diff options
| -rw-r--r-- | .gitignore | 1 | ||||
| -rw-r--r-- | DESCRIPTION | 17 | ||||
| -rw-r--r-- | GNUmakefile | 16 | ||||
| -rw-r--r-- | NEWS.md | 81 | ||||
| -rw-r--r-- | R/mkinerrmin.R | 16 | ||||
| -rw-r--r-- | R/mkinfit.R | 175 | ||||
| -rw-r--r-- | R/mkinresplot.R | 3 | ||||
| -rw-r--r-- | R/plot.mkinfit.R | 2 | ||||
| -rw-r--r-- | R/transform_odeparms.R | 37 | ||||
| -rw-r--r-- | README.md | 48 | ||||
| -rw-r--r-- | TODO | 4 | ||||
| -rw-r--r-- | inst/unitTests/runit.mkinerrmin.R | 62 | ||||
| -rw-r--r-- | inst/unitTests/runit.mkinfit.R | 38 | ||||
| -rw-r--r-- | man/DFOP.solution.Rd | 2 | ||||
| -rw-r--r-- | man/mkinerrmin.Rd | 10 | ||||
| -rw-r--r-- | man/mkinfit.Rd | 69 | ||||
| -rw-r--r-- | man/transform_odeparms.Rd | 2 | ||||
| -rw-r--r-- | tests/doRUnit.R | 1 | ||||
| -rw-r--r-- | vignettes/FOCUS_L.Rmd | 81 | ||||
| -rw-r--r-- | vignettes/FOCUS_L.html | 638 | ||||
| -rw-r--r-- | vignettes/FOCUS_Z.Rnw | 1 | ||||
| -rw-r--r-- | vignettes/FOCUS_Z.pdf | bin | 217963 -> 398825 bytes | |||
| -rw-r--r-- | vignettes/mkin.pdf | bin | 160429 -> 295336 bytes |
23 files changed, 798 insertions, 506 deletions
@@ -6,5 +6,6 @@ vignettes/*.blg vignettes/*.log vignettes/*.out vignettes/*.toc +vignettes/.build.timestamp vignettes/mkin.tex vignettes/FOCUS_Z.tex diff --git a/DESCRIPTION b/DESCRIPTION index 833acd8e..da7037a6 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,9 +1,9 @@ Package: mkin Type: Package -Title: Routines for fitting kinetic models with one or more state - variables to chemical degradation data -Version: 0.9-32 -Date: 2014-07-14 +Title: Routines for Fitting Kinetic Models with One or More State + Variables to Chemical Degradation Data +Version: 0.9-34 +Date: 2014-10-22 Authors@R: c(person("Johannes", "Ranke", role = c("aut", "cre", "cph"), email = "jranke@uni-bremen.de"), person("Katrin", "Lindenberger", role = "ctb"), @@ -12,9 +12,9 @@ Authors@R: c(person("Johannes", "Ranke", role = c("aut", "cre", "cph"), Description: Calculation routines based on the FOCUS Kinetics Report (2006). Includes a function for conveniently defining differential equation models, model solution based on eigenvalues if possible or using numerical solvers - and a choice of the optimisation methods made available by the FME package - (default is a Levenberg-Marquardt variant). Please note that no warranty is - implied for correctness of results or fitness for a particular purpose. + and a choice of the optimisation methods made available by the FME package. + Please note that no warranty is implied for correctness of results or fitness + for a particular purpose. Depends: minpack.lm, rootSolve Imports: FME, deSolve Suggests: knitr, RUnit @@ -24,5 +24,6 @@ LazyData: yes Encoding: UTF-8 VignetteBuilder: knitr BugReports: http://github.com/jranke/mkin/issues -URL: http://kinfit.r-forge.r-project.org, http://cran.r-project.org/package=mkin, +URL: http://cran.r-project.org/package=mkin, + http://kinfit.r-forge.r-project.org/mkin_static, http://github.com/jranke/mkin diff --git a/GNUmakefile b/GNUmakefile index b8cc5d82..126dede1 100644 --- a/GNUmakefile +++ b/GNUmakefile @@ -65,15 +65,23 @@ check-no-vignettes: build-no-vignettes clean: $(RM) -r $(PKGNAME).Rcheck/ + $(RM) vignettes/*.R test: install-no-vignettes cd tests;\ "$(RBIN)/Rscript" doRUnit.R -.PHONY: vignettes -vignettes: - "$(RBIN)/Rscript" -e "tools::buildVignettes(dir = '.')" - +vignettes/mkin.pdf: vignettes/mkin.Rnw + "$(RBIN)/Rscript" -e "tools::buildVignette(file = 'vignettes/mkin.Rnw', dir = 'vignettes')" + +vignettes/FOCUS_L.html: vignettes/FOCUS_L.Rmd + "$(RBIN)/Rscript" -e "tools::buildVignette(file = 'vignettes/FOCUS_L.Rmd', dir = 'vignettes')" + +vignettes/FOCUS_Z.pdf: vignettes/FOCUS_Z.Rnw + "$(RBIN)/Rscript" -e "tools::buildVignette(file = 'vignettes/FOCUS_Z.Rnw', dir = 'vignettes')" + +vignettes: vignettes/mkin.pdf vignettes/FOCUS_L.html vignettes/FOCUS_Z.pdf + sd: "$(RBIN)/Rscript" -e "library(staticdocs); build_site()" @@ -1,17 +1,86 @@ -# CHANGES in mkin VERSION 0.9-32 +# CHANGES in mkin VERSION 0.9-34 ## NEW FEATURES + - Add the possibility to fit indeterminate order rate equation (IORE) models using an analytical solution (parent only) or a numeric solution. Paths from IORE compounds to metabolites are supported when using of formation fractions (use_of_ff = 'max'). Note that the numerical solution (method.ode = 'deSolve') of the IORE differential equations sometimes fails due to numerical problems. -# CHANGES in mkin VERSION 0.9-31 +- Switch to using the Port algorithm (using a model/trust region approach) per default. While needing more iterations than the Levenberg-Marquardt algorithm previously used per default, it is less sensitive to starting parameters. +## MINOR CHANGES + +- The formatting of differential equations in the summary was further improved + +- Always include 0 on y axis when plotting during the fit + +# CHANGES in mkin VERSION 0.9-33 + +## NEW FEATURES + +- The initial value (state.ini) for the observed variable with the highest observed residue is set to 100 in case it has no time zero observation and `state.ini = "auto"` + +- A basic unit test for `mkinerrmin()` was written ## BUG FIXES -- The internal renaming of optimised parameters in Version 0.9-30 led to errors in the determination of the degrees of freedom for the chi2 error level calulations in `mkinerrmin()` used by the summary function. +- `mkinfit()`: The internally fitted parameter for `g` was named `g_ilr` even when `transform_fractions=FALSE` -- Initial values for formation fractions were not set in all cases +- `mkinfit()`: The initial value (state.ini) for the parent compound was not set when the parent was not the (only) variable with the highest value in the observed data. + +- `mkinerrmin()`: When checking for degrees of freedom for metabolites, check if their time zero value is fixed instead of checking if the observed value is zero. This ensures correct calculation of degrees of freedom also in cases where the metabolite residue at time zero is greater zero. + +- `plot.mkinfit()`: Avoid a warning message about only using the first component of ylim that occurred when ylim was specified explicitly + +## MINOR CHANGES + +- The formatting of differential equations in the summary was improved by wrapping overly long lines + +- The FOCUS_Z vignette was rebuilt with the above improvement and using a width of 70 to avoid output outside of the grey area + +- `print.summary.mkinfit()`: Avoid a warning that occurred when gmkin showed summaries ofinitial fits without iterations + +- `mkinfit()`: Avoid a warning that occurred when summarising a fit that was performed with maxitmodFit = 0 as done in gmkin for configuring new fits. + +# CHANGES in mkin VERSION 0.9-32 + +## NEW FEATURES +- The number of degrees of freedom is difficult to define in the case of ilr transformation of formation fractions. Now for each source compartment the number of ilr parameters (=number of optimised parameters) is divided by the number of pathways to metabolites (=number of affected data series) which leads to fractional degrees of freedom in some cases. + +- The default for the initial value for the first state value is now taken from the mean of the observations at time zero, if available. + +- The kinetic model can alternatively be specified with a shorthand name for parent only degradation models, e.g. `SFO`, or `DFOP`. + +- Optimisation method, number of model evaluations and time elapsed during optimisation are given in the summary of mkinfit objects. + +- The maximum number of iterations in the optimisation algorithm can be specified using the argument `maxit.modFit` to the mkinfit function. + +- mkinfit gives a warning when the fit does not converge (does not apply to SANN method). This warning is included in the summary. + +## BUG FIXES + +- Avoid plotting an artifical 0 residual at time zero in `mkinresplot` + +- In the determination of the degrees of freedom in `mkinerrmin`, formation fractions were accounted for multiple times in the case of parallel formation of metabolites. See the new feature described above for the solution. + +- `transform_rates=FALSE` in `mkinfit` now also works for FOMC and HS models. + +- Initial values for formation fractions were not set in all cases. + +- No warning was given when the fit did not converge when a method other than the default Levenberg-Marquardt method `Marq` was used. + +## MINOR CHANGES + +- Vignettes were rebuilt to reflect the changes in the summary method. + +- Algorithm `Pseudo` was excluded because it needs user-defined parameter limits which are not supported. + +- Algorithm `Newton` was excluded because of its different way to specify the maximum number of iterations and because it does not appear to provide additional benefits. + +# CHANGES in mkin VERSION 0.9-31 + +## BUG FIXES + +- The internal renaming of optimised parameters in Version 0.9-30 led to errors in the determination of the degrees of freedom for the chi2 error level calulations in `mkinerrmin()` used by the summary function. # CHANGES in mkin VERSION 0.9-30 ## NEW FEATURES @@ -22,13 +91,13 @@ - The original and the transformed parameters now have different names (e.g. `k_parent` and `log_k_parent`. They also differ in how many they are when we have formation fractions but no pathway to sink. -- The order of some of the information blocks in `print.summary.mkinfit.R()` has been ordered in a more logical way +- The order of some of the information blocks in `print.summary.mkinfit.R()` has been ordered in a more logical way. ## MINOR CHANGES - The vignette FOCUS_Z has been simplified to use formation fractions with turning off the sink, and slightly amended to use the new versions of DT50 values calculated since mkin 0.9-29. -- All vignettes have been rebuilt so they reflect all changes +- All vignettes have been rebuilt so they reflect all changes. - The ChangeLog was renamed to NEWS.md and the entries were converted to markdown syntax compatible with the `tools::news()` function built into R. diff --git a/R/mkinerrmin.R b/R/mkinerrmin.R index 4137d33a..b28235a6 100644 --- a/R/mkinerrmin.R +++ b/R/mkinerrmin.R @@ -36,10 +36,11 @@ mkinerrmin <- function(fit, alpha = 0.05) suffixes = c("_mean", "_pred")) errdata <- errdata[order(errdata$time, errdata$name), ] - # Any value that is set to exactly zero is not really an observed value - # Remove those at time 0 - those are caused by the FOCUS recommendation - # to set metabolites occurring at time 0 to 0 - errdata <- subset(errdata, !(time == 0 & value_mean == 0)) + # Remove values at time zero for variables whose value for state.ini is fixed, + # as these will not have any effect in the optimization and should therefore not + # be counted as degrees of freedom. + fixed_initials = gsub("_0$", "", rownames(subset(fit$fixed, type = "state"))) + errdata <- subset(errdata, !(time == 0 & name %in% fixed_initials)) n.optim.overall <- length(parms.optim) @@ -71,11 +72,12 @@ mkinerrmin <- function(fit, alpha = 0.05) # Formation fractions are attributed to the target variable, so look # for source compartments with formation fractions for (source_var in fit$obs_vars) { + n.ff.source = length(grep(paste("^f", source_var, sep = "_"), + names(parms.optim))) + n.paths.source = length(fit$mkinmod$spec[[source_var]]$to) for (target_var in fit$mkinmod$spec[[source_var]]$to) { if (obs_var == target_var) { - n.ff.optim <- n.ff.optim + - length(grep(paste("^f", source_var, sep = "_"), - names(parms.optim))) + n.ff.optim <- n.ff.optim + n.ff.source/n.paths.source } } } diff --git a/R/mkinfit.R b/R/mkinfit.R index 46121c6d..a6889b0b 100644 --- a/R/mkinfit.R +++ b/R/mkinfit.R @@ -23,12 +23,13 @@ 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$diffs) - 1)),
+ state.ini = "auto",
fixed_parms = NULL,
fixed_initials = names(mkinmod$diffs)[-1],
solution_type = "auto",
method.ode = "lsoda",
- method.modFit = "Marq",
+ method.modFit = c("Port", "Marq", "SANN", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B"),
+ maxit.modFit = "auto",
control.modFit = list(),
transform_rates = TRUE,
transform_fractions = TRUE,
@@ -40,11 +41,36 @@ mkinfit <- function(mkinmod, observed, 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")
+ if (class(mkinmod) != "mkinmod") {
+ presumed_parent_name = observed[which.max(observed$value), "name"]
+ if (mkinmod[[1]] %in% parent_models_available) {
+ speclist <- list(list(type = mkinmod, sink = TRUE))
+ names(speclist) <- presumed_parent_name
+ mkinmod <- mkinmod(speclist = speclist)
+ } else {
+ stop("Argument mkinmod must be of class mkinmod or a string containing one of\n ",
+ paste(parent_models_available, collapse = ", "))
+ }
+ }
+
+ # Check optimisation method and set maximum number of iterations if specified
+ method.modFit = match.arg(method.modFit)
+ if (maxit.modFit != "auto") {
+ if (method.modFit == "Marq") control.modFit$maxiter = maxit.modFit
+ if (method.modFit == "Port") control.modFit$iter.max = maxit.modFit
+ if (method.modFit %in% c("SANN", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B")) {
+ control.modFit$maxit = maxit.modFit
+ }
+ }
+
# 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)
+ obs_vars <- names(mkinmod$spec)
# Subset observed data with names of observed data in the model
observed <- subset(observed, name %in% obs_vars)
@@ -128,6 +154,18 @@ mkinfit <- function(mkinmod, observed, }
}
+ # Set default for state.ini if appropriate
+ parent_name = names(mkinmod$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$diffs) - 1))
+ }
+ }
+
# Name the inital state variable values if they are not named yet
if(is.null(names(state.ini))) names(state.ini) <- mod_vars
@@ -245,7 +283,7 @@ mkinfit <- function(mkinmod, observed, atol = atol, rtol = rtol, ...)
plot(0, type="n",
- xlim = range(observed$time), ylim = range(observed$value, na.rm=TRUE),
+ xlim = range(observed$time), ylim = c(0, max(observed$value, na.rm=TRUE)),
xlab = "Time", ylab = "Observed")
col_obs <- pch_obs <- 1:length(obs_vars)
lty_obs <- rep(1, length(obs_vars))
@@ -270,7 +308,7 @@ mkinfit <- function(mkinmod, observed, if (!transform_rates) {
index_k <- grep("^k_", names(lower))
lower[index_k] <- 0
- other_rate_parms <- intersect(c("alpha", "beta", "k1", "k2"), names(lower))
+ other_rate_parms <- intersect(c("alpha", "beta", "k1", "k2", "tb"), names(lower))
lower[other_rate_parms] <- 0
}
@@ -283,41 +321,65 @@ mkinfit <- function(mkinmod, observed, upper[other_fraction_parms] <- 1
}
- fit <- modFit(cost, c(state.ini.optim, transparms.optim),
- method = method.modFit, control = control.modFit,
- lower = lower, upper = upper, ...)
-
- # Reiterate the fit until convergence of the variance components (IRLS)
- # if requested by the user
- weight.ini = weight
- if (!is.null(err)) weight.ini = "manual"
-
- if (!is.null(reweight.method)) {
- if (reweight.method != "obs") stop("Only reweighting method 'obs' is implemented")
- if(!quiet) {
- cat("IRLS based on variance estimates for each observed variable\n")
- }
- if (!quiet) {
- cat("Initial variance estimates are:\n")
- print(signif(fit$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)
+ # Do the fit and take the time
+ fit_time <- system.time({
+ fit <- modFit(cost, c(state.ini.optim, transparms.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("Iteration", n.iter, "yields variance estimates:\n")
+ cat("Initial variance estimates are:\n")
print(signif(fit$var_ms_unweighted, 8))
- cat("Sum of squared differences to last variance estimates:",
- signif(reweight.diff, 2), "\n")
}
+ reweight.diff = 1
+ n.iter <- 0
+ if (!is.null(err)) observed$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")
+ }
+ }
+ }
+ })
+
+ # Check for convergence
+ if (method.modFit == "Marq") {
+ if (!fit$info %in% c(1, 2, 3)) {
+ fit$warning = paste0("Optimisation by method ", method.modFit,
+ " did not converge.\n",
+ "The message returned by nls.lm is:\n",
+ fit$message)
+ warning(fit$warning)
+ }
+ }
+ if (method.modFit %in% c("Port", "SANN", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B")) {
+ if (fit$convergence != 0) {
+ fit$warning = paste0("Optimisation by method ", method.modFit,
+ " did not converge.\n",
+ "Convergence code is ", fit$convergence,
+ ifelse(is.null(fit$message), "",
+ paste0("\nMessage is ", fit$message)))
+ warning(fit$warning)
}
}
@@ -325,6 +387,10 @@ mkinfit <- function(mkinmod, observed, fit$solution_type <- solution_type
fit$transform_rates <- transform_rates
fit$transform_fractions <- transform_fractions
+ fit$method.modFit <- method.modFit
+ fit$maxit.modFit <- maxit.modFit
+ fit$calls <- calls
+ fit$time <- fit_time
# We also need the model for summary and plotting
fit$mkinmod <- mkinmod
@@ -380,8 +446,11 @@ mkinfit <- function(mkinmod, observed, fit$bparms.optim <- bparms.optim
fit$bparms.fixed <- bparms.fixed
- # Return ode parameters for further fitting
+ # 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$bparms.state))
fit$date <- date()
@@ -451,6 +520,8 @@ summary.mkinfit <- function(object, data = TRUE, distimes = TRUE, alpha = 0.05, date.fit = object$date,
date.summary = date(),
solution_type = object$solution_type,
+ method.modFit = object$method.modFit,
+ warning = object$warning,
use_of_ff = object$mkinmod$use_of_ff,
weight.ini = object$weight.ini,
reweight.method = object$reweight.method,
@@ -463,6 +534,8 @@ summary.mkinfit <- function(object, data = TRUE, distimes = TRUE, alpha = 0.05, cov.scaled = covar * resvar,
info = object$info,
niter = object$iterations,
+ calls = object$calls,
+ time = object$time,
stopmess = message,
par = param,
bpar = bparam)
@@ -493,13 +566,17 @@ print.summary.mkinfit <- function(x, digits = max(3, getOption("digits") - 3), . 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")
- print(noquote(as.character(x[["diffs"]])))
+ writeLines(strwrap(x[["diffs"]], exdent = 11))
df <- x$df
rdf <- df[2]
- cat("\nMethod used for solution of differential equation system:\n")
- cat(x$solution_type, "\n")
+ 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("\nWeighting:", x$weight.ini)
if(!is.null(x$reweight.method)) cat(" then iterative reweighting method",
@@ -519,13 +596,15 @@ print.summary.mkinfit <- function(x, digits = max(3, getOption("digits") - 3), . 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")
+ if (x$niter != 0) {
+ cat("\nParameter correlation:\n")
+ if (!is.null(x$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:",
diff --git a/R/mkinresplot.R b/R/mkinresplot.R index c9a801fd..82ffd2cb 100644 --- a/R/mkinresplot.R +++ b/R/mkinresplot.R @@ -36,7 +36,8 @@ mkinresplot <- function (object, col_obs <- pch_obs <- 1:length(obs_vars)
names(col_obs) <- names(pch_obs) <- obs_vars
- plot(0, xlab = xlab, ylab = ylab,
+ plot(0, type = "n",
+ xlab = xlab, ylab = ylab,
xlim = xlim,
ylim = c(-1.2 * maxabs, 1.2 * maxabs), ...)
diff --git a/R/plot.mkinfit.R b/R/plot.mkinfit.R index 4132d96c..31746fb8 100644 --- a/R/plot.mkinfit.R +++ b/R/plot.mkinfit.R @@ -31,7 +31,7 @@ plot.mkinfit <- function(x, fit = x, { if (add && show_residuals) stop("If adding to an existing plot we can not show residuals") - if (ylim == "default") { + if (ylim[[1]] == "default") { ylim = c(0, max(subset(fit$data, variable %in% obs_vars)$observed, na.rm = TRUE)) } diff --git a/R/transform_odeparms.R b/R/transform_odeparms.R index a36b7eae..778f56cd 100644 --- a/R/transform_odeparms.R +++ b/R/transform_odeparms.R @@ -75,12 +75,22 @@ transform_odeparms <- function(parms, mkinmod, # and HS parameter tb if transformation of rates is requested
for (pname in c("alpha", "beta", "k1", "k2", "tb")) {
if (!is.na(parms[pname])) {
- transparms[paste0("log_", pname)] <- ifelse(transform_rates, log(parms[pname]), parms[pname])
+ if (transform_rates) {
+ transparms[paste0("log_", pname)] <- log(parms[pname])
+ } else {
+ transparms[pname] <- parms[pname]
+ }
}
}
+
+ # DFOP parameter g is treated as a fraction
if (!is.na(parms["g"])) {
g <- parms["g"]
- transparms["g_ilr"] <- ifelse(transform_fractions, ilr(c(g, 1 - g)), g)
+ if (transform_fractions) {
+ transparms["g_ilr"] <- ilr(c(g, 1 - g))
+ } else {
+ transparms["g"] <- g
+ }
}
return(transparms)
@@ -142,16 +152,25 @@ backtransform_odeparms <- function(transparms, mkinmod, # Transform parameters also for FOMC, DFOP and HS models
for (pname in c("alpha", "beta", "k1", "k2", "tb")) {
- pname_trans = paste0("log_", pname)
- if (!is.na(transparms[pname_trans])) {
- parms[pname] <- ifelse(transform_rates,
- exp(transparms[pname_trans]),
- transparms[pname])
- }
+ if (transform_rates) {
+ pname_trans = paste0("log_", pname)
+ if (!is.na(transparms[pname_trans])) {
+ parms[pname] <- exp(transparms[pname_trans])
+ }
+ } else {
+ if (!is.na(transparms[pname])) {
+ parms[pname] <- transparms[pname]
+ }
+ }
}
+
+ # DFOP parameter g is treated as a fraction
if (!is.na(transparms["g_ilr"])) {
g_ilr <- transparms["g_ilr"]
- parms["g"] <- ifelse(transform_fractions, invilr(g_ilr)[1], g_ilr)
+ parms["g"] <- invilr(g_ilr)[1]
+ }
+ if (!is.na(transparms["g"])) {
+ parms["g"] <- transparms["g"]
}
return(parms)
@@ -11,7 +11,7 @@ You can install the latest released version from [CRAN](http://cran.r-project.org/package=mkin) from within R: ```s -install.packages('mkin') +install.packages("mkin") ``` If looking for the latest features, you can install directly from @@ -21,7 +21,7 @@ vignettes, to make installation as fast and painless as possible. ```s require(devtools) -install_github("mkin", "jranke", quick = TRUE) +install_github("jranke/mkin", quick = TRUE) ``` ## Background @@ -34,20 +34,26 @@ detailed guidance and helpful tools have been developed as detailed in ## Usage -A very simple usage example would be +The simplest usage example that I can think of, using model shorthand notation +(available since mkin 0.9-32) and a built-in dataset is + + library(mkin) + fit <- mkinfit("SFO", FOCUS_2006_C) + plot(fit, show_residuals = TRUE) + summary(fit) + +A still very simple usage example including the definition of the same data in R +code would be - library("mkin") example_data = data.frame( name = rep("parent", 9), time = c(0, 1, 3, 7, 14, 28, 63, 91, 119), value = c(85.1, 57.9, 29.9, 14.6, 9.7, 6.6, 4, 3.9, 0.6) ) - SFO <- mkinmod(parent = list(type = "SFO")) - SFO.fit <- mkinfit(SFO, example_data) - plot(SFO.fit, show_residuals = TRUE) - summary(SFO.fit) + fit2 <- mkinfit("FOMC", example_data) + plot(fit2, show_residuals = TRUE) -A fairly complex usage example using a built-in dataset: +A fairly complex usage example using another built-in dataset: data <- mkin_wide_to_long(schaefer07_complex_case, time = "time") @@ -58,16 +64,15 @@ A fairly complex usage example using a built-in dataset: C1 = list(type = "SFO"), A2 = list(type = "SFO"), use_of_ff = "max") - fit <- mkinfit(model, data, method.modFit = "Port") + fit3 <- mkinfit(model, data, method.modFit = "Port") - plot(fit, show_residuals = TRUE) - summary(fit) - mkinparplot(fit) + plot(fit3, show_residuals = TRUE) + summary(fit3) + mkinparplot(fit3) For more examples and to see results, have a look at the examples provided in the [`mkinfit`](http://kinfit.r-forge.r-project.org/mkin_static/mkinfit.html) -documentation -or the package vignettes referenced from the +documentation or the package vignettes referenced from the [mkin package documentation page](http://kinfit.r-forge.r-project.org/mkin_static/index.html) ## Features @@ -88,8 +93,7 @@ or the package vignettes referenced from the * Model optimisation with [`mkinfit`](http://kinfit.r-forge.r-project.org/mkin_static/mkinfit.html) internally using the `modFit` function from the `FME` package, - which uses the least-squares Levenberg-Marquardt algorithm from - `minpack.lm` per default. + but using the Port routine `nlminb` per default. * By default, kinetic rate constants and kinetic formation fractions are transformed internally using [`transform_odeparms`](http://kinfit.r-forge.r-project.org/mkin_static/transform_odeparms.html) @@ -120,10 +124,9 @@ or the package vignettes referenced from the ## GUI -There is a graphical user interface that I consider useful for real work. -It is available from github in the separate package -[gmkin](http://github.com/jranke/gmkin). - +There is a graphical user interface that I consider useful for real work. Please +refer to its [documentation page](http://kinfit.r-forge.r-project.org/gmkin_static) +for installation instructions and a manual. ## Credits and historical remarks @@ -153,7 +156,8 @@ The first `mkin` code was [first CRAN version](http://cran.r-project.org/src/contrib/Archive/mkin) on 18 May 2010. -After this, Bayer has developed an R based successor to KinGUI named KinGUII +After this, Bayer has developed an R based successor to KinGUI named +[KinGUII](https://kinguii.github.io) whose R code is based on `mkin`, but which added, amongst other refinements, a closed source graphical user interface (GUI), iteratively reweighted least squares (IRLS) optimisation of the variance for each of the observed @@ -1,9 +1,11 @@ TODO for version 1.0 - Think about what a user would expect from version 1.0 - Complete the main package vignette named mkin to include a method description -- Improve formatting of differential equations in the summary +- Improve order of parameters in output Nice to have: +- Get starting values for formation fractions from data +- Calculate confidence intervals for more than one formation fraction using Monte Carlo simulations - Calculate confidence intervals for DT50 and DT90 values when only one parameter is involved - Calculate transformation only DT50 values (exclude pathways to sink) as diff --git a/inst/unitTests/runit.mkinerrmin.R b/inst/unitTests/runit.mkinerrmin.R new file mode 100644 index 00000000..56a33ff9 --- /dev/null +++ b/inst/unitTests/runit.mkinerrmin.R @@ -0,0 +1,62 @@ +# Test SFO_SFO model with FOCUS_2006_D against Schaefer 2007 paper, tolerance = 1% # {{{ +# and check chi2 error values against values obtained with mkin 0.33 +test.FOCUS_2006_D_SFO_SFO <- function() +{ + SFO_SFO.1 <- mkinmod(parent = list(type = "SFO", to = "m1"), + m1 = list(type = "SFO"), use_of_ff = "min") + SFO_SFO.2 <- mkinmod(parent = list(type = "SFO", to = "m1"), + m1 = list(type = "SFO"), use_of_ff = "max") + + fit.1.e <- mkinfit(SFO_SFO.1, FOCUS_2006_D) + fit.1.d <- mkinfit(SFO_SFO.1, solution_type = "deSolve", FOCUS_2006_D) + fit.2.e <- mkinfit(SFO_SFO.2, FOCUS_2006_D) + fit.2.d <- mkinfit(SFO_SFO.2, solution_type = "deSolve", FOCUS_2006_D) + + FOCUS_2006_D_results_schaefer07_means <- c( + parent_0 = 99.65, DT50_parent = 7.04, DT50_m1 = 131.34) + + r.1.e <- c(fit.1.e$bparms.optim[[1]], endpoints(fit.1.e)$distimes[[1]]) + r.1.d <- c(fit.1.d$bparms.optim[[1]], endpoints(fit.1.d)$distimes[[1]]) + r.2.e <- c(fit.2.e$bparms.optim[[1]], endpoints(fit.2.e)$distimes[[1]]) + r.2.d <- c(fit.2.d$bparms.optim[[1]], endpoints(fit.2.d)$distimes[[1]]) + + dev.1.e <- 100 * (r.1.e - FOCUS_2006_D_results_schaefer07_means)/r.1.e + checkIdentical(as.numeric(abs(dev.1.e)) < 1, rep(TRUE, 3)) + dev.1.d <- 100 * (r.1.d - FOCUS_2006_D_results_schaefer07_means)/r.1.d + checkIdentical(as.numeric(abs(dev.1.d)) < 1, rep(TRUE, 3)) + dev.2.e <- 100 * (r.2.e - FOCUS_2006_D_results_schaefer07_means)/r.2.e + checkIdentical(as.numeric(abs(dev.2.e)) < 1, rep(TRUE, 3)) + dev.2.d <- 100 * (r.2.d - FOCUS_2006_D_results_schaefer07_means)/r.2.d + checkIdentical(as.numeric(abs(dev.2.d)) < 1, rep(TRUE, 3)) + + round(mkinerrmin(fit.2.e), 4) + round(mkinerrmin(fit.2.d), 4) + + errmin.FOCUS_2006_D_rounded = data.frame( + err.min = c(0.0640, 0.0646, 0.0469), + n.optim = c(4, 2, 2), + df = c(15, 7, 8), + row.names = c("All data", "parent", "m1")) + checkEqualsNumeric(round(mkinerrmin(fit.2.e), 4), + errmin.FOCUS_2006_D_rounded) +} # }}} + +# Test SFO_SFO model with FOCUS_2006_E against values obtained with mkin 0.33 {{{ +test.FOCUS_2006_E_SFO_SFO <- function() +{ + SFO_SFO.2 <- mkinmod(parent = list(type = "SFO", to = "m1"), + m1 = list(type = "SFO"), use_of_ff = "max") + + fit.2.e <- mkinfit(SFO_SFO.2, FOCUS_2006_E) + + round(mkinerrmin(fit.2.e), 4) + errmin.FOCUS_2006_E_rounded = data.frame( + err.min = c(0.1544, 0.1659, 0.1095), + n.optim = c(4, 2, 2), + df = c(13, 7, 6), + row.names = c("All data", "parent", "m1")) + checkEqualsNumeric(round(mkinerrmin(fit.2.e), 4), + errmin.FOCUS_2006_E_rounded) +} # }}} + + diff --git a/inst/unitTests/runit.mkinfit.R b/inst/unitTests/runit.mkinfit.R index fdbc86e0..8eefb995 100644 --- a/inst/unitTests/runit.mkinfit.R +++ b/inst/unitTests/runit.mkinfit.R @@ -1,6 +1,4 @@ -# $Id: runit.mkinfit.R 68 2010-09-09 22:40:04Z jranke $
-
-# Copyright (C) 2010-2013 Johannes Ranke
+# Copyright (C) 2010-2014 Johannes Ranke
# Contact: jranke@uni-bremen.de
# This file is part of the R package mkin
@@ -189,40 +187,6 @@ test.FOCUS_2006_SFORB <- function() checkIdentical(dev.B.SFORB.2 < 1, rep(TRUE, length(dev.B.SFORB.2)))
} # }}}
-# Test SFO_SFO model with FOCUS_2006_D against Schaefer 2007 paper, tolerance = 1% # {{{
-test.FOCUS_2006_D_SFO_SFO <- function()
-{
- SFO_SFO.1 <- mkinmod(parent = list(type = "SFO", to = "m1"),
- m1 = list(type = "SFO"), use_of_ff = "min")
- SFO_SFO.2 <- mkinmod(parent = list(type = "SFO", to = "m1"),
- m1 = list(type = "SFO"), use_of_ff = "max")
-
- fit.1.e <- mkinfit(SFO_SFO.1, FOCUS_2006_D)
- fit.1.d <- mkinfit(SFO_SFO.1, solution_type = "deSolve", FOCUS_2006_D)
- fit.2.e <- mkinfit(SFO_SFO.2, FOCUS_2006_D)
- SFO <- mkinmod(parent = list(type = "SFO"))
- f.SFO <- mkinfit(SFO, FOCUS_2006_D)
- fit.2.d <- mkinfit(SFO_SFO.2, solution_type = "deSolve", FOCUS_2006_D)
- fit.2.e <- mkinfit(SFO_SFO.2, FOCUS_2006_D)
-
- FOCUS_2006_D_results_schaefer07_means <- c(
- parent_0 = 99.65, DT50_parent = 7.04, DT50_m1 = 131.34)
-
- r.1.e <- c(fit.1.e$bparms.optim[[1]], endpoints(fit.1.e)$distimes[[1]])
- r.1.d <- c(fit.1.d$bparms.optim[[1]], endpoints(fit.1.d)$distimes[[1]])
- r.2.e <- c(fit.2.e$bparms.optim[[1]], endpoints(fit.2.e)$distimes[[1]])
- r.2.d <- c(fit.2.d$bparms.optim[[1]], endpoints(fit.2.d)$distimes[[1]])
-
- dev.1.e <- 100 * (r.1.e - FOCUS_2006_D_results_schaefer07_means)/r.1.e
- checkIdentical(as.numeric(abs(dev.1.e)) < 1, rep(TRUE, 3))
- dev.1.d <- 100 * (r.1.d - FOCUS_2006_D_results_schaefer07_means)/r.1.d
- checkIdentical(as.numeric(abs(dev.1.d)) < 1, rep(TRUE, 3))
- dev.2.e <- 100 * (r.2.e - FOCUS_2006_D_results_schaefer07_means)/r.2.e
- checkIdentical(as.numeric(abs(dev.2.e)) < 1, rep(TRUE, 3))
- dev.2.d <- 100 * (r.2.d - FOCUS_2006_D_results_schaefer07_means)/r.2.d
- checkIdentical(as.numeric(abs(dev.2.d)) < 1, rep(TRUE, 3))
-} # }}}
-
# Test eigenvalue based fit to Schaefer 2007 data against solution from conference paper {{{
test.mkinfit.schaefer07_complex_example <- function()
{
diff --git a/man/DFOP.solution.Rd b/man/DFOP.solution.Rd index d30cf7f3..2d8b1735 100644 --- a/man/DFOP.solution.Rd +++ b/man/DFOP.solution.Rd @@ -2,7 +2,7 @@ \Rdversion{1.1}
\alias{DFOP.solution}
\title{
-Dual First-Order in Parallel kinetics
+Double First-Order in Parallel kinetics
}
\description{
Function describing decline from a defined starting value using the sum
diff --git a/man/mkinerrmin.Rd b/man/mkinerrmin.Rd index c43d87a1..78ab414e 100644 --- a/man/mkinerrmin.Rd +++ b/man/mkinerrmin.Rd @@ -34,6 +34,16 @@ mkinerrmin(fit, alpha = 0.05) \details{
This function is used internally by \code{\link{summary.mkinfit}}.
}
+\examples{
+SFO_SFO = mkinmod(parent = list(type = "SFO", to = "m1"),
+ m1 = list(type = "SFO"),
+ use_of_ff = "max")
+
+fit_FOCUS_D = mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)
+round(mkinerrmin(fit_FOCUS_D), 4)
+fit_FOCUS_E = mkinfit(SFO_SFO, FOCUS_2006_E, quiet = TRUE)
+round(mkinerrmin(fit_FOCUS_E), 4)
+}
\references{
FOCUS (2006) \dQuote{Guidance Document on Estimating Persistence and
Degradation Kinetics from Environmental Fate Studies on Pesticides in EU
diff --git a/man/mkinfit.Rd b/man/mkinfit.Rd index bd7f73b7..c40dff83 100644 --- a/man/mkinfit.Rd +++ b/man/mkinfit.Rd @@ -7,8 +7,10 @@ This function uses the Flexible Modelling Environment package \code{\link{FME}} to create a function calculating the model cost, i.e. the deviation between the kinetic model and the observed data. This model cost is - then minimised using the Levenberg-Marquardt algorithm \code{\link{nls.lm}}, + then minimised using the Port algorithm \code{\link{nlminb}}, using the specified initial or fixed parameters and starting values. + Per default, parameters in the kinetic models are internally transformed in order + to better satisfy the assumption of a normal distribution of their estimators. In each step of the optimsation, the kinetic model is solved using the function \code{\link{mkinpredict}}. The variance of the residuals for each observed variable can optionally be iteratively reweighted until convergence @@ -17,11 +19,12 @@ \usage{ mkinfit(mkinmod, observed, parms.ini = "auto", - state.ini = c(100, rep(0, length(mkinmod$diffs) - 1)), + state.ini = "auto", fixed_parms = NULL, fixed_initials = names(mkinmod$diffs)[-1], solution_type = "auto", method.ode = "lsoda", - method.modFit = "Marq", + method.modFit = c("Port", "Marq", "SANN", "Nelder-Mead", "BFSG", "CG", "L-BFGS-B"), + maxit.modFit = "auto", control.modFit = list(), transform_rates = TRUE, transform_fractions = TRUE, @@ -34,7 +37,11 @@ mkinfit(mkinmod, observed, } \arguments{ \item{mkinmod}{ - A list of class \code{\link{mkinmod}}, containing the kinetic model to be fitted to the data. + A list of class \code{\link{mkinmod}}, containing the kinetic model to be + fitted to the data, or one of the shorthand names ("SFO", "FOMC", "DFOP", + "HS", "SFORB"). If a shorthand name is given, a parent only degradation + model is generated for the variable with the highest value in + \code{observed}. } \item{observed}{ The observed data. It has to be in the long format as described in @@ -64,7 +71,9 @@ mkinfit(mkinmod, observed, case the observed variables are represented by more than one model variable, the names will differ from the names of the observed variables (see \code{map} component of \code{\link{mkinmod}}). The default is to set - the initial value of the first model variable to 100 and all others to 0. + the initial value of the first model variable to the mean of the time zero + values for the variable with the maximum observed value, and all others to 0. + If this variable has no time zero observations, its initial value is set to 100. } \item{fixed_parms}{ The names of parameters that should not be optimised but rather kept at the @@ -94,37 +103,51 @@ mkinfit(mkinmod, observed, "lsoda" is performant, but sometimes fails to converge. } \item{method.modFit}{ - The optimisation method passed to \code{\link{modFit}}. The default "Marq" - is the Levenberg Marquardt algorithm \code{\link{nls.lm}} from the package - \code{minpack.lm} and usually needs the least number of iterations. + The optimisation method passed to \code{\link{modFit}}. - For more complex problems where local minima occur, the "Port" algorithm is - recommended as it is less prone to get trapped in local minima and depends - less on starting values for parameters. However, it needs more iterations. + In order to optimally deal with problems where local minima occur, the + "Port" algorithm is now used per default as it is less prone to get trapped + in local minima and depends less on starting values for parameters than + the Levenberg Marquardt variant selected by "Marq". However, "Port" needs + more iterations. - When using "Pseudo", "upper" and "lower" need to be specified for the - transformed parameters. + The former default "Marq" is the Levenberg Marquardt algorithm + \code{\link{nls.lm}} from the package \code{minpack.lm} and usually needs + the least number of iterations. + + The "Pseudo" algorithm is not included because it needs finite parameter bounds + which are currently not supported. + + The "Newton" algorithm is not included because its number of iterations + can not be controlled by \code{control.modFit} and it does not appear + to provide advantages over the other algorithms. + } + \item{maxit.modFit}{ + Maximum number of iterations in the optimisation. If not "auto", this will + be passed to the method called by \code{\link{modFit}}, overriding + what may be specified in the next argument \code{control.modFit}. } \item{control.modFit}{ Additional arguments passed to the optimisation method used by - \code{\link{modFit}}. + \code{\link{modFit}}. } \item{transform_rates}{ Boolean specifying if kinetic rate constants should be transformed in the model specification used in the fitting for better compliance with the assumption of normal distribution of the estimator. If TRUE, also alpha and beta parameters of the FOMC model are log-transformed, as well - as k1 and k2 rate constants for the DFOP and HS models. - If TRUE, zero is used as a lower bound for the rates in the optimisation. + as k1 and k2 rate constants for the DFOP and HS models and the break point + tb of the HS model. + If FALSE, zero is used as a lower bound for the rates in the optimisation. } \item{transform_fractions}{ Boolean specifying if formation fractions constants should be transformed in the model specification used in the fitting for better compliance with the assumption of normal distribution of the estimator. The default (TRUE) is - to do transformations. The g parameter of the DFOP and HS models are also - transformed, as they can also be seen as compositional data. The - transformation used for these transformations is the \code{\link{ilr}} - transformation. + to do transformations. If TRUE, the g parameter of the DFOP and HS + models are also transformed, as they can also be seen as compositional + data. The transformation used for these transformations is the + \code{\link{ilr}} transformation. } \item{plot}{ Should the observed values and the numerical solutions be plotted at each @@ -194,9 +217,13 @@ mkinfit(mkinmod, observed, other GUI derivative of mkin, sponsored by Syngenta. } \author{ - Johannes Ranke <jranke@uni-bremen.de> + Johannes Ranke } \examples{ +# Use shorthand notation for parent only degradation +fit <- mkinfit("FOMC", FOCUS_2006_C) +summary(fit) + # One parent compound, one metabolite, both single first order. SFO_SFO <- mkinmod( parent = list(type = "SFO", to = "m1", sink = TRUE), diff --git a/man/transform_odeparms.Rd b/man/transform_odeparms.Rd index ea0b5024..ba93af7d 100644 --- a/man/transform_odeparms.Rd +++ b/man/transform_odeparms.Rd @@ -41,7 +41,7 @@ backtransform_odeparms(transparms, mkinmod, assumption of normal distribution of the estimator. If TRUE, also alpha and beta parameters of the FOMC model are log-transformed, as well as k1 and k2 rate constants for the DFOP and HS models and the break point tb - of the HS model + of the HS model. } \item{transform_fractions}{ Boolean specifying if formation fractions constants should be transformed in the diff --git a/tests/doRUnit.R b/tests/doRUnit.R index f0f82812..9faee940 100644 --- a/tests/doRUnit.R +++ b/tests/doRUnit.R @@ -1,4 +1,3 @@ -# $Id: doRUnit.R 96 2011-04-29 11:10:40Z jranke $ # Adapted from a version around 2.9 of the rcdk package by Rajarshi Guha if(require("RUnit", quietly=TRUE)) { diff --git a/vignettes/FOCUS_L.Rmd b/vignettes/FOCUS_L.Rmd index 04d5f831..cd7711f6 100644 --- a/vignettes/FOCUS_L.Rmd +++ b/vignettes/FOCUS_L.Rmd @@ -13,7 +13,7 @@ opts_chunk$set(tidy = FALSE, cache = TRUE) ## Laboratory Data L1
The following code defines example dataset L1 from the FOCUS kinetics
-report, p. 284
+report, p. 284:
```{r}
library("mkin")
@@ -25,27 +25,18 @@ FOCUS_2006_L1 = data.frame( FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
```
-The next step is to set up the models used for the kinetic analysis. Note that
-the model definitions contain the names of the observed variables in the data.
-In this case, there is only one variable called `parent`.
+Here we use the assumptions of simple first order (SFO), the case of declining
+rate constant over time (FOMC) and the case of two different phases of the
+kinetics (DFOP). For a more detailed discussion of the models, please see the
+FOCUS kinetics report.
-```{r}
-SFO <- mkinmod(parent = list(type = "SFO"))
-FOMC <- mkinmod(parent = list(type = "FOMC"))
-DFOP <- mkinmod(parent = list(type = "DFOP"))
-```
-
-The three models cover the first assumption of simple first order (SFO),
-the case of declining rate constant over time (FOMC) and the case of two
-different phases of the kinetics (DFOP). For a more detailed discussion
-of the models, please see the FOCUS kinetics report.
-
-The following two lines fit the model and produce the summary report
-of the model fit. This covers the numerical analysis given in the
-FOCUS report.
+Since mkin version 0.9-32 (July 2014), we can use shorthand notation like `SFO`
+for parent only degradation models. The following two lines fit the model and
+produce the summary report of the model fit. This covers the numerical analysis
+given in the FOCUS report.
```{r}
-m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE)
+m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet=TRUE)
summary(m.L1.SFO)
```
@@ -64,32 +55,30 @@ For comparison, the FOMC model is fitted as well, and the chi^2 error level is checked.
```{r}
-m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE)
+m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
summary(m.L1.FOMC, data = FALSE)
```
Due to the higher number of parameters, and the lower number of degrees of
freedom of the fit, the chi^2 error level is actually higher for the FOMC
-model (3.6%) than for the SFO model (3.4%). Additionally, the covariance
-matrix can not be obtained, indicating overparameterisation of the model.
-As a consequence, no standard errors for transformed parameters nor
-confidence intervals for backtransformed parameters are available.
+model (3.6%) than for the SFO model (3.4%). Additionally, the parameters
+`log_alpha` and `log_beta` internally fitted in the model have p-values for the two
+sided t-test of 0.18 and 0.125, and their correlation is 1.000, indicating that
+the model is overparameterised.
The chi^2 error levels reported in Appendix 3 and Appendix 7 to the FOCUS
kinetics report are rounded to integer percentages and partly deviate by one
percentage point from the results calculated by mkin. The reason for
this is not known. However, mkin gives the same chi^2 error levels
-as the kinfit package.
-
-Furthermore, the calculation routines of the kinfit package have been extensively
-compared to the results obtained by the KinGUI software, as documented in the
-kinfit package vignette. KinGUI is a widely used standard package in this field.
-Therefore, the reason for the difference was not investigated further.
+as the kinfit package. Furthermore, the calculation routines of the kinfit
+package have been extensively compared to the results obtained by the KinGUI
+software, as documented in the kinfit package vignette. KinGUI is a widely used
+standard package in this field.
## Laboratory Data L2
The following code defines example dataset L2 from the FOCUS kinetics
-report, p. 287
+report, p. 287:
```{r}
FOCUS_2006_L2 = data.frame(
@@ -100,10 +89,10 @@ FOCUS_2006_L2 = data.frame( FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
```
-Again, the SFO model is fitted and a summary is obtained.
+Again, the SFO model is fitted and a summary is obtained:
```{r}
-m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE)
+m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
summary(m.L2.SFO)
```
@@ -130,7 +119,7 @@ For comparison, the FOMC model is fitted as well, and the chi^2 error level is checked.
```{r fig.height = 8}
-m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE)
+m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
par(mfrow = c(2, 1))
plot(m.L2.FOMC)
mkinresplot(m.L2.FOMC)
@@ -144,7 +133,7 @@ experimental error has to be assumed in order to explain the data. Fitting the four parameter DFOP model further reduces the chi^2 error level.
```{r fig.height = 5}
-m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE)
+m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
plot(m.L2.DFOP)
```
@@ -153,7 +142,7 @@ to a reasonable solution. Therefore the fit is repeated with different starting parameters.
```{r fig.height = 5}
-m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin,
+m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin,
parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8),
quiet=TRUE)
plot(m.L2.DFOP)
@@ -180,7 +169,7 @@ FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3) SFO model, summary and plot:
```{r fig.height = 5}
-m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE)
+m.L3.SFO <- mkinfit("SFO", FOCUS_2006_L3_mkin, quiet = TRUE)
plot(m.L3.SFO)
summary(m.L3.SFO)
```
@@ -191,7 +180,7 @@ does not fit very well. The FOMC model performs better:
```{r fig.height = 5}
-m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE)
+m.L3.FOMC <- mkinfit("FOMC", FOCUS_2006_L3_mkin, quiet = TRUE)
plot(m.L3.FOMC)
summary(m.L3.FOMC, data = FALSE)
```
@@ -202,7 +191,7 @@ Fitting the four parameter DFOP model further reduces the chi^2 error level considerably:
```{r fig.height = 5}
-m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE)
+m.L3.DFOP <- mkinfit("DFOP", FOCUS_2006_L3_mkin, quiet = TRUE)
plot(m.L3.DFOP)
summary(m.L3.DFOP, data = FALSE)
```
@@ -212,10 +201,15 @@ and the correlation matrix suggest that the parameter estimates are reliable, an the DFOP model can be used as the best-fit model based on the chi^2 error
level criterion for laboratory data L3.
+This is also an example where the standard t-test for the parameter `g_ilr` is
+misleading, as it tests for a significant difference from zero. In this case,
+zero appears to be the correct value for this parameter, and the confidence
+interval for the backtransformed parameter `g` is quite narrow.
+
## Laboratory Data L4
The following code defines example dataset L4 from the FOCUS kinetics
-report, p. 293
+report, p. 293:
```{r}
FOCUS_2006_L4 = data.frame(
@@ -227,7 +221,7 @@ FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4) SFO model, summary and plot:
```{r fig.height = 5}
-m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE)
+m.L4.SFO <- mkinfit("SFO", FOCUS_2006_L4_mkin, quiet = TRUE)
plot(m.L4.SFO)
summary(m.L4.SFO, data = FALSE)
```
@@ -235,14 +229,13 @@ summary(m.L4.SFO, data = FALSE) The chi^2 error level of 3.3% as well as the plot suggest that the model
fits very well.
-The FOMC model for comparison
+The FOMC model for comparison:
```{r fig.height = 5}
-m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE)
+m.L4.FOMC <- mkinfit("FOMC", FOCUS_2006_L4_mkin, quiet = TRUE)
plot(m.L4.FOMC)
summary(m.L4.FOMC, data = FALSE)
```
The error level at which the chi^2 test passes is slightly lower for the FOMC
model. However, the difference appears negligible.
-
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-hljs.initHighlightingOnLoad(); -</script> - -<!-- MathJax scripts --> -<script type="text/javascript" src="https://c328740.ssl.cf1.rackcdn.com/mathjax/2.0-latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"> -</script> </head> @@ -189,10 +211,16 @@ hljs.initHighlightingOnLoad(); <h2>Laboratory Data L1</h2> <p>The following code defines example dataset L1 from the FOCUS kinetics -report, p. 284</p> +report, p. 284:</p> <pre><code class="r">library("mkin") -FOCUS_2006_L1 = data.frame( +</code></pre> + +<pre><code>## Loading required package: minpack.lm +## Loading required package: rootSolve +</code></pre> + +<pre><code class="r">FOCUS_2006_L1 = data.frame( t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2), parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6, 72.0, 71.9, 50.3, 59.4, 47.0, 45.1, @@ -200,50 +228,43 @@ FOCUS_2006_L1 = data.frame( FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1) </code></pre> -<p>The next step is to set up the models used for the kinetic analysis. Note that -the model definitions contain the names of the observed variables in the data. -In this case, there is only one variable called <code>parent</code>.</p> - -<pre><code class="r">SFO <- mkinmod(parent = list(type = "SFO")) -FOMC <- mkinmod(parent = list(type = "FOMC")) -DFOP <- mkinmod(parent = list(type = "DFOP")) -</code></pre> +<p>Here we use the assumptions of simple first order (SFO), the case of declining +rate constant over time (FOMC) and the case of two different phases of the +kinetics (DFOP). For a more detailed discussion of the models, please see the +FOCUS kinetics report.</p> -<p>The three models cover the first assumption of simple first order (SFO), -the case of declining rate constant over time (FOMC) and the case of two -different phases of the kinetics (DFOP). For a more detailed discussion -of the models, please see the FOCUS kinetics report.</p> +<p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation like <code>SFO</code> +for parent only degradation models. The following two lines fit the model and +produce the summary report of the model fit. This covers the numerical analysis +given in the FOCUS report. </p> -<p>The following two lines fit the model and produce the summary report -of the model fit. This covers the numerical analysis given in the -FOCUS report.</p> - -<pre><code class="r">m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE) +<pre><code class="r">m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet=TRUE) summary(m.L1.SFO) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:26 2014 -## Date of summary: Mon Jul 14 19:59:26 2014 +## Date of fit: Wed Oct 15 00:58:15 2014 +## Date of summary: Wed Oct 15 00:58:15 2014 ## ## Equations: -## [1] d_parent = - k_parent_sink * parent +## d_parent = - k_parent_sink * parent +## +## Model predictions using solution type analytical ## -## Method used for solution of differential equation system: -## analytical +## Fitted with method Port using 37 model solutions performed in 0.203 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100.0 state -## k_parent_sink 0.1 deparm +## parent_0 89.85 state +## k_parent_sink 0.10 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k_parent_sink -2.303 -Inf Inf +## value lower upper +## parent_0 89.850 -Inf Inf +## log_k_parent_sink -2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -308,66 +329,80 @@ summary(m.L1.SFO) <pre><code class="r">plot(m.L1.SFO) </code></pre> -<p><img 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" alt="plot of chunk unnamed-chunk-5"/> </p> - -<p>The residual plot can be easily obtained by</p> +<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-4"/> +The residual plot can be easily obtained by</p> <pre><code class="r">mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time") </code></pre> -<p><img src="data:image/png;base64,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alt="plot of chunk unnamed-chunk-5"/> </p> <p>For comparison, the FOMC model is fitted as well, and the chi<sup>2</sup> error level is checked.</p> -<pre><code class="r">m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE) -summary(m.L1.FOMC, data = FALSE) +<pre><code class="r">m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE) +</code></pre> + +<pre><code>## Warning: Optimisation by method Port did not converge. +## Convergence code is 1 +</code></pre> + +<pre><code class="r">summary(m.L1.FOMC, data = FALSE) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:26 2014 -## Date of summary: Mon Jul 14 19:59:26 2014 +## Date of fit: Wed Oct 15 00:58:16 2014 +## Date of summary: Wed Oct 15 00:58:16 2014 +## +## +## Warning: Optimisation by method Port did not converge. +## Convergence code is 1 +## ## ## Equations: -## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent ## -## Method used for solution of differential equation system: -## analytical +## Model predictions using solution type analytical +## +## Fitted with method Port using 188 model solutions performed in 1.011 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100 state -## alpha 1 deparm -## beta 10 deparm +## parent_0 89.85 state +## alpha 1.00 deparm +## beta 10.00 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_alpha 0.000 -Inf Inf -## log_beta 2.303 -Inf Inf +## value lower upper +## parent_0 89.850 -Inf Inf +## log_alpha 0.000 -Inf Inf +## log_beta 2.303 -Inf Inf ## ## Fixed parameter values: ## None ## ## Optimised, transformed parameters: -## Estimate Std. Error Lower Upper t value Pr(>|t|) Pr(>t) -## parent_0 92.5 NA NA NA NA NA NA -## log_alpha 25.6 NA NA NA NA NA NA -## log_beta 28.0 NA NA NA NA NA NA +## Estimate Std. Error Lower Upper t value Pr(>|t|) Pr(>t) +## parent_0 92.5 1.42 89.4 95.5 65.00 8.32e-20 4.16e-20 +## log_alpha 15.4 15.10 -16.7 47.6 1.02 3.22e-01 1.61e-01 +## log_beta 17.8 15.10 -14.4 49.9 1.18 2.57e-01 1.28e-01 ## ## Parameter correlation: -## Could not estimate covariance matrix; singular system: +## parent_0 log_alpha log_beta +## parent_0 1.000 0.113 0.111 +## log_alpha 0.113 1.000 1.000 +## log_beta 0.111 1.000 1.000 ## ## Residual standard error: 3.05 on 15 degrees of freedom ## ## Backtransformed parameters: -## Estimate Lower Upper -## parent_0 9.25e+01 NA NA -## alpha 1.35e+11 NA NA -## beta 1.41e+12 NA NA +## Estimate Lower Upper +## parent_0 9.25e+01 8.94e+01 9.55e+01 +## alpha 5.04e+06 5.51e-08 4.62e+20 +## beta 5.28e+07 5.73e-07 4.86e+21 ## ## Chi2 error levels in percent: ## err.min n.optim df @@ -381,26 +416,24 @@ summary(m.L1.FOMC, data = FALSE) <p>Due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the chi<sup>2</sup> error level is actually higher for the FOMC -model (3.6%) than for the SFO model (3.4%). Additionally, the covariance -matrix can not be obtained, indicating overparameterisation of the model. -As a consequence, no standard errors for transformed parameters nor -confidence intervals for backtransformed parameters are available.</p> +model (3.6%) than for the SFO model (3.4%). Additionally, the parameters +<code>log_alpha</code> and <code>log_beta</code> internally fitted in the model have p-values for the two +sided t-test of 0.18 and 0.125, and their correlation is 1.000, indicating that +the model is overparameterised. </p> <p>The chi<sup>2</sup> error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same chi<sup>2</sup> error levels -as the kinfit package.</p> - -<p>Furthermore, the calculation routines of the kinfit package have been extensively -compared to the results obtained by the KinGUI software, as documented in the -kinfit package vignette. KinGUI is a widely used standard package in this field. -Therefore, the reason for the difference was not investigated further.</p> +as the kinfit package. Furthermore, the calculation routines of the kinfit +package have been extensively compared to the results obtained by the KinGUI +software, as documented in the kinfit package vignette. KinGUI is a widely used +standard package in this field. </p> <h2>Laboratory Data L2</h2> <p>The following code defines example dataset L2 from the FOCUS kinetics -report, p. 287</p> +report, p. 287:</p> <pre><code class="r">FOCUS_2006_L2 = data.frame( t = rep(c(0, 1, 3, 7, 14, 28), each = 2), @@ -410,34 +443,35 @@ report, p. 287</p> FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2) </code></pre> -<p>Again, the SFO model is fitted and a summary is obtained.</p> +<p>Again, the SFO model is fitted and a summary is obtained:</p> -<pre><code class="r">m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE) +<pre><code class="r">m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE) summary(m.L2.SFO) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:27 2014 -## Date of summary: Mon Jul 14 19:59:27 2014 +## Date of fit: Wed Oct 15 00:58:17 2014 +## Date of summary: Wed Oct 15 00:58:17 2014 ## ## Equations: -## [1] d_parent = - k_parent_sink * parent +## d_parent = - k_parent_sink * parent +## +## Model predictions using solution type analytical ## -## Method used for solution of differential equation system: -## analytical +## Fitted with method Port using 41 model solutions performed in 0.22 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100.0 state -## k_parent_sink 0.1 deparm +## parent_0 93.95 state +## k_parent_sink 0.10 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k_parent_sink -2.303 -Inf Inf +## value lower upper +## parent_0 93.950 -Inf Inf +## log_k_parent_sink -2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -479,8 +513,8 @@ summary(m.L2.SFO) ## time variable observed predicted residual ## 0 parent 96.1 9.15e+01 4.634 ## 0 parent 91.8 9.15e+01 0.334 -## 1 parent 41.4 4.71e+01 -5.740 -## 1 parent 38.7 4.71e+01 -8.440 +## 1 parent 41.4 4.71e+01 -5.739 +## 1 parent 38.7 4.71e+01 -8.439 ## 3 parent 19.3 1.25e+01 6.779 ## 3 parent 22.3 1.25e+01 9.779 ## 7 parent 4.6 8.83e-01 3.717 @@ -499,7 +533,7 @@ plot(m.L2.SFO) mkinresplot(m.L2.SFO) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-9"/> </p> <p>In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at @@ -514,41 +548,42 @@ models generally only implement SFO kinetics.</p> <p>For comparison, the FOMC model is fitted as well, and the chi<sup>2</sup> error level is checked.</p> -<pre><code class="r">m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE) +<pre><code class="r">m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE) par(mfrow = c(2, 1)) plot(m.L2.FOMC) mkinresplot(m.L2.FOMC) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-10"/> </p> <pre><code class="r">summary(m.L2.FOMC, data = FALSE) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:28 2014 -## Date of summary: Mon Jul 14 19:59:28 2014 +## Date of fit: Wed Oct 15 00:58:17 2014 +## Date of summary: Wed Oct 15 00:58:17 2014 ## ## Equations: -## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## +## Model predictions using solution type analytical ## -## Method used for solution of differential equation system: -## analytical +## Fitted with method Port using 81 model solutions performed in 0.438 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100 state -## alpha 1 deparm -## beta 10 deparm +## parent_0 93.95 state +## alpha 1.00 deparm +## beta 10.00 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_alpha 0.000 -Inf Inf -## log_beta 2.303 -Inf Inf +## value lower upper +## parent_0 93.950 -Inf Inf +## log_alpha 0.000 -Inf Inf +## log_beta 2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -589,53 +624,56 @@ experimental error has to be assumed in order to explain the data.</p> <p>Fitting the four parameter DFOP model further reduces the chi<sup>2</sup> error level. </p> -<pre><code class="r">m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE) +<pre><code class="r">m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE) plot(m.L2.DFOP) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-11"/> </p> <p>Here, the default starting parameters for the DFOP model obviously do not lead to a reasonable solution. Therefore the fit is repeated with different starting parameters.</p> -<pre><code class="r">m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, +<pre><code class="r">m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8), quiet=TRUE) plot(m.L2.DFOP) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-12"/> </p> <pre><code class="r">summary(m.L2.DFOP, data = FALSE) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:28 2014 -## Date of summary: Mon Jul 14 19:59:28 2014 +## Date of fit: Wed Oct 15 00:58:21 2014 +## Date of summary: Wed Oct 15 00:58:21 2014 ## ## Equations: -## [1] d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) * parent +## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * +## time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * +## time))) * parent +## +## Model predictions using solution type analytical ## -## Method used for solution of differential equation system: -## analytical +## Fitted with method Port using 336 model solutions performed in 1.844 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 1e+02 state -## k1 1e+00 deparm -## k2 1e-02 deparm -## g 8e-01 deparm +## parent_0 93.95 state +## k1 1.00 deparm +## k2 0.01 deparm +## g 0.80 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.0000 -Inf Inf -## log_k1 0.0000 -Inf Inf -## log_k2 -4.6052 -Inf Inf -## g_ilr 0.9803 -Inf Inf +## value lower upper +## parent_0 93.9500 -Inf Inf +## log_k1 0.0000 -Inf Inf +## log_k2 -4.6052 -Inf Inf +## g_ilr 0.9803 -Inf Inf ## ## Fixed parameter values: ## None @@ -643,7 +681,7 @@ plot(m.L2.DFOP) ## Optimised, transformed parameters: ## Estimate Std. Error Lower Upper t value Pr(>|t|) Pr(>t) ## parent_0 93.900 NA NA NA NA NA NA -## log_k1 4.960 NA NA NA NA NA NA +## log_k1 3.120 NA NA NA NA NA NA ## log_k2 -1.090 NA NA NA NA NA NA ## g_ilr -0.282 NA NA NA NA NA NA ## @@ -655,7 +693,7 @@ plot(m.L2.DFOP) ## Backtransformed parameters: ## Estimate Lower Upper ## parent_0 93.900 NA NA -## k1 142.000 NA NA +## k1 22.700 NA NA ## k2 0.337 NA NA ## g 0.402 NA NA ## @@ -666,7 +704,7 @@ plot(m.L2.DFOP) ## ## Estimated disappearance times: ## DT50 DT90 DT50_k1 DT50_k2 -## parent NA NA 0.00487 2.06 +## parent NA NA 0.0306 2.06 </code></pre> <p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the @@ -687,37 +725,38 @@ FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3) <p>SFO model, summary and plot:</p> -<pre><code class="r">m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE) +<pre><code class="r">m.L3.SFO <- mkinfit("SFO", FOCUS_2006_L3_mkin, quiet = TRUE) plot(m.L3.SFO) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-14"/> </p> <pre><code class="r">summary(m.L3.SFO) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:29 2014 -## Date of summary: Mon Jul 14 19:59:29 2014 +## Date of fit: Wed Oct 15 00:58:22 2014 +## Date of summary: Wed Oct 15 00:58:22 2014 ## ## Equations: -## [1] d_parent = - k_parent_sink * parent +## d_parent = - k_parent_sink * parent +## +## Model predictions using solution type analytical ## -## Method used for solution of differential equation system: -## analytical +## Fitted with method Port using 43 model solutions performed in 0.232 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100.0 state +## parent_0 97.8 state ## k_parent_sink 0.1 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k_parent_sink -2.303 -Inf Inf +## value lower upper +## parent_0 97.800 -Inf Inf +## log_k_parent_sink -2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -757,14 +796,14 @@ plot(m.L3.SFO) ## ## Data: ## time variable observed predicted residual -## 0 parent 97.8 74.87 22.9273 -## 3 parent 60.0 69.41 -9.4065 +## 0 parent 97.8 74.87 22.9281 +## 3 parent 60.0 69.41 -9.4061 ## 7 parent 51.0 62.73 -11.7340 -## 14 parent 43.0 52.56 -9.5634 -## 30 parent 35.0 35.08 -0.0828 -## 60 parent 22.0 16.44 5.5614 -## 91 parent 15.0 7.51 7.4896 -## 120 parent 12.0 3.61 8.3908 +## 14 parent 43.0 52.56 -9.5638 +## 30 parent 35.0 35.08 -0.0839 +## 60 parent 22.0 16.44 5.5602 +## 91 parent 15.0 7.51 7.4887 +## 120 parent 12.0 3.61 8.3903 </code></pre> <p>The chi<sup>2</sup> error level of 21% as well as the plot suggest that the model @@ -772,39 +811,40 @@ does not fit very well. </p> <p>The FOMC model performs better:</p> -<pre><code class="r">m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE) +<pre><code class="r">m.L3.FOMC <- mkinfit("FOMC", FOCUS_2006_L3_mkin, quiet = TRUE) plot(m.L3.FOMC) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-15"/> </p> <pre><code class="r">summary(m.L3.FOMC, data = FALSE) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:29 2014 -## Date of summary: Mon Jul 14 19:59:29 2014 +## Date of fit: Wed Oct 15 00:58:22 2014 +## Date of summary: Wed Oct 15 00:58:22 2014 ## ## Equations: -## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## +## Model predictions using solution type analytical ## -## Method used for solution of differential equation system: -## analytical +## Fitted with method Port using 83 model solutions performed in 0.442 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100 state -## alpha 1 deparm -## beta 10 deparm +## parent_0 97.8 state +## alpha 1.0 deparm +## beta 10.0 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_alpha 0.000 -Inf Inf -## log_beta 2.303 -Inf Inf +## value lower upper +## parent_0 97.800 -Inf Inf +## log_alpha 0.000 -Inf Inf +## log_beta 2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -844,41 +884,44 @@ plot(m.L3.FOMC) <p>Fitting the four parameter DFOP model further reduces the chi<sup>2</sup> error level considerably:</p> -<pre><code class="r">m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE) +<pre><code class="r">m.L3.DFOP <- mkinfit("DFOP", FOCUS_2006_L3_mkin, quiet = TRUE) plot(m.L3.DFOP) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-16"/> </p> <pre><code class="r">summary(m.L3.DFOP, data = FALSE) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:30 2014 -## Date of summary: Mon Jul 14 19:59:30 2014 +## Date of fit: Wed Oct 15 00:58:23 2014 +## Date of summary: Wed Oct 15 00:58:23 2014 ## ## Equations: -## [1] d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) * parent +## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * +## time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * +## time))) * parent +## +## Model predictions using solution type analytical ## -## Method used for solution of differential equation system: -## analytical +## Fitted with method Port using 137 model solutions performed in 0.778 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 1e+02 state -## k1 1e-01 deparm -## k2 1e-02 deparm -## g 5e-01 deparm +## parent_0 97.80 state +## k1 0.10 deparm +## k2 0.01 deparm +## g 0.50 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k1 -2.303 -Inf Inf -## log_k2 -4.605 -Inf Inf -## g_ilr 0.000 -Inf Inf +## value lower upper +## parent_0 97.800 -Inf Inf +## log_k1 -2.303 -Inf Inf +## log_k2 -4.605 -Inf Inf +## g_ilr 0.000 -Inf Inf ## ## Fixed parameter values: ## None @@ -921,10 +964,15 @@ and the correlation matrix suggest that the parameter estimates are reliable, an the DFOP model can be used as the best-fit model based on the chi<sup>2</sup> error level criterion for laboratory data L3.</p> +<p>This is also an example where the standard t-test for the parameter <code>g_ilr</code> is +misleading, as it tests for a significant difference from zero. In this case, +zero appears to be the correct value for this parameter, and the confidence +interval for the backtransformed parameter <code>g</code> is quite narrow.</p> + <h2>Laboratory Data L4</h2> <p>The following code defines example dataset L4 from the FOCUS kinetics -report, p. 293</p> +report, p. 293:</p> <pre><code class="r">FOCUS_2006_L4 = data.frame( t = c(0, 3, 7, 14, 30, 60, 91, 120), @@ -934,37 +982,38 @@ FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4) <p>SFO model, summary and plot:</p> -<pre><code class="r">m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE) +<pre><code class="r">m.L4.SFO <- mkinfit("SFO", FOCUS_2006_L4_mkin, quiet = TRUE) plot(m.L4.SFO) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-18"/> </p> <pre><code class="r">summary(m.L4.SFO, data = FALSE) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:30 2014 -## Date of summary: Mon Jul 14 19:59:30 2014 +## Date of fit: Wed Oct 15 00:58:24 2014 +## Date of summary: Wed Oct 15 00:58:24 2014 ## ## Equations: -## [1] d_parent = - k_parent_sink * parent +## d_parent = - k_parent_sink * parent ## -## Method used for solution of differential equation system: -## analytical +## Model predictions using solution type analytical +## +## Fitted with method Port using 46 model solutions performed in 0.246 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100.0 state +## parent_0 96.6 state ## k_parent_sink 0.1 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_k_parent_sink -2.303 -Inf Inf +## value lower upper +## parent_0 96.600 -Inf Inf +## log_k_parent_sink -2.303 -Inf Inf ## ## Fixed parameter values: ## None @@ -1006,41 +1055,42 @@ plot(m.L4.SFO) <p>The chi<sup>2</sup> error level of 3.3% as well as the plot suggest that the model fits very well. </p> -<p>The FOMC model for comparison</p> +<p>The FOMC model for comparison:</p> -<pre><code class="r">m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE) +<pre><code class="r">m.L4.FOMC <- mkinfit("FOMC", FOCUS_2006_L4_mkin, quiet = TRUE) plot(m.L4.FOMC) </code></pre> -<p><img 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alt="plot of chunk unnamed-chunk-19"/> </p> <pre><code class="r">summary(m.L4.FOMC, data = FALSE) </code></pre> -<pre><code>## mkin version: 0.9.32 +<pre><code>## mkin version: 0.9.34 ## R version: 3.1.1 -## Date of fit: Mon Jul 14 19:59:31 2014 -## Date of summary: Mon Jul 14 19:59:31 2014 +## Date of fit: Wed Oct 15 00:58:24 2014 +## Date of summary: Wed Oct 15 00:58:24 2014 ## ## Equations: -## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent +## +## Model predictions using solution type analytical ## -## Method used for solution of differential equation system: -## analytical +## Fitted with method Port using 66 model solutions performed in 0.359 s ## ## Weighting: none ## ## Starting values for parameters to be optimised: ## value type -## parent_0 100 state -## alpha 1 deparm -## beta 10 deparm +## parent_0 96.6 state +## alpha 1.0 deparm +## beta 10.0 deparm ## ## Starting values for the transformed parameters actually optimised: -## value lower upper -## parent_0 100.000 -Inf Inf -## log_alpha 0.000 -Inf Inf -## log_beta 2.303 -Inf Inf +## value lower upper +## parent_0 96.600 -Inf Inf +## log_alpha 0.000 -Inf Inf +## log_beta 2.303 -Inf Inf ## ## Fixed parameter values: ## None diff --git a/vignettes/FOCUS_Z.Rnw b/vignettes/FOCUS_Z.Rnw index 5b0ee79e..e2a2473e 100644 --- a/vignettes/FOCUS_Z.Rnw +++ b/vignettes/FOCUS_Z.Rnw @@ -20,6 +20,7 @@ <<include=FALSE>>= require(knitr) opts_chunk$set(engine='R', tidy=FALSE) +options(width=70) @ \title{Example evaluation of FOCUS dataset Z} diff --git a/vignettes/FOCUS_Z.pdf b/vignettes/FOCUS_Z.pdf Binary files differindex a3f0ce1e..a22a3a2e 100644 --- a/vignettes/FOCUS_Z.pdf +++ b/vignettes/FOCUS_Z.pdf diff --git a/vignettes/mkin.pdf b/vignettes/mkin.pdf Binary files differindex 991e54d3..d14b86bf 100644 --- a/vignettes/mkin.pdf +++ b/vignettes/mkin.pdf |