# Copyright (C) 2010-2019 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", "time", "value"))
mkinfit <- function(mkinmod, observed,
parms.ini = "auto",
state.ini = "auto",
fixed_parms = NULL,
fixed_initials = names(mkinmod$diffs)[-1],
from_max_mean = FALSE,
solution_type = c("auto", "analytical", "eigen", "deSolve"),
method.ode = "lsoda",
use_compiled = "auto",
control = list(eval.max = 300, iter.max = 200),
transform_rates = TRUE,
transform_fractions = TRUE,
plot = FALSE, quiet = FALSE,
atol = 1e-8, rtol = 1e-10, n.outtimes = 100,
error_model = c("const", "obs", "tc", "obs_tc"),
trace_parms = FALSE,
...)
{
# Check mkinmod and generate a model for the variable whith the highest value
# if a suitable string is given
parent_models_available = c("SFO", "FOMC", "DFOP", "HS", "SFORB", "IORE", "logistic")
if (class(mkinmod) != "mkinmod") {
presumed_parent_name = observed[which.max(observed$value), "name"]
if (mkinmod[[1]] %in% parent_models_available) {
speclist <- list(list(type = mkinmod, sink = TRUE))
names(speclist) <- presumed_parent_name
mkinmod <- mkinmod(speclist = speclist)
} else {
stop("Argument mkinmod must be of class mkinmod or a string containing one of\n ",
paste(parent_models_available, collapse = ", "))
}
}
# 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 and remove NA values
observed <- subset(observed, name %in% obs_vars)
observed <- subset(observed, !is.na(value))
# Also remove zero values to avoid instabilities (e.g. of the 'tc' error model)
if (any(observed$value == 0)) {
warning("Observations with value of zero were removed from the data")
observed <- subset(observed, value != 0)
}
# Obtain data for decline from maximum mean value if requested
if (from_max_mean) {
# This is only used for simple decline models
if (length(obs_vars) > 1)
stop("Decline from maximum is only implemented for models with a single observed variable")
means <- aggregate(value ~ time, data = observed, mean, na.rm=TRUE)
t_of_max <- means[which.max(means$value), "time"]
observed <- subset(observed, time >= t_of_max)
observed$time <- observed$time - t_of_max
}
# Number observations used for fitting
n_observed <- nrow(observed)
# Define starting values for parameters where not specified by the user
if (parms.ini[[1]] == "auto") parms.ini = vector()
# Warn for inital parameter specifications that are not in the model
wrongpar.names <- setdiff(names(parms.ini), mkinmod$parms)
if (length(wrongpar.names) > 0) {
warning("Initial parameter(s) ", paste(wrongpar.names, collapse = ", "),
" not used in the model")
}
# Warn that the sum of formation fractions may exceed one if they are not
# fitted in the transformed way
if (mkinmod$use_of_ff == "max" & transform_fractions == FALSE) {
warning("The sum of formation fractions may exceed one if you do not use ",
"transform_fractions = TRUE." )
for (box in mod_vars) {
# Stop if formation fractions are not transformed and we have no sink
if (mkinmod$spec[[box]]$sink == FALSE) {
stop("If formation fractions are not transformed during the fitting, ",
"it is not supported to turn off pathways to sink.\n ",
"Consider turning on the transformation of formation fractions or ",
"setting up a model with use_of_ff = 'min'.\n")
}
}
}
# Do not allow fixing formation fractions if we are using the ilr transformation,
# this is not supported
if (transform_fractions == TRUE && length(fixed_parms) > 0) {
if (any(grepl("^f_", fixed_parms))) {
stop("Fixing formation fractions is not supported when using the ilr ",
"transformation.")
}
}
# 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$parms, names(parms.ini))
for (parmname in defaultpar.names) {
# Default values for rate constants, depending on the parameterisation
if (grepl("^k", parmname)) {
parms.ini[parmname] = 0.1 + k_salt
k_salt = k_salt + 1e-4
}
# Default values for rate constants for reversible binding
if (grepl("free_bound$", parmname)) parms.ini[parmname] = 0.1
if (grepl("bound_free$", parmname)) parms.ini[parmname] = 0.02
# Default values for IORE exponents
if (grepl("^N", parmname)) parms.ini[parmname] = 1.1
# Default values for the FOMC, DFOP and HS models
if (parmname == "alpha") parms.ini[parmname] = 1
if (parmname == "beta") parms.ini[parmname] = 10
if (parmname == "k1") parms.ini[parmname] = 0.1
if (parmname == "k2") parms.ini[parmname] = 0.01
if (parmname == "tb") parms.ini[parmname] = 5
if (parmname == "g") parms.ini[parmname] = 0.5
if (parmname == "kmax") parms.ini[parmname] = 0.1
if (parmname == "k0") parms.ini[parmname] = 0.0001
if (parmname == "r") parms.ini[parmname] = 0.2
}
# Default values for formation fractions in case they are present
for (box in mod_vars) {
f_names <- mkinmod$parms[grep(paste0("^f_", box), mkinmod$parms)]
if (length(f_names) > 0) {
# We need to differentiate between default and specified fractions
# and set the unspecified to 1 - sum(specified)/n_unspecified
f_default_names <- intersect(f_names, defaultpar.names)
f_specified_names <- setdiff(f_names, defaultpar.names)
sum_f_specified = sum(parms.ini[f_specified_names])
if (sum_f_specified > 1) {
stop("Starting values for the formation fractions originating from ",
box, " sum up to more than 1.")
}
if (mkinmod$spec[[box]]$sink) n_unspecified = length(f_default_names) + 1
else {
n_unspecified = length(f_default_names)
}
parms.ini[f_default_names] <- (1 - sum_f_specified) / n_unspecified
}
}
# Set default for state.ini if appropriate
parent_name = names(mkinmod$spec)[[1]]
if (state.ini[1] == "auto") {
parent_time_0 = subset(observed, time == 0 & name == parent_name)$value
parent_time_0_mean = mean(parent_time_0, na.rm = TRUE)
if (is.na(parent_time_0_mean)) {
state.ini = c(100, rep(0, length(mkinmod$diffs) - 1))
} else {
state.ini = c(parent_time_0_mean, rep(0, length(mkinmod$diffs) - 1))
}
}
# Name the inital state variable values if they are not named yet
if(is.null(names(state.ini))) names(state.ini) <- mod_vars
# Transform initial parameter values for fitting
transparms.ini <- transform_odeparms(parms.ini, mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
# Parameters to be optimised:
# Kinetic parameters in parms.ini whose names are not in fixed_parms
parms.fixed <- parms.ini[fixed_parms]
parms.optim <- parms.ini[setdiff(names(parms.ini), fixed_parms)]
transparms.fixed <- transform_odeparms(parms.fixed, mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
transparms.optim <- transform_odeparms(parms.optim, mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
# Inital state variables in state.ini whose names are not in fixed_initials
state.ini.fixed <- state.ini[fixed_initials]
state.ini.optim <- state.ini[setdiff(names(state.ini), fixed_initials)]
# Preserve names of state variables before renaming initial state variable
# parameters
state.ini.optim.boxnames <- names(state.ini.optim)
state.ini.fixed.boxnames <- names(state.ini.fixed)
if(length(state.ini.optim) > 0) {
names(state.ini.optim) <- paste(names(state.ini.optim), "0", sep="_")
}
if(length(state.ini.fixed) > 0) {
names(state.ini.fixed) <- paste(names(state.ini.fixed), "0", sep="_")
}
# Decide if the solution of the model can be based on a simple analytical
# formula, the spectral decomposition of the matrix (fundamental system)
# or a numeric ode solver from the deSolve package
# Prefer deSolve over eigen if a compiled model is present and use_compiled
# is not set to FALSE
solution_type = match.arg(solution_type)
if (solution_type == "analytical" && length(mkinmod$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.null(mkinmod$cf) & use_compiled[1] != FALSE) {
solution_type = "deSolve"
} else {
if (is.matrix(mkinmod$coefmat)) {
solution_type = "eigen"
if (max(observed$value, na.rm = TRUE) < 0.1) {
stop("The combination of small observed values (all < 0.1) and solution_type = eigen is error-prone")
}
} else {
solution_type = "deSolve"
}
}
}
}
# Get the error model and specify starting values as well as fixed components
err_mod <- match.arg(error_model)
if (err_mod == "const") {
errparms = c(sigma = 1)
}
if (err_mod == "obs") {
errparms <- rep(1, length(obs_vars))
names(errparms) = paste0("sigma_", obs_vars)
}
if (err_mod == "tc") {
errparms <- c(sigma_low = 0.5, rsd_high = 0.07)
}
if (err_mod == "obs_tc") {
errparms <- rep(1, length(obs_vars))
names(errparms) = paste0("sigma_", obs_vars)
errparms <- c(errparms, a = 0.1)
}
# Define outtimes for model solution.
# Include time points at which observed data are available
outtimes = sort(unique(c(observed$time, seq(min(observed$time),
max(observed$time),
length.out = n.outtimes))))
# Define log-likelihood function for optimisation, including (back)transformations
nlogLik <- function(P, trans = TRUE)
{
assign("calls", calls+1, inherits=TRUE) # Increase the model solution counter
# Trace parameter values if requested
if(trace_parms) cat(P, "\n")
# Initial states for t0
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.optim <- P[(length(state.ini.optim) + 1):(length(P) - length(errparms))]
if (trans == TRUE) {
odeparms <- c(odeparms.optim, transparms.fixed)
parms <- backtransform_odeparms(odeparms, mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
} else {
parms <- c(odeparms.optim, parms.fixed)
}
# Solve the system with current parameter values
out <- mkinpredict(mkinmod, parms,
odeini, outtimes,
solution_type = solution_type,
use_compiled = use_compiled,
method.ode = method.ode,
atol = atol, rtol = rtol, ...)
out_long <- mkin_wide_to_long(out, time = "time")
assign("out_predicted", out_long, inherits=TRUE)
if (err_mod == "const") {
observed$std <- P["sigma"]
}
if (err_mod == "obs") {
std_names <- paste0("sigma_", observed$name)
observed$std <- P[std_names]
}
if (err_mod == "tc") {
tmp <- merge(observed, out_long, by = c("time", "name"))
tmp$name <- ordered(tmp$name, levels = obs_vars)
tmp <- tmp[order(tmp$name, tmp$time), ]
observed$std <- sqrt(P["sigma_low"]^2 + tmp$value.y^2 * P["rsd_high"]^2)
}
if (err_mod == "obs_tc") {
tmp <- merge(observed, out_long, by = c("time", "name"))
tmp$name <- ordered(tmp$name, levels = obs_vars)
tmp <- tmp[order(tmp$name, tmp$time), ]
std_names <- paste0("sigma_", observed$name)
observed$std <- sqrt(P[std_names] * (1 + P["a"] * tmp$value.y^2))
}
data_log_lik <- merge(observed[c("name", "time", "value", "std")], out_long,
by = c("name", "time"))
nlogLik <- - with(data_log_lik,
sum(dnorm(x = value.x, mean = value.y, sd = std, log = TRUE)))
if (nlogLik < nlogLik.current) {
assign("nlogLik.current", nlogLik, inherits = TRUE)
if (!quiet) cat("Negative log-likelihood at call ", calls, ": ", nlogLik.current, "\n", sep = "")
}
return(nlogLik)
}
n_optim <- length(c(state.ini.optim, transparms.optim, errparms))
names_optim <- c(names(state.ini.optim),
names(transparms.optim),
names(errparms))
# Define lower and upper bounds other than -Inf and Inf for parameters
# for which no internal transformation is requested in the call to mkinfit
# and for error model parameters
lower <- rep(-Inf, n_optim)
upper <- rep(Inf, n_optim)
names(lower) <- names(upper) <- names_optim
# IORE exponentes are not transformed, but need a lower bound of zero
index_N <- grep("^N", names(lower))
lower[index_N] <- 0
if (!transform_rates) {
index_k <- grep("^k_", names(lower))
lower[index_k] <- 0
index_k__iore <- grep("^k__iore_", names(lower))
lower[index_k__iore] <- 0
other_rate_parms <- intersect(c("alpha", "beta", "k1", "k2", "tb", "r"), 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
}
if (err_mod == "const") {
lower["sigma"] <- 0
}
if (err_mod == "obs") {
index_sigma <- grep("^sigma_", names(lower))
lower[index_sigma] <- 0
}
if (err_mod == "tc") {
lower["sigma_low"] <- 0
lower["rsd_high"] <- 0
}
if (err_mod == "obs_tc") {
index_sigma <- grep("^sigma_", names(lower))
lower[index_sigma] <- 0
lower["a"] <- 0
}
# Counter for likelihood evaluations
calls = 0
nlogLik.current <- Inf
# Show parameter names if tracing is requested
if(trace_parms) cat(names_optim, "\n")
# Do the fit and take the time
fit_time <- system.time({
fit <- nlminb(c(state.ini.optim, transparms.optim, errparms),
nlogLik, control = control,
lower = lower, upper = upper, ...)})
if (fit$convergence != 0) {
fit$warning = paste0("Optimisation did not converge:\n", fit$message)
warning(fit$warning)
} else {
if(!quiet) cat("Optimisation successfully terminated.\n")
}
fit$logLik <- - nlogLik.current
# We need to return some more data for summary and plotting
fit$solution_type <- solution_type
fit$transform_rates <- transform_rates
fit$transform_fractions <- transform_fractions
fit$control <- control
fit$calls <- calls
fit$time <- fit_time
# We also need the model for summary and plotting
fit$mkinmod <- mkinmod
# We need data and predictions for summary and plotting
fit$observed <- observed
fit$obs_vars <- obs_vars
fit$predicted <- out_predicted
# Backtransform parameters
bparms.optim = backtransform_odeparms(fit$par, fit$mkinmod,
transform_rates = transform_rates,
transform_fractions = transform_fractions)
bparms.fixed = c(state.ini.fixed, parms.fixed)
bparms.all = c(bparms.optim, parms.fixed)
# Attach the negative log-likelihood function for post-hoc parameter uncertainty analysis
fit$nlogLik <- nlogLik
fit$hessian <- hessian(nlogLik, fit$par)
fit$hessian_notrans <- hessian(nlogLik, c(bparms.optim, fit$par[names(errparms)]), trans = FALSE)
# Collect initial parameter values in three dataframes
fit$start <- data.frame(value = c(state.ini.optim,
parms.optim, errparms))
fit$start$type = c(rep("state", length(state.ini.optim)),
rep("deparm", length(parms.optim)),
rep("error", length(errparms)))
fit$start_transformed = data.frame(
value = c(state.ini.optim, transparms.optim, errparms),
lower = lower,
upper = upper)
fit$fixed <- data.frame(value = c(state.ini.fixed, parms.fixed))
fit$fixed$type = c(rep("state", length(state.ini.fixed)),
rep("deparm", length(parms.fixed)))
# Collect observed, predicted, residuals and weighting
data <- merge(fit$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
fit$atol <- atol
fit$rtol <- rtol
fit$err_mod <- err_mod
# Return different sets of backtransformed parameters for summary and plotting
fit$bparms.optim <- bparms.optim
fit$bparms.fixed <- bparms.fixed
# Return ode and state parameters for further fitting
fit$bparms.ode <- bparms.all[mkinmod$parms]
fit$bparms.state <- c(bparms.all[setdiff(names(bparms.all), names(fit$bparms.ode))],
state.ini.fixed)
names(fit$bparms.state) <- gsub("_0$", "", names(fit$bparms.state))
fit$errparms.optim <- fit$par[names(errparms)]
fit$df.residual <- n_observed - n_optim
fit$date <- date()
fit$version <- as.character(utils::packageVersion("mkin"))
fit$Rversion <- paste(R.version$major, R.version$minor, sep=".")
class(fit) <- c("mkinfit", "modFit")
return(fit)
}
summary.mkinfit <- function(object, data = TRUE, distimes = TRUE, alpha = 0.05, ...) {
param <- object$par
pnames <- names(param)
bpnames <- names(object$bparms.optim)
epnames <- names(object$errparms.optim)
p <- length(param)
mod_vars <- names(object$mkinmod$diffs)
covar <- try(solve(object$hessian), silent = TRUE)
covar_notrans <- try(solve(object$hessian_notrans), silent = TRUE)
rdf <- object$df.residual
if (!is.numeric(covar) | is.na(covar[1])) {
covar <- NULL
se <- lci <- uci <- rep(NA, p)
} else {
rownames(covar) <- colnames(covar) <- pnames
se <- sqrt(diag(covar))
lci <- param + qt(alpha/2, rdf) * se
uci <- param + qt(1-alpha/2, rdf) * se
}
beparms.optim <- c(object$bparms.optim, object$par[epnames])
if (!is.numeric(covar_notrans) | is.na(covar_notrans[1])) {
covar_notrans <- NULL
se_notrans <- tval <- pval <- rep(NA, p)
} else {
rownames(covar_notrans) <- colnames(covar_notrans) <- c(bpnames, epnames)
se_notrans <- sqrt(diag(covar_notrans))
tval <- beparms.optim / se_notrans
pval <- pt(abs(tval), rdf, lower.tail = FALSE)
}
names(se) <- pnames
param <- cbind(param, se, lci, uci)
dimnames(param) <- list(pnames, c("Estimate", "Std. Error", "Lower", "Upper"))
bparam <- cbind(Estimate = beparms.optim, se_notrans,
"t value" = tval, "Pr(>t)" = pval, Lower = NA, Upper = NA)
# 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) {
if (!pname %in% f_names_skip) {
par.lower <- param[pname, "Lower"]
par.upper <- param[pname, "Upper"]
names(par.lower) <- names(par.upper) <- pname
bpl <- backtransform_odeparms(par.lower, object$mkinmod,
object$transform_rates,
object$transform_fractions)
bpu <- backtransform_odeparms(par.upper, object$mkinmod,
object$transform_rates,
object$transform_fractions)
bparam[names(bpl), "Lower"] <- bpl
bparam[names(bpu), "Upper"] <- bpu
}
}
bparam[epnames, c("Lower", "Upper")] <- param[epnames, c("Lower", "Upper")]
ans <- list(
version = as.character(utils::packageVersion("mkin")),
Rversion = paste(R.version$major, R.version$minor, sep="."),
date.fit = object$date,
date.summary = date(),
solution_type = object$solution_type,
warning = object$warning,
use_of_ff = object$mkinmod$use_of_ff,
df = c(p, rdf),
cov.unscaled = covar,
#cov.scaled = covar * resvar,
niter = object$iterations,
calls = object$calls,
time = object$time,
par = param,
bpar = bparam)
if (!is.null(object$version)) {
ans$fit_version <- object$version
ans$fit_Rversion <- object$Rversion
}
ans$diffs <- object$mkinmod$diffs
if(data) ans$data <- object$data
ans$start <- object$start
ans$start_transformed <- object$start_transformed
ans$fixed <- object$fixed
ans$errmin <- mkinerrmin(object, alpha = 0.05)
if (object$calls > 0) {
if (!is.null(ans$cov.unscaled)){
Corr <- cov2cor(ans$cov.unscaled)
rownames(Corr) <- colnames(Corr) <- rownames(ans$par)
ans$Corr <- Corr
} else {
warning("Could not estimate covariance matrix; singular system.")
}
}
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), ...) {
if (is.null(x$fit_version)) {
cat("mkin version: ", x$version, "\n")
cat("R version: ", x$Rversion, "\n")
} else {
cat("mkin version used for fitting: ", x$fit_version, "\n")
cat("R version used for fitting: ", x$fit_Rversion, "\n")
}
cat("Date of fit: ", x$date.fit, "\n")
cat("Date of summary:", x$date.summary, "\n")
if (!is.null(x$warning)) cat("\n\nWarning:", x$warning, "\n\n")
cat("\nEquations:\n")
nice_diffs <- gsub("^(d.*) =", "\\1/dt =", x[["diffs"]])
writeLines(strwrap(nice_diffs, exdent = 11))
df <- x$df
rdf <- df[2]
cat("\nModel predictions using solution type", x$solution_type, "\n")
cat("\nFitted with method", x$method.modFit,
"using", x$calls, "model solutions performed in", x$time[["elapsed"]], "s\n")
cat("\nError model:\n")
print(x$err_mod)
cat("\nStarting values for parameters to be optimised:\n")
print(x$start)
cat("\nStarting values for the transformed parameters actually optimised:\n")
print(x$start_transformed)
cat("\nFixed parameter values:\n")
if(length(x$fixed$value) == 0) cat("None\n")
else print(x$fixed)
cat("\nOptimised, transformed parameters with symmetric confidence intervals:\n")
print(signif(x$par, digits = digits))
if (x$calls > 0) {
cat("\nParameter correlation:\n")
if (!is.null(x$cov.unscaled)){
print(x$Corr, digits = digits, ...)
} else {
cat("Could not estimate covariance matrix; singular system.")
}
}
cat("\nBacktransformed parameters:\n")
cat("Confidence intervals for internally transformed parameters are asymmetric.\n")
if ((x$version) < "0.9-36") {
cat("To get the usual (questionable) t-test, upgrade mkin and repeat the fit.\n")
print(signif(x$bpar, digits = digits))
} else {
cat("t-test (unrealistically) based on the assumption of normal distribution\n")
cat("for estimators of untransformed parameters.\n")
print(signif(x$bpar[, c(1, 3, 4, 5, 6)], digits = digits))
}
cat("\nChi2 error levels in percent:\n")
x$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$ff)
if(printff){
cat("\nResulting formation fractions:\n")
print(data.frame(ff = x$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:
