# $Id: mkinfit.R 120 2011-09-02 14:25:35Z jranke $
# Copyright (C) 2010-2012 Johannes Ranke
# Contact: jranke@uni-bremen.de
# The summary function is an adapted and extended version of summary.modFit
# from the FME package, v 1.1 by Soetart and Petzoldt, which was in turn
# inspired by summary.nls.lm
# This file is part of the R package mkin
# mkin is free software: you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software
# Foundation, either version 3 of the License, or (at your option) any later
# version.
# This program is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
# details.
# You should have received a copy of the GNU General Public License along with
# this program. If not, see <http://www.gnu.org/licenses/>
mkinfit <- function(mkinmod, observed,
parms.ini = "auto",
state.ini = c(100, rep(0, length(mkinmod$diffs) - 1)),
fixed_parms = NULL,
fixed_initials = names(mkinmod$diffs)[-1],
eigen = FALSE,
plot = FALSE, quiet = FALSE,
err = NULL, weight = "none", scaleVar = FALSE,
atol = 1e-6,
...)
{
mod_vars <- names(mkinmod$diffs)
# Subset dataframe of observed variables with mapped (modelled) variables
observed <- subset(observed, name %in% names(mkinmod$map))
# Get names of observed variables
obs_vars = unique(as.character(observed$name))
# Define initial values for parameters where not specified by the user
if (parms.ini[[1]] == "auto") parms.ini = vector()
defaultpar.names <- setdiff(mkinmod$parms, names(parms.ini))
for (parmname in defaultpar.names) {
# Default values for the FOMC model
if (parmname == "alpha") parms.ini[parmname] = 1
if (parmname == "beta") parms.ini[parmname] = 10
# Default values for log of rate constants, depending on the parameterisation
if (substr(parmname, 1, 2) == "k_") parms.ini[parmname] = -2.3
# Default values for ilr of formation fractions
if (substr(parmname, 1, 2) == "f_") parms.ini[parmname] = 0.1
}
# 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="_")
}
# Decide if the solution of the model can be based on a simple analytical
# formula, the spectral decomposition of the matrix (fundamental system)
# or a numeric ode solver from the deSolve package
if (length(mkinmod$map) == 1) {
solution = "analytical"
} else {
if (is.matrix(mkinmod$coefmat) & eigen) solution = "eigen"
else solution = "deSolve"
}
# Create a function calculating the differentials specified by the model
# if necessary
if(solution == "deSolve") {
mkindiff <- function(t, state, parms) {
transparms <- vector()
transparms <- c(transparms, exp(parms[grep("^k_", names(parms))]))
for (box in mod_vars) {
path_indices <- grep(paste("^f", box, sep = "_"), names(parms))
n_paths <- length(path_indices)
if (n_paths > 0) {
f <- invilr(parms[grep(paste("^f", box, sep="_"), names(parms))])
transparms <- c(transparms, f[1:n_paths])
}
}
otherparms <- parms[setdiff(names(parms), names(transparms))]
parms <- c(transparms, otherparms)
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$diffs[[box]])))
}
return(list(c(diffs)))
}
}
cost.old <- 1e100
calls <- 0
out_predicted <- NA
# Define the model cost function
cost <- function(P)
{
assign("calls", calls+1, inherits=TRUE)
if(length(state.ini.optim) > 0) {
odeini <- c(P[1:length(state.ini.optim)], state.ini.fixed)
names(odeini) <- c(state.ini.optim.boxnames, names(state.ini.fixed))
} else odeini <- state.ini.fixed
odeparms <- c(P[(length(state.ini.optim) + 1):length(P)], parms.fixed)
outtimes = unique(observed$time)
evalparse <- function(string)
{
eval(parse(text=string), as.list(c(odeparms, odeini)))
}
# Solve the system
if (solution == "analytical") {
parent.type = names(mkinmod$map[[1]])[1]
parent.name = names(mkinmod$diffs)[[1]]
o <- switch(parent.type,
SFO = SFO.solution(outtimes,
evalparse(parent.name),
evalparse(paste("k", parent.name, "sink", sep="_"))),
FOMC = FOMC.solution(outtimes,
evalparse(parent.name),
evalparse("alpha"), evalparse("beta")),
DFOP = DFOP.solution(outtimes,
evalparse(parent.name),
evalparse("k1"), evalparse("k2"),
evalparse("g")),
HS = HS.solution(outtimes,
evalparse(parent.name),
evalparse("k1"), evalparse("k2"),
evalparse("tb")),
SFORB = SFORB.solution(outtimes,
evalparse(parent.name),
evalparse(paste("k", parent.name, "bound", sep="_")),
evalparse(paste("k", sub("free", "bound", parent.name), "free", sep="_")),
evalparse(paste("k", parent.name, "sink", sep="_")))
)
out <- cbind(outtimes, o)
dimnames(out) <- list(outtimes, c("time", sub("_free", "", parent.name)))
}
if (solution == "eigen") {
coefmat.num <- matrix(sapply(as.vector(mkinmod$coefmat), evalparse),
nrow = length(mod_vars))
e <- eigen(coefmat.num)
c <- solve(e$vectors, odeini)
f.out <- function(t) {
e$vectors %*% diag(exp(e$values * t), nrow=length(mod_vars)) %*% c
}
o <- matrix(mapply(f.out, outtimes),
nrow = length(mod_vars), ncol = length(outtimes))
dimnames(o) <- list(mod_vars, outtimes)
out <- cbind(time = outtimes, t(o))
}
if (solution == "deSolve")
{
out <- ode(
y = odeini,
times = outtimes,
func = mkindiff,
parms = odeparms,
atol = atol
)
}
# 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) || solution == "analytical") {
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$time), length.out=100)
if (solution == "analytical") {
o_plot <- switch(parent.type,
SFO = SFO.solution(outtimes_plot,
evalparse(parent.name),
evalparse(paste("k", parent.name, "sink", sep="_"))),
FOMC = FOMC.solution(outtimes_plot,
evalparse(parent.name),
evalparse("alpha"), evalparse("beta")),
DFOP = DFOP.solution(outtimes_plot,
evalparse(parent.name),
evalparse("k1"), evalparse("k2"),
evalparse("g")),
HS = HS.solution(outtimes_plot,
evalparse(parent.name),
evalparse("k1"), evalparse("k2"),
evalparse("tb")),
SFORB = SFORB.solution(outtimes_plot,
evalparse(parent.name),
evalparse(paste("k", parent.name, "bound", sep="_")),
evalparse(paste("k", sub("free", "bound", parent.name), "free", sep="_")),
evalparse(paste("k", parent.name, "sink", sep="_")))
)
out_plot <- cbind(outtimes_plot, o_plot)
dimnames(out_plot) <- list(outtimes_plot, c("time", sub("_free", "", parent.name)))
}
if(solution == "eigen") {
o_plot <- matrix(mapply(f.out, outtimes_plot),
nrow = length(mod_vars), ncol = length(outtimes_plot))
dimnames(o_plot) <- list(mod_vars, outtimes_plot)
out_plot <- cbind(time = outtimes_plot, t(o_plot))
}
if (solution == "deSolve") {
out_plot <- ode(
y = odeini,
times = outtimes_plot,
func = mkindiff,
parms = odeparms)
}
out_transformed_plot <- data.frame(time = out_plot[,"time"])
for (var in obs_vars) {
if((length(mkinmod$map[[var]]) == 1) || solution == "analytical") {
out_transformed_plot[var] <- out_plot[, var]
} else {
out_transformed_plot[var] <- rowSums(out_plot[, mkinmod$map[[var]]])
}
}
out_transformed_plot <<- out_transformed_plot
plot(0, type="n",
xlim = range(observed$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$model, inherits=TRUE)
}
return(mC)
}
fit <- modFit(cost, c(state.ini.optim, parms.optim), ...)
# We need to return some more data for summary and plotting
fit$solution <- solution
if (solution == "eigen") {
fit$coefmat <- mkinmod$coefmat
}
if (solution == "deSolve") {
fit$mkindiff <- mkindiff
}
if (plot == TRUE) {
fit$out_transformed_plot = out_transformed_plot
}
# 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$df)
rownames(errmin) <- "All data"
for (obs_var in obs_vars)
{
errdata.var <- subset(errdata, name == obs_var)
n.k.optim <- length(grep(paste("k", obs_var, sep="_"), names(parms.optim)))
n.initials.optim <- length(grep(paste(obs_var, ".*", "_0", sep=""), names(state.ini.optim)))
n.optim <- n.k.optim + n.initials.optim
if ("alpha" %in% names(parms.optim)) n.optim <- n.optim + 1
if ("beta" %in% names(parms.optim)) n.optim <- n.optim + 1
if ("k1" %in% names(parms.optim)) n.optim <- n.optim + 1
if ("k2" %in% names(parms.optim)) n.optim <- n.optim + 1
if ("g" %in% names(parms.optim)) n.optim <- n.optim + 1
if ("tb" %in% names(parms.optim)) n.optim <- n.optim + 1
errmin.tmp <- mkinerrmin(errdata.var, n.optim)
errmin[obs_var, c("err.min", "n.optim", "df")] <- errmin.tmp
}
fit$errmin <- errmin
# Calculate dissipation times DT50 and DT90 and formation fractions
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)
fit$ff <- vector()
fit$SFORB <- vector()
for (obs_var in obs_vars) {
type = names(mkinmod$map[[obs_var]])[1]
if (type == "SFO") {
k_names = grep(paste("k", obs_var, sep="_"), names(parms.all), value=TRUE)
k_tot = sum(parms.all[k_names])
DT50 = log(2)/k_tot
DT90 = log(10)/k_tot
for (k_name in k_names)
{
fit$ff[[sub("^k_", "", k_name)]] = parms.all[[k_name]] / 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 == "DFOP") {
k1 = parms.all["k1"]
k2 = parms.all["k2"]
g = parms.all["g"]
f <- function(t, x) {
fraction <- g * exp( - k1 * t) + (1 - g) * exp( - k2 * t)
(fraction - (1 - x/100))^2
}
DTmax <- 1000
DT50.o <- optimize(f, c(0.001, DTmax), x=50)$minimum
DT50 = ifelse(DTmax - DT50.o < 0.1, NA, DT50.o)
DT90.o <- optimize(f, c(0.001, DTmax), x=90)$minimum
DT90 = ifelse(DTmax - DT90.o < 0.1, NA, DT90.o)
}
if (type == "HS") {
k1 = parms.all["k1"]
k2 = parms.all["k2"]
tb = parms.all["tb"]
DTx <- function(x) {
DTx.a <- (log(100/(100 - x)))/k1
DTx.b <- tb + (log(100/(100 - x)) - k1 * tb)/k2
if (DTx.a < tb) DTx <- DTx.a
else DTx <- DTx.b
return(DTx)
}
DT50 <- DTx(50)
DT90 <- DTx(90)
}
# Back-calculation of formation fractions in case of nonlinear parent kinetics
if (type %in% c("FOMC", "DFOP", "HS")) {
ff_names = names(mkinmod$ff)
for (ff_name in ff_names)
{
fit$ff[[paste(obs_var, ff_name, sep="_")]] =
eval(parse(text = mkinmod$ff[ff_name]), as.list(parms.all))
}
fit$ff[[paste(obs_var, "sink", sep="_")]] = 1 - sum(fit$ff)
}
if (type == "SFORB") {
# FOCUS kinetics (2006), p. 60 f
k_out_names = grep(paste("k", obs_var, "free", sep="_"), names(parms.all), value=TRUE)
k_out_names = setdiff(k_out_names, paste("k", obs_var, "free", "bound", sep="_"))
k_1output = sum(parms.all[k_out_names])
k_12 = parms.all[paste("k", obs_var, "free", "bound", sep="_")]
k_21 = parms.all[paste("k", obs_var, "bound", "free", sep="_")]
sqrt_exp = sqrt(1/4 * (k_12 + k_21 + k_1output)^2 + k_12 * k_21 - (k_12 + k_1output) * k_21)
b1 = 0.5 * (k_12 + k_21 + k_1output) + sqrt_exp
b2 = 0.5 * (k_12 + k_21 + k_1output) - sqrt_exp
SFORB_fraction = function(t) {
((k_12 + k_21 - b1)/(b2 - b1)) * exp(-b1 * t) +
((k_12 + k_21 - b2)/(b1 - b2)) * exp(-b2 * t)
}
f_50 <- function(t) (SFORB_fraction(t) - 0.5)^2
max_DT <- 1000
DT50.o <- optimize(f_50, c(0.01, max_DT))$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, max_DT))$minimum
if (abs(DT90.o - max_DT) < 0.01) DT90 = NA else DT90 = DT90.o
for (k_out_name in k_out_names)
{
fit$ff[[sub("^k_", "", k_out_name)]] = parms.all[[k_out_name]] / k_1output
}
# Return the eigenvalues for comparison with DFOP rate constants
fit$SFORB[[paste(obs_var, "b1", sep="_")]] = b1
fit$SFORB[[paste(obs_var, "b2", sep="_")]] = b2
}
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$time), ]
fit$atol <- atol
class(fit) <- c("mkinfit", "modFit")
return(fit)
}
summary.mkinfit <- function(object, data = TRUE, distimes = TRUE, ff = TRUE, ...) {
param <- object$par
if (object$logk) {
names(param) <- sub("^k_", "log k_", names(param))
}
pnames <- names(param)
p <- length(param)
covar <- try(solve(0.5*object$hessian), silent = TRUE) # unscaled covariance
if (!is.numeric(covar)) {
message <- "Cannot estimate covariance; system is singular"
warning(message)
covar <- matrix(data = NA, nrow = p, ncol = p)
} else message <- "ok"
rownames(covar) <- colnames(covar) <-pnames
rdf <- object$df.residual
resvar <- object$ssr / rdf
se <- sqrt(diag(covar) * resvar)
names(se) <- pnames
tval <- param / se
modVariance <- object$ssr / length(object$residuals)
if (!all(object$start$lower >=0)) {
message <- "Note that the one-sided t-test may not be appropriate if
parameter values below zero are possible."
warning(message)
} else message <- "ok"
param <- cbind(param, se)
dimnames(param) <- list(pnames, c("Estimate", "Std. Error"))
ans <- list(residuals = object$residuals,
residualVariance = resvar,
sigma = sqrt(resvar),
modVariance = modVariance,
df = c(p, rdf), cov.unscaled = covar,
cov.scaled = covar * resvar,
info = object$info, niter = object$iterations,
stopmess = message,
par = param)
ans$diffs <- object$diffs
if(data) ans$data <- object$data
ans$start <- object$start
if (object$logk) {
names(ans$start) <- sub("^k_", "log k_", names(ans$start))
}
ans$fixed <- object$fixed
ans$errmin <- object$errmin
if(distimes) ans$distimes <- object$distimes
if(ff) ans$ff <- object$ff
if(length(object$SFORB) != 0) ans$SFORB <- object$SFORB
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), tval = TRUE, ...) {
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$fixed)
cat("\nOptimised parameters:\n")
if (tval) printCoefmat(x$par, digits = digits, ...)
else {
printCoefmat(x$par[,c(1,2,4)], cs.in = c(1,2), tst.ind = integer(0),
P.values = TRUE, has.Pvalue = TRUE, digits = digits, ...)
}
cat("\nResidual standard error:",
format(signif(x$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$distimes, digits=digits,...)
}
printff <- !is.null(x$ff)
if(printff){
cat("\nEstimated formation fractions:\n")
print(data.frame(ff = x$ff), digits=digits,...)
}
printSFORB <- !is.null(x$SFORB)
if(printSFORB){
cat("\nEstimated Eigenvalues of SFORB model(s):\n")
print(x$SFORB, digits=digits,...)
}
printcor <- !is.null(x$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)
}
