# Copyright (C) 2010-2014 Johannes Ranke
# Portions of this code are copyright (C) 2013 Eurofins Regulatory AG
# 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/>
if(getRversion() >= '2.15.1') utils::globalVariables(c("name", "value"))
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],
solution_type = "auto",
method.ode = "lsoda",
method.modFit = "Marq",
control.modFit = list(),
transform_rates = TRUE,
transform_fractions = TRUE,
plot = FALSE, quiet = FALSE,
err = NULL, weight = "none", scaleVar = FALSE,
atol = 1e-8, rtol = 1e-10, n.outtimes = 100,
reweight.method = NULL,
reweight.tol = 1e-8, reweight.max.iter = 10,
trace_parms = FALSE,
...)
{
# Get the names of the state variables in the model
mod_vars <- names(mkinmod$diffs)
# Get the names of observed variables
obs_vars = names(mkinmod$spec)
# Subset observed data with names of observed data in the model
observed <- subset(observed, name %in% obs_vars)
# Define starting values for parameters where not specified by the user
if (parms.ini[[1]] == "auto") parms.ini = vector()
# Prevent inital parameter specifications that are not in the model
wrongpar.names <- setdiff(names(parms.ini), mkinmod$parms)
if (length(wrongpar.names) > 0) {
stop("Initial parameter(s) ", paste(wrongpar.names, collapse = ", "),
" not used in the model")
}
# Set initial parameter values, including a small increment (salt)
# to avoid linear dependencies (singular matrix) in Eigenvalue based solutions
k_salt = 0
defaultpar.names <- setdiff(mkinmod$parms, names(parms.ini))
for (parmname in defaultpar.names) {
# Default values for rate constants, depending on the parameterisation
if (substr(parmname, 1, 2) == "k_") {
parms.ini[parmname] = 0.1 + k_salt
k_salt = k_salt + 1e-4
}
# Default values for rate constants for reversible binding
if (grepl("free_bound$", parmname)) parms.ini[parmname] = 0.1
if (grepl("bound_free$", parmname)) parms.ini[parmname] = 0.02
# Default values for formation fractions
if (substr(parmname, 1, 2) == "f_") parms.ini[parmname] = 0.2
# Default values for the FOMC, DFOP and HS models
if (parmname == "alpha") parms.ini[parmname] = 1
if (parmname == "beta") parms.ini[parmname] = 10
if (parmname == "k1") parms.ini[parmname] = 0.1
if (parmname == "k2") parms.ini[parmname] = 0.01
if (parmname == "tb") parms.ini[parmname] = 5
if (parmname == "g") parms.ini[parmname] = 0.5
}
# Name the inital state variable values if they are not named yet
if(is.null(names(state.ini))) names(state.ini) <- mod_vars
# Transform initial parameter values for fitting
transparms.ini <- transform_odeparms(parms.ini, mod_vars,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
# Parameters to be optimised:
# Kinetic parameters in parms.ini whose names are not in fixed_parms
parms.fixed <- transparms.ini[fixed_parms]
parms.optim <- transparms.ini[setdiff(names(transparms.ini), fixed_parms)]
# Inital state variables in state.ini whose names are not in fixed_initials
state.ini.fixed <- state.ini[fixed_initials]
state.ini.optim <- state.ini[setdiff(names(state.ini), fixed_initials)]
# Preserve names of state variables before renaming initial state variable
# parameters
state.ini.optim.boxnames <- names(state.ini.optim)
state.ini.fixed.boxnames <- names(state.ini.fixed)
if(length(state.ini.optim) > 0) {
names(state.ini.optim) <- paste(names(state.ini.optim), "0", sep="_")
}
if(length(state.ini.fixed) > 0) {
names(state.ini.fixed) <- paste(names(state.ini.fixed), "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 (!solution_type %in% c("auto", "analytical", "eigen", "deSolve"))
stop("solution_type must be auto, analytical, eigen or de Solve")
if (solution_type == "analytical" && length(mkinmod$spec) > 1)
stop("Analytical solution not implemented for models with metabolites.")
if (solution_type == "eigen" && !is.matrix(mkinmod$coefmat))
stop("Eigenvalue based solution not possible, coefficient matrix not present.")
if (solution_type == "auto") {
if (length(mkinmod$spec) == 1) {
solution_type = "analytical"
} else {
if (is.matrix(mkinmod$coefmat)) {
solution_type = "eigen"
if (max(observed$value, na.rm = TRUE) < 0.1) {
stop("The combination of small observed values (all < 0.1) and solution_type = eigen is error-prone")
}
} else {
solution_type = "deSolve"
}
}
}
cost.old <- 1e100 # The first model cost should be smaller than this value
calls <- 0 # Counter for number of model solutions
out_predicted <- NA
# Define the model cost function
cost <- function(P)
{
assign("calls", calls+1, inherits=TRUE) # Increase the model solution counter
# Trace parameter values if requested
if(trace_parms) cat(P, "\n")
# Time points at which observed data are available
# Make sure we include time 0, so initial values for state variables are for time 0
outtimes = sort(unique(c(observed$time, seq(min(observed$time),
max(observed$time),
length.out = n.outtimes))))
if(length(state.ini.optim) > 0) {
odeini <- c(P[1:length(state.ini.optim)], state.ini.fixed)
names(odeini) <- c(state.ini.optim.boxnames, state.ini.fixed.boxnames)
} else {
odeini <- state.ini.fixed
names(odeini) <- state.ini.fixed.boxnames
}
odeparms <- c(P[(length(state.ini.optim) + 1):length(P)], parms.fixed)
parms <- backtransform_odeparms(odeparms, mod_vars,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
# Solve the system with current transformed parameter values
out <- mkinpredict(mkinmod, parms, odeini, outtimes,
solution_type = solution_type,
method.ode = method.ode,
atol = atol, rtol = rtol, ...)
assign("out_predicted", out, inherits=TRUE)
mC <- modCost(out, 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 <- mkinpredict(mkinmod, parms, odeini, outtimes_plot,
solution_type = solution_type,
method.ode = method.ode,
atol = atol, rtol = rtol, ...)
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)
lty_obs <- rep(1, length(obs_vars))
names(col_obs) <- names(pch_obs) <- names(lty_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_plot$time, out_plot[-1], col = col_obs, lty = lty_obs)
legend("topright", inset=c(0.05, 0.05), legend=obs_vars,
col=col_obs, pch=pch_obs, lty=1:length(pch_obs))
}
assign("cost.old", mC$model, inherits=TRUE)
}
return(mC)
}
lower <- rep(-Inf, length(c(state.ini.optim, parms.optim)))
upper <- rep(Inf, length(c(state.ini.optim, parms.optim)))
names(lower) <- names(upper) <- c(names(state.ini.optim), names(parms.optim))
if (!transform_rates) {
index_k <- grep("^k_", names(lower))
lower[index_k] <- 0
other_rate_parms <- intersect(c("alpha", "beta", "k1", "k2"), names(lower))
lower[other_rate_parms] <- 0
}
if (!transform_fractions) {
index_f <- grep("^f_", names(upper))
lower[index_f] <- 0
upper[index_f] <- 1
other_fraction_parms <- intersect(c("g"), names(upper))
lower[other_fraction_parms] <- 0
upper[other_fraction_parms] <- 1
}
fit <- modFit(cost, c(state.ini.optim, parms.optim),
method = method.modFit, control = control.modFit,
lower = lower, upper = upper, ...)
# Reiterate the fit until convergence of the variance components (IRLS)
# if requested by the user
weight.ini = weight
if (!is.null(err)) weight.ini = "manual"
if (!is.null(reweight.method)) {
if (reweight.method != "obs") stop("Only reweighting method 'obs' is implemented")
if(!quiet) {
cat("IRLS based on variance estimates for each observed variable\n")
}
if (!quiet) {
cat("Initial variance estimates are:\n")
print(signif(fit$var_ms_unweighted, 8))
}
reweight.diff = 1
n.iter <- 0
if (!is.null(err)) observed$err.ini <- observed[[err]]
err = "err.irls"
while (reweight.diff > reweight.tol & n.iter < reweight.max.iter) {
n.iter <- n.iter + 1
sigma.old <- sqrt(fit$var_ms_unweighted)
observed[err] <- sqrt(fit$var_ms_unweighted)[as.character(observed$name)]
fit <- modFit(cost, fit$par, method = method.modFit,
control = control.modFit, lower = lower, upper = upper, ...)
reweight.diff = sum((sqrt(fit$var_ms_unweighted) - sigma.old)^2)
if (!quiet) {
cat("Iteration", n.iter, "yields variance estimates:\n")
print(signif(fit$var_ms_unweighted, 8))
cat("Sum of squared differences to last variance estimates:",
signif(reweight.diff, 2), "\n")
}
}
}
# We need to return some more data for summary and plotting
fit$solution_type <- solution_type
fit$transform_rates <- transform_rates
fit$transform_fractions <- transform_fractions
# We also need the model for summary and plotting
fit$mkinmod <- mkinmod
# We need data and predictions for summary and plotting
fit$observed <- observed
fit$obs_vars <- obs_vars
fit$predicted <- mkin_wide_to_long(out_predicted, time = "time")
# Collect initial parameter values in two dataframes
fit$start <- data.frame(value = c(state.ini.optim,
backtransform_odeparms(parms.optim, mod_vars,
transform_rates = transform_rates,
transform_fractions = transform_fractions)))
fit$start$type = c(rep("state", length(state.ini.optim)),
rep("deparm", length(parms.optim)))
fit$start$transformed = c(state.ini.optim, parms.optim)
fit$start$lower_bound = lower
fit$start$upper_bound = upper
fit$fixed <- data.frame(value = c(state.ini.fixed,
backtransform_odeparms(parms.fixed, mod_vars,
transform_rates = transform_rates,
transform_fractions = transform_fractions)))
fit$fixed$type = c(rep("state", length(state.ini.fixed)),
rep("deparm", length(parms.fixed)))
bparms.optim = backtransform_odeparms(fit$par, mod_vars,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
bparms.fixed = backtransform_odeparms(c(state.ini.fixed, parms.fixed),
mod_vars,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
bparms.all = c(bparms.optim, bparms.fixed)
# Collect observed, predicted, residuals and weighting
data <- merge(fit$observed, fit$predicted, by = c("time", "name"))
data$name <- ordered(data$name, levels = obs_vars)
data <- data[order(data$name, data$time), ]
fit$data <- data.frame(time = data$time,
variable = data$name,
observed = data$value.x,
predicted = data$value.y)
fit$data$residual <- fit$data$observed - fit$data$predicted
if (!is.null(data$err.ini)) fit$data$err.ini <- data$err.ini
if (!is.null(err)) fit$data[[err]] <- data[[err]]
fit$atol <- atol
fit$rtol <- rtol
fit$weight.ini <- weight.ini
fit$reweight.method <- reweight.method
fit$reweight.tol <- reweight.tol
fit$reweight.max.iter <- reweight.max.iter
# Return all backtransformed parameters for summary
fit$bparms.optim <- bparms.optim
fit$bparms.fixed <- bparms.fixed
fit$bparms.ode <- bparms.all[mkinmod$parms] # Return ode parameters for further fitting
fit$date <- date()
class(fit) <- c("mkinfit", "modFit")
return(fit)
}
summary.mkinfit <- function(object, data = TRUE, distimes = TRUE, alpha = 0.05, ...) {
param <- object$par
pnames <- names(param)
p <- length(param)
mod_vars <- names(object$mkinmod$diffs)
covar <- try(solve(0.5*object$hessian), silent = TRUE) # unscaled covariance
rdf <- object$df.residual
resvar <- object$ssr / rdf
if (!is.numeric(covar)) {
covar <- NULL
se <- lci <- uci <- tval <- pval1 <- pval2 <- rep(NA, p)
} else {
rownames(covar) <- colnames(covar) <- pnames
se <- sqrt(diag(covar) * resvar)
lci <- param + qt(alpha/2, rdf) * se
uci <- param + qt(1-alpha/2, rdf) * se
tval <- param/se
pval1 <- 2 * pt(abs(tval), rdf, lower.tail = FALSE)
pval2 <- pt(abs(tval), rdf, lower.tail = FALSE)
}
names(se) <- pnames
modVariance <- object$ssr / length(object$residuals)
param <- cbind(param, se, lci, uci, tval, pval1, pval2)
dimnames(param) <- list(pnames, c("Estimate", "Std. Error", "Lower", "Upper",
"t value", "Pr(>|t|)", "Pr(>t)"))
blci <- buci <- numeric()
# Transform boundaries of CI for one parameter at a time,
# with the exception of sets of formation fractions (single fractions are OK).
f_names_skip <- character(0)
for (box in mod_vars) { # Figure out sets of fractions to skip
f_names <- grep(paste("^f", box, sep = "_"), pnames, value = TRUE)
n_paths <- length(f_names)
if (n_paths > 1) f_names_skip <- c(f_names_skip, f_names)
}
for (pname in pnames) {
par.lower <- par.upper <- object$par
par.lower[pname] <- param[pname, "Lower"]
par.upper[pname] <- param[pname, "Upper"]
if (!pname %in% f_names_skip) {
blci[pname] <- backtransform_odeparms(par.lower, mod_vars,
object$transform_rates, object$transform_fractions)[pname]
buci[pname] <- backtransform_odeparms(par.upper, mod_vars,
object$transform_rates, object$transform_fractions)[pname]
} else {
blci[pname] <- buci[pname] <- NA
}
}
bparam <- cbind(object$bparms.optim, blci, buci)
dimnames(bparam) <- list(pnames, c("Estimate", "Lower", "Upper"))
ans <- list(
version = as.character(packageVersion("mkin")),
Rversion = paste(R.version$major, R.version$minor, sep="."),
date.fit = object$date,
date.summary = date(),
solution_type = object$solution_type,
use_of_ff = object$mkinmod$use_of_ff,
weight.ini = object$weight.ini,
reweight.method = object$reweight.method,
residuals = object$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,
bpar = bparam)
ans$diffs <- object$mkinmod$diffs
if(data) ans$data <- object$data
ans$start <- object$start
ans$fixed <- object$fixed
ans$errmin <- mkinerrmin(object, alpha = 0.05)
ans$bparms.ode <- object$bparms.ode
ep <- endpoints(object)
if (length(ep$ff) != 0)
ans$ff <- ep$ff
if(distimes) ans$distimes <- ep$distimes
if(length(ep$SFORB) != 0) ans$SFORB <- ep$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), ...) {
cat("mkin version: ", x$version, "\n")
cat("R version: ", x$Rversion, "\n")
cat("Date of fit: ", x$date.fit, "\n")
cat("Date of summary:", x$date.summary, "\n")
cat("\nEquations:\n")
print(noquote(as.character(x[["diffs"]])))
df <- x$df
rdf <- df[2]
cat("\nMethod used for solution of differential equation system:\n")
cat(x$solution_type, "\n")
cat("\nWeighting:", x$weight.ini)
if(!is.null(x$reweight.method)) cat(" then iterative reweighting method",
x$reweight.method)
cat("\n")
cat("\nStarting values for optimised parameters:\n")
print(x$start)
cat("\nFixed parameter values:\n")
if(length(x$fixed$value) == 0) cat("None\n")
else print(x$fixed)
cat("\nOptimised, transformed parameters:\n")
print(signif(x$par, digits = digits))
cat("\nParameter correlation:\n")
if (!is.null(x$cov.unscaled)){
Corr <- cov2cor(x$cov.unscaled)
rownames(Corr) <- colnames(Corr) <- rownames(x$par)
print(Corr, digits = digits, ...)
} else {
cat("Could not estimate covariance matrix; singular system:\n")
}
cat("\nResidual standard error:",
format(signif(x$sigma, digits)), "on", rdf, "degrees of freedom\n")
cat("\nBacktransformed parameters:\n")
print(signif(x$bpar, digits = digits))
cat("\nChi2 error levels in percent:\n")
x$errmin$err.min <- 100 * x$errmin$err.min
print(x$errmin, digits=digits,...)
printSFORB <- !is.null(x$SFORB)
if(printSFORB){
cat("\nEstimated Eigenvalues of SFORB model(s):\n")
print(x$SFORB, digits=digits,...)
}
printff <- !is.null(x$ff)
if(printff & x$use_of_ff == "min"){
cat("\nEstimated formation fractions:\n")
print(data.frame(ff = x$ff), digits=digits,...)
}
printdistimes <- !is.null(x$distimes)
if(printdistimes){
cat("\nEstimated disappearance times:\n")
print(x$distimes, digits=digits,...)
}
printdata <- !is.null(x$data)
if (printdata){
cat("\nData:\n")
print(format(x$data, digits = digits, ...), row.names = FALSE)
}
invisible(x)
}
# vim: set ts=2 sw=2 expandtab:
