mkinfit <- function(mkinmod, observed,
parms.ini = rep(0.1, length(mkinmod$parms)),
state.ini = c(100, rep(0, length(mkinmod$diffs) - 1)),
lower = 0, upper = Inf,
fixed_parms = NULL,
fixed_initials = names(mkinmod$diffs)[-1],
plot = FALSE, quiet = FALSE,
err = NULL, weight = "none", scaleVar = FALSE,
...)
{
mod_vars <- names(mkinmod$diffs)
# Subset dataframe with mapped (modelled) variables
observed <- subset(observed, name %in% names(mkinmod$map))
# Get names of observed variables
obs_vars = unique(as.character(observed$name))
# Name the parameters if they are not named yet
if(is.null(names(parms.ini))) names(parms.ini) <- mkinmod$parms
# Create a function calculating the differentials specified by the model
mkindiff <- function(t, state, parms) {
time <- t
diffs <- vector()
for (box in mod_vars)
{
diffname <- paste("d", box, sep="_")
diffs[diffname] <- with(as.list(c(time,state, parms)),
eval(parse(text=mkinmod$diffs[[box]])))
}
return(list(c(diffs)))
}
# Name the inital parameter values if they are not named yet
if(is.null(names(state.ini))) names(state.ini) <- mod_vars
# Parameters to be optimised
parms.fixed <- parms.ini[fixed_parms]
optim_parms <- setdiff(names(parms.ini), fixed_parms)
parms.optim <- parms.ini[optim_parms]
state.ini.fixed <- state.ini[fixed_initials]
optim_initials <- setdiff(names(state.ini), fixed_initials)
state.ini.optim <- state.ini[optim_initials]
state.ini.optim.boxnames <- names(state.ini.optim)
if(length(state.ini.optim) > 0) {
names(state.ini.optim) <- paste(names(state.ini.optim), "0", sep="_")
}
cost.old <- 1e100
calls <- 0
out_predicted <- NA
# Define the model cost function
cost <- function(P)
{
assign("calls", calls+1, inherits=TRUE)
if(length(state.ini.optim) > 0) {
odeini <- c(P[1:length(state.ini.optim)], state.ini.fixed)
names(odeini) <- c(state.ini.optim.boxnames, names(state.ini.fixed))
} else odeini <- state.ini.fixed
odeparms <- c(P[(length(state.ini.optim) + 1):length(P)], parms.fixed)
outtimes = unique(observed$time)
# Solve the ode
out <- ode(
y = odeini,
times = outtimes,
func = mkindiff,
parms = odeparms)
# Output transformation for models with unobserved compartments like SFORB
out_transformed <- data.frame(time = out[,"time"])
for (var in names(mkinmod$map)) {
if(length(mkinmod$map[[var]]) == 1) {
out_transformed[var] <- out[, var]
} else {
out_transformed[var] <- rowSums(out[, mkinmod$map[[var]]])
}
}
assign("out_predicted", out_transformed, inherits=TRUE)
mC <- modCost(out_transformed, observed, y = "value",
err = err, weight = weight, scaleVar = scaleVar)
# Report and/or plot if the model is improved
if (mC$model < cost.old) {
if(!quiet) cat("Model cost at call ", calls, ": ", mC$model, "\n")
# Plot the data and current model output if requested
if(plot) {
outtimes_plot = seq(min(observed$time), max(observed$time), length.out=100)
out_plot <- ode(
y = odeini,
times = outtimes_plot,
func = mkindiff,
parms = odeparms)
out_transformed_plot <- data.frame(time = out_plot[,"time"])
for (var in names(mkinmod$map)) {
if(length(mkinmod$map[[var]]) == 1) {
out_transformed_plot[var] <- out_plot[, var]
} else {
out_transformed_plot[var] <- rowSums(out_plot[, mkinmod$map[[var]]])
}
}
plot(0, type="n",
xlim = range(observed$time), ylim = range(observed$value, na.rm=TRUE),
xlab = "Time", ylab = "Observed")
col_obs <- pch_obs <- 1:length(obs_vars)
names(col_obs) <- names(pch_obs) <- obs_vars
for (obs_var in obs_vars) {
points(subset(observed, name == obs_var, c(time, value)),
pch = pch_obs[obs_var], col = col_obs[obs_var])
}
matlines(out_transformed_plot$time, out_transformed_plot[-1])
legend("topright", inset=c(0.05, 0.05), legend=obs_vars,
col=col_obs, pch=pch_obs, lty=1:length(pch_obs))
}
assign("cost.old", mC$model, inherits=TRUE)
}
return(mC)
}
fit <- modFit(cost, c(state.ini.optim, parms.optim), lower = lower, upper = upper, ...)
# We need the function for plotting
fit$mkindiff <- mkindiff
# We also need various other information for summary and plotting
fit$map <- mkinmod$map
fit$diffs <- mkinmod$diffs
fit$observed <- mkin_long_to_wide(observed)
predicted_long <- mkin_wide_to_long(out_predicted, time = "time")
fit$predicted <- out_predicted
# Collect initial parameter values in two dataframes
fit$start <- data.frame(initial = c(state.ini.optim, parms.optim))
fit$start$type = c(rep("state", length(state.ini.optim)), rep("deparm", length(parms.optim)))
fit$start$lower <- lower
fit$start$upper <- upper
fit$fixed <- data.frame(
value = c(state.ini.fixed, parms.fixed))
fit$fixed$type = c(rep("state", length(state.ini.fixed)), rep("deparm", length(parms.fixed)))
# Calculate chi2 error levels according to FOCUS (2006)
means <- aggregate(value ~ time + name, data = observed, mean, na.rm=TRUE)
errdata <- merge(means, predicted_long, by = c("time", "name"), suffixes = c("_mean", "_pred"))
errdata <- errdata[order(errdata$time, errdata$name), ]
errmin.overall <- mkinerrmin(errdata, length(parms.optim) + length(state.ini.optim))
errmin <- data.frame(err.min = errmin.overall$err.min,
n.optim = errmin.overall$n.optim, df = errmin.overall$df)
rownames(errmin) <- "All data"
for (obs_var in obs_vars)
{
errdata.var <- subset(errdata, name == obs_var)
n.k.optim <- length(grep(paste("k", obs_var, sep="_"), names(parms.optim)))
n.initials.optim <- length(grep(paste(obs_var, ".*", "_0", sep=""), names(state.ini.optim)))
n.optim <- n.k.optim + n.initials.optim
if ("alpha" %in% names(parms.optim)) n.optim <- n.optim + 1
if ("beta" %in% names(parms.optim)) n.optim <- n.optim + 1
errmin.tmp <- mkinerrmin(errdata.var, n.optim)
errmin[obs_var, c("err.min", "n.optim", "df")] <- errmin.tmp
}
fit$errmin <- errmin
# Calculate dissipation times DT50 and DT90
parms.all = c(fit$par, parms.fixed)
fit$distimes <- data.frame(DT50 = rep(NA, length(obs_vars)), DT90 = rep(NA, length(obs_vars)),
row.names = obs_vars)
for (obs_var in obs_vars) {
type = names(mkinmod$map[[obs_var]])[1]
if (type == "SFO") {
k_names = grep(paste("k", obs_var, sep="_"), names(parms.all), value=TRUE)
k_tot = sum(parms.all[k_names])
DT50 = log(2)/k_tot
DT90 = log(10)/k_tot
}
if (type == "FOMC") {
alpha = parms.all["alpha"]
beta = parms.all["beta"]
DT50 = beta * (2^(1/alpha) - 1)
DT90 = beta * (10^(1/alpha) - 1)
}
if (type == "SFORB") {
# FOCUS kinetics (2006), p. 60 f
k_out_names = grep(paste("k", obs_var, "free", sep="_"), names(parms.all), value=TRUE)
k_out_names = setdiff(k_out_names, paste("k", obs_var, "free", "bound", sep="_"))
k_1output = sum(parms.all[k_out_names])
k_12 = parms.all[paste("k", obs_var, "free", "bound", sep="_")]
k_21 = parms.all[paste("k", obs_var, "bound", "free", sep="_")]
sqrt_exp = sqrt(1/4 * (k_12 + k_21 + k_1output)^2 + k_12 * k_21 - (k_12 + k_1output) * k_21)
b1 = 0.5 * (k_12 + k_21 + k_1output) + sqrt_exp
b2 = 0.5 * (k_12 + k_21 + k_1output) - sqrt_exp
SFORB_fraction = function(t) {
((k_12 + k_21 - b1)/(b2 - b1)) * exp(-b1 * t) +
((k_12 + k_21 - b2)/(b1 - b2)) * exp(-b2 * t)
}
f_50 <- function(t) (SFORB_fraction(t) - 0.5)^2
max_DT <- 1000
DT50.o <- optimize(f_50, c(0.01, max_DT))$minimum
if (abs(DT50.o - max_DT) < 0.01) DT50 = NA else DT50 = DT50.o
f_90 <- function(t) (SFORB_fraction(t) - 0.1)^2
DT90.o <- optimize(f_90, c(0.01, 1000))$minimum
if (abs(DT90.o - max_DT) < 0.01) DT90 = NA else DT90 = DT90.o
}
fit$distimes[obs_var, ] = c(DT50, DT90)
}
# Collect observed, predicted and residuals
data <- merge(observed, predicted_long, by = c("time", "name"))
names(data) <- c("time", "variable", "observed", "predicted")
data$residual <- data$observed - data$predicted
data$variable <- ordered(data$variable, levels = obs_vars)
fit$data <- data[order(data$variable, data$time), ]
class(fit) <- c("mkinfit", "modFit")
return(fit)
}
summary.mkinfit <- function(object, data = TRUE, distimes = TRUE, cov = FALSE,...) {
ans <- FME:::summary.modFit(object, cov = cov)
ans$diffs <- object$diffs
if(data) ans$data <- object$data
ans$start <- object$start
ans$fixed <- object$fixed
ans$errmin <- object$errmin
if(distimes) ans$distimes <- object$distimes
class(ans) <- c("summary.mkinfit", "summary.modFit")
return(ans)
}
# Expanded from print.summary.modFit
print.summary.mkinfit <- function(x, digits = max(3, getOption("digits") - 3), ...) {
cat("\nEquations:\n")
print(noquote(as.character(x[["diffs"]])))
df <- x$df
rdf <- df[2]
cat("\nStarting values for optimised parameters:\n")
print(x$start)
cat("\nFixed parameter values:\n")
if(length(x$fixed$value) == 0) cat("None\n")
else print(x$fixed)
cat("\nOptimised parameters:\n")
printCoefmat(x$par, digits = digits, ...)
cat("\nResidual standard error:",
format(signif(x$sigma, digits)), "on", rdf, "degrees of freedom\n")
cat("\nChi2 error levels in percent:\n")
x$errmin$err.min <- 100 * x$errmin$err.min
print(x$errmin, digits=digits,...)
printdistimes <- !is.null(x$distimes)
if(printdistimes){
cat("\nEstimated disappearance times\n")
print(x$distimes, digits=digits,...)
}
printcor <- !is.null(x$cov.unscaled)
if (printcor){
Corr <- cov2cor(x$cov.unscaled)
rownames(Corr) <- colnames(Corr) <- rownames(x$par)
cat("\nParameter correlation:\n")
print(Corr, digits = digits, ...)
}
printdata <- !is.null(x$data)
if (printdata){
cat("\nData:\n")
print(format(x$data, digits = digits, scientific = FALSE,...), row.names = FALSE)
}
invisible(x)
}
