes 0, k3 is estimated as ",signif(k3,4),". We suggest considering option zero_order = TRUE"))}
SIG = vcov(fit)
pred_fct = function(coef.fit)
{
degrad = 1 - ((1 - coef.fit[3]) * (1/(1 - coef.fit[3]) - pred$time * exp(coef.fit[1] - coef.fit[2] / pred$K + coef.fit[2] / Kref)))^(1/(1-coef.fit[3]))
conc = coef.fit[4] - coef.fit[4]*degrad
return(conc)
}
# Multi T bootstrap
rand.coef = rmvt(draw, sigma = SIG, df = nrow(dat) - 4) + matrix(nrow = draw, ncol = 4, byrow = TRUE, coef(fit))
}else if(!reparameterisation & !zero_order){ # No re-parameterisation and k3 not zero
MyFctNL = function(parms) {
k1 = parms$k1
k2 = parms$k2
k3 = parms$k3
c0 = parms$c0
test = c0 - c0 * (1 - ((1 - k3) * (1/(1 - k3) - dat$time * exp(k1 - k2 / dat$K)))^(1/(1-k3)))
residual = dat$y - test
return(residual)
}
if (!is.null(parms)) { # Fitting the model
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
else {
repeat {
parms = list(k1 = stats::runif(1, 0, 60), k2 = stats::runif(1,
1000, 20000), k3 = stats::runif(1, 0, 11), c0 = c0_initial)
fit = suppressWarnings(minpack.lm::nls.lm(par = parms,
fn = MyFctNL, lower = rep(0, length(parms))))
res = tryCatch({
summary(fit)
}, error = function(e) e, warning = function(w) w)
res2 = tryCatch({
stats::vcov(fit)
}, error = function(e) e)
if (any(stats::coef(fit) != parms) && !inherits(res, "error") &&
!inherits(res2, "error"))
(break)()
}
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
k3 = coef(fit)[3]
if (k3 == 0){print("k3 is fitted to be exactly 0, we strongly suggest using option zero_order = TRUE")
}else if(confint(fit,'k3')[1] < 0 && confint(fit,'k3')[2] > 0){print(paste0("The 95% Wald Confidence Interval for k3 includes 0, k3 is estimated as ",signif(k3,4),". We suggest considering option zero_order = TRUE"))}
SIG = vcov(fit)
pred_fct = function(coef.fit)
{
degrad = 1 - ((1 - coef.fit[3]) * (1/(1 - coef.fit[3]) - pred$time * exp(coef.fit[1] - coef.fit[2] / pred$K)))^(1/(1-coef.fit[3]))
conc = coef.fit[4] - coef.fit[4]*degrad
return(conc)
}
# Multi T bootstrap
rand.coef = rmvt(draw, sigma = SIG, df = nrow(dat) - 4) + matrix(nrow = draw, ncol = 4, byrow = TRUE, coef(fit))
}
if(zero_order){
colnames(rand.coef) <- c("k1","k2","c0")
}else{
colnames(rand.coef) <- c("k1","k2","k3","c0")
}
return(rand.coef)
}
globalVariables(c('pred'))
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#' @title Sample the Multivariate t Distribution
#'
#' @description Take a selected number of samples from the multivariate t distribution (mvt).
#'
#' @details Using the provided data the function creates a fit of the
#' Šesták–Berggren kinetic model and then draws a selected number of
#' samples from the mvt of the model parameters.
#'
#' @param data Dataframe containing accelerated stability data (required).
#' @param y Name of decreasing variable (e.g. concentration) contained within data
#' (required).
#' @param .time Time variable contained within data (required).
#' @param K Kelvin variable (numeric or column name) (optional).
#' @param C Celsius variable (numeric or column name) (optional).
#' @param validation Validation dummy variable (column name) (optional).
#' @param draw Number of samples to draw from mvt (required).
#' @param parms Starting values for the parameters as a list - k1, k2, k3, and c0 (optional).
#' @param reparameterisation Use alternative parameterisation of the one-step
#' model which aims to reduce correlation between k1 and k2.
#' @param zero_order Set kinetic order, k3, to zero (straight lines).
#'
#' @return A matrix containing parameter draws from the mvt distribution.
#'
#' @examples #load antigenicity data.
#' data(antigenicity)
#'
#' #Basic use of the step1_sample_mvt function with C column defined and 1000 draws.
#' sample1 <- step1_sample_mvt(data = antigenicity, y = "conc", .time = "time",
#' C = "Celsius", draw = 1000)
#'
#' #Basic use of the step1_sample_mvt function with K column defined and 50000 draws
#' sample2 <- step1_sample_mvt(data = antigenicity, y = "conc", .time = "time",
#' K = "K", draw = 50000)
#'
#' #reparameterisation is TRUE and 10000 draws.
#' sample3 <- step1_sample_mvt(data = antigenicity, y = "conc", .time = "time",
#' C = "Celsius", reparameterisation = TRUE, draw = 10000)
#'
#' @importFrom stats vcov coef runif confint rnorm quantile qt complete.cases
#' @importFrom minpack.lm nls.lm
#' @importFrom mvtnorm rmvt
#'
#' @export step1_sample_mvt
step1_sample_mvt <- function (data, y, .time, K = NULL, C = NULL, validation = NULL,
draw, parms = NULL, reparameterisation = FALSE, zero_order = FALSE){
if (is.null(K) & is.null(C))
stop("Select the temperature variable in Kelvin or Celsius")
if (!is.null(parms) & !is.list(parms))
stop("The starting values for parameters must be a list, or keep as NULL")
if(!is.null(C) & !is.null(K)) {
data[, C] <- ifelse(is.na(data[, C]) & !is.na(data[, K]),
data$K - 273.15,
data[, C])
data[, K] <- ifelse(is.na(data[, K]) & !is.na(data[, C]),
data$C + 273.15,
data[, K])
}
data <- data[complete.cases(data[, c(C,K,y,.time)]), ]
dat = data
if (!is.null(validation))
if (!all(dat[,validation] %in% c(0,1)))
stop("Validation column must contain 1s and 0s only")
if (is.null(K))
dat$K = dat[, C] + 273.15
if (is.null(C)) {
dat$C = dat[, K] - 273.15
C = "C"}
Kref = mean(dat$K)
dat$Celsius = as.factor(dat[, C])
dat$time = dat[, .time]
dat$y = dat[, y]
if(!is.null(validation)){
dat$validation = ifelse(dat[,validation] == 0, "Fit", "Validation")
if(validation != "validation"){
dat <- dat[, !names(dat) %in% c(validation)]
}
}
if(.time != "time"){
dat <- dat[, !names(dat) %in% c(.time)]
}
if(y != "y"){
dat <- dat[, !names(dat) %in% c(y)]
}
dat_full <- dat
if(!is.null(validation)){
dat <- dat[dat$validation == "Fit",]
}
if(is.null(parms)){
sorted_data <- dat[order(dat$time), ]
min_time <- min(sorted_data$time)
if (sum(sorted_data$time == min_time) > 3) {
selected_rows <- sorted_data$time == min_time
} else {
selected_rows <- seq_len(min(3, nrow(sorted_data)))
}
c0_initial <- mean(sorted_data$y[selected_rows])
}
if(reparameterisation & zero_order){ # reparameterisation and k3 is 0
MyFctNL = function(parms) { # Make function
k1 = parms$k1
k2 = parms$k2
c0 = parms$c0
Model = c0 - c0 * dat$time * exp(k1 - k2/dat$K +
k2/Kref)
residual = dat$y - Model
return(residual)
}
# Fit model :
if (!is.null(parms)) {
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
else {
repeat {
parms = list(k1 = stats::runif(1, 0, 40), k2 = stats::runif(1,
1000, 20000), c0 = c0_initial)
fit = suppressWarnings(minpack.lm::nls.lm(par = parms,
fn = MyFctNL, lower = rep(0, length(parms))))
res = tryCatch({
summary(fit)
}, error = function(e) e, warning = function(w) w)
res2 = tryCatch({
stats::vcov(fit)
}, error = function(e) e)
if (any(stats::coef(fit) != parms) && !inherits(res, "error") &&
!inherits(res2, "error"))
(break)()
}
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
SIG = stats::vcov(fit)
pred_fct = function(coef.fit)
{
degrad = pred$time * exp(coef.fit[1] - coef.fit[2] / pred$K + coef.fit[2] / Kref)
conc = coef.fit[3] - coef.fit[3]*degrad
return(conc)
}
# Multi T bootstrap
rand.coef = rmvt(draw, sigma = SIG, df = nrow(dat) - 3) + matrix(nrow = draw, ncol = 3, byrow = TRUE, coef(fit))
}else if(!reparameterisation & zero_order){ # no reparameterisation and k3 is 0
MyFctNL = function(parms) { # make function
k1 = parms$k1
k2 = parms$k2
c0 = parms$c0
Model = c0 - c0 * dat$time * exp(k1 - k2 / dat$K)
residual = dat$y - Model
return(residual)
}
if (!is.null(parms)) { # fit model
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
else {
repeat {
parms = list(k1 = stats::runif(1, 0, 40), k2 = stats::runif(1,
1000, 20000), c0 = c0_initial)
fit = suppressWarnings(minpack.lm::nls.lm(par = parms,
fn = MyFctNL, lower = rep(0, length(parms))))
res = tryCatch({
summary(fit)
}, error = function(e) e, warning = function(w) w)
res2 = tryCatch({
stats::vcov(fit)
}, error = function(e) e)
if (any(stats::coef(fit) != parms) && !inherits(res, "error") &&
!inherits(res2, "error"))
(break)()
}
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
SIG = vcov(fit)
pred_fct = function(coef.fit)
{
degrad = pred$time * exp(coef.fit[1] - coef.fit[2] / pred$K)
conc = coef.fit[3] - coef.fit[3]*degrad
return(conc)
}
# Multi T bootstrap
rand.coef = rmvt(draw, sigma = SIG, df = nrow(dat) - 3) + matrix(nrow = draw, ncol = 3, byrow = TRUE, coef(fit))
}else if(reparameterisation & !zero_order){ #reparameterisation and k3 is not zero
MyFctNL = function(parms) {
k1 = parms$k1
k2 = parms$k2
k3 = parms$k3
c0 = parms$c0
Model = c0 - c0 * (1 - ((1 - k3) * (1/(1 - k3) - dat$time *
exp(k1 - k2/dat$K + k2/Kref)))^(1/(1 - k3)))
residual = dat$y - Model
return(residual)
}
if (!is.null(parms)) { # Fit the model
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
else {
repeat {
parms = list(k1 = stats::runif(1, 0, 60), k2 = stats::runif(1,
1000, 20000), k3 = stats::runif(1, 0, 11), c0 = c0_initial)
fit = suppressWarnings(minpack.lm::nls.lm(par = parms,
fn = MyFctNL, lower = rep(0, length(parms))))
res = tryCatch({
summary(fit)
}, error = function(e) e, warning = function(w) w)
res2 = tryCatch({
stats::vcov(fit)
}, error = function(e) e)
if (any(stats::coef(fit) != parms) && !inherits(res, "error") &&
!inherits(res2, "error"))
(break)()
}
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
k3 = coef(fit)[3]
if (k3 == 0){print("k3 is fitted to be exactly 0, we strongly suggest using option zero_order = TRUE")
}else if(confint(fit,'k3')[1] < 0 && confint(fit,'k3')[2] > 0){print(paste0("The 95% Wald Confidence Interval for k3 includes 0, k3 is estimated as ",signif(k3,4),". We suggest considering option zero_order = TRUE"))}
SIG = vcov(fit)
pred_fct = function(coef.fit)
{
degrad = 1 - ((1 - coef.fit[3]) * (1/(1 - coef.fit[3]) - pred$time * exp(coef.fit[1] - coef.fit[2] / pred$K + coef.fit[2] / Kref)))^(1/(1-coef.fit[3]))
conc = coef.fit[4] - coef.fit[4]*degrad
return(conc)
}
# Multi T bootstrap
rand.coef = rmvt(draw, sigma = SIG, df = nrow(dat) - 4) + matrix(nrow = draw, ncol = 4, byrow = TRUE, coef(fit))
}else if(!reparameterisation & !zero_order){ # No re-parameterisation and k3 not zero
MyFctNL = function(parms) {
k1 = parms$k1
k2 = parms$k2
k3 = parms$k3
c0 = parms$c0
test = c0 - c0 * (1 - ((1 - k3) * (1/(1 - k3) - dat$time * exp(k1 - k2 / dat$K)))^(1/(1-k3)))
residual = dat$y - test
return(residual)
}
if (!is.null(parms)) { # Fitting the model
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
else {
repeat {
parms = list(k1 = stats::runif(1, 0, 60), k2 = stats::runif(1,
1000, 20000), k3 = stats::runif(1, 0, 11), c0 = c0_initial)
fit = suppressWarnings(minpack.lm::nls.lm(par = parms,
fn = MyFctNL, lower = rep(0, length(parms))))
res = tryCatch({
summary(fit)
}, error = function(e) e, warning = function(w) w)
res2 = tryCatch({
stats::vcov(fit)
}, error = function(e) e)
if (any(stats::coef(fit) != parms) && !inherits(res, "error") &&
!inherits(res2, "error"))
(break)()
}
fit = minpack.lm::nls.lm(par = parms, fn = MyFctNL, lower = rep(0,
length(parms)))
}
k3 = coef(fit)[3]
if (k3 == 0){print("k3 is fitted to be exactly 0, we strongly suggest using option zero_order = TRUE")
}else if(confint(fit,'k3')[1] < 0 && confint(fit,'k3')[2] > 0){print(paste0("The 95% Wald Confidence Interval for k3 includes 0, k3 is estimated as ",signif(k3,4),". We suggest considering option zero_order = TRUE"))}
SIG = vcov(fit)
pred_fct = function(coef.fit)
{
degrad = 1 - ((1 - coef.fit[3]) * (1/(1 - coef.fit[3]) - pred$time * exp(coef.fit[1] - coef.fit[2] / pred$K)))^(1/(1-coef.fit[3]))
conc = coef.fit[4] - coef.fit[4]*degrad
return(conc)
}
# Multi T bootstrap
rand.coef = rmvt(draw, sigma = SIG, df = nrow(dat) - 4) + matrix(nrow = draw, ncol = 4, byrow = TRUE, coef(fit))
}
if(zero_order){
colnames(rand.coef) <- c("k1","k2","c0")
}else{
colnames(rand.coef) <- c("k1","k2","k3","c0")
}
return(rand.coef)
}
globalVariables(c('pred'))
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