Step back regarding confidence intervals of formation fractions

- Don't give confidence intervals for formation fractions that belong
  to a set, only for single formation fractions
- Update the vignette with history and background
- Correct 'isotropic' into 'isometric' in the ilr documentation, the
  README and the comments in transform_odeparms
- Candidate for release to CRAN

4 files changed, 112 insertions, 19 deletions

diff --git a/vignettes/header.tex b/vignettes/header.tex
index 476415e5..e0775d34 100644
--- a/vignettes/header.tex
+++ b/vignettes/header.tex
@@ -8,7 +8,6 @@
 \usepackage[round]{natbib}

 \usepackage{amstext}

 \usepackage{hyperref}

-\usepackage[utf8]{inputenc}

 

 \newcommand{\Rpackage}[1]{{\normalfont\fontseries{b}\selectfont #1}}

 \newcommand{\Robject}[1]{\texttt{#1}}

diff --git a/vignettes/mkin.Rnw b/vignettes/mkin.Rnw
index 0ac114ed..1befe009 100644
--- a/vignettes/mkin.Rnw
+++ b/vignettes/mkin.Rnw
@@ -2,6 +2,7 @@
 %\VignetteEngine{knitr::knitr}
 \documentclass[12pt,a4paper]{article}
 \usepackage{a4wide}
+\usepackage[utf8]{inputenc}
 \input{header}
 \hypersetup{  
   pdftitle = {mkin - Routines for fitting kinetic models with one or more state variables to chemical degradation data},
@@ -29,7 +30,7 @@ chemical degradation data}
 Wissenschaftlicher Berater\\
 Kronacher Str. 8, 79639 Grenzach-Wyhlen, Germany\\[0.5cm]
 and\\[0.5cm]
-University of Bremen\\
+Privatdozent at the University of Bremen\\
 }
 \maketitle
 
@@ -58,14 +59,100 @@ metabolites.
 
 Many approaches are possible regarding the evaluation of chemical degradation
 data.  The \Rpackage{kinfit} package \citep{pkg:kinfit} in \RR{}
-\citep{rcore2013} implements the approach recommended in the kinetics report
+\citep{rcore2014} implements the approach recommended in the kinetics report
 provided by the FOrum for Co-ordination of pesticide fate models and their
 USe \citep{FOCUS2006, FOCUSkinetics2011} for simple data series for one parent
 compound in one compartment.
 
 The \Rpackage{mkin} package \citep{pkg:mkin} extends this approach to data series
-with metabolites and more than one compartment and includes the possibility 
-for back reactions.
+with transformation products, commonly termed metabolites, and to more than one
+compartment. It is also possible to include back reactions, so equilibrium reactions
+and equilibrium partitioning can be specified, although this oftentimes leads 
+to an overparameterisation of the model.
+
+When mkin was first published in May 2010, the most commonly used tools
+for fitting more complex kinetic degradation models to experimental data were KinGUI
+\citep{schaefer2007}, a MATLAB$^\circledR$ based tool with a graphical user
+interface that was specifically tailored to the task and included some output
+as proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general purpose
+compartment based tool providing infrastructure for fitting dynamic simulation
+models based on differential equations to data.
+
+At that time, the R package \Rpackage{FME} (Flexible Modelling Environment) 
+\citep{soetaert2010} was already available, and provided a good basis for
+developing a package specifically tailored to the task. The remaining challenge
+was to make it as easy as possible for the users (including the author of this
+vignette) to specify the system of differential equations and to include the
+output requested by the FOCUS guidance, such as the relative standard deviation
+that has to be assumed for the residuals, such that the $\chi^2$
+goodness-of-fit test as defined by the FOCUS kinetics workgroup would pass
+using an significance level $\alpha$ of 0.05.
+
+Also, mkin introduced using analytical solutions for parent only kinetics for
+improved optimization speed. Later, Eigenvalue based solutions were
+introduced to mkin for the case of linear differential equations (\textit{i.e.}
+where the FOMC or DFOP models were not used for the parent compound), greatly
+improving the optimization speed for these cases.
+
+Soon after the publication of mkin, two derived tools were published, namely
+KinGUII (available from Bayer Crop Science) and CAKE (commissioned to Tessella
+by Syngenta), which added a graphical user interface (GUI), and added fitting by
+iteratively reweighted least squares (IRLS) and characterisation of likely
+parameter distributions by Markov Chain Monte Carlo (MCMC) sampling.
+
+CAKE focuses on a smooth use experience, sacrificing some flexibility in the model
+definition, allowing only two primary metabolites in parallel. KinGUI offers
+quite a flexible widget for specifying complex kinetic models. Back-reactions
+(non-instanteneous equilibria) were not present in the first version of
+KinGUII, and only simple first-order models could be specified for
+transformation products.  As of May 2014 (KinGUII version 2.1), back-reactions
+and biphasic modelling of metabolites are also available in KinGUII.
+
+Currently (May 2014), the main feature available in \Rpackage{mkin} which is
+not present in KinGUII or CAKE, is the estimation of parameter confidence
+intervals based on transformed parameters. For rate constants, the log
+transformation is used, as proposed by Bates and Watts \citep[p. 77, p.
+149]{bates1988}. Approximate intervals are constructed for the transformed rate
+constants \citep[compare][p. 153]{bates1988}, \textit{i.e.} for their logarithms.
+Confidence intervals for the rate constants are then obtained using the
+appropriate backtransformation using the exponential function.
+
+In the first version of \Rpackage{mkin} allowing for specifying models using 
+formation fractions, a home-made reparameterisation was used in order to ensure
+that the sum of formation fractions would not exceed unity. 
+
+This method is still used in the current version of KinGUII (v2.1), with a
+modification that allows for fixing the pathway to sink to zero. CAKE uses
+penalties in the objective function in order to enforce this constraint.
+
+In 2012, an alternative reparameterisation of the formation fractions was
+proposed together with René Lehmann \citep{ranke2012}, based on isometric
+logratio transformation (ILR). The aim was to improve the validity of the
+linear approximation of the objective function during the parameter
+estimation procedure as well as in the subsequent calculation of parameter
+confidence intervals.
+
+In the first attempt at providing improved parameter confidence intervals
+introduced to \Rpackage{mkin} in 2013, confidence intervals obtained from 
+FME on the transformed parameters were simply all backtransformed one by one
+to yield asymetric confidence intervals for the backtransformed parameters.
+
+However, while there is a 1:1 relation between the rate constants in the model
+and the transformed parameters fitted in the model, the parameters obtained by the
+isometric logratio transformation are calculated from the set of formation
+fractions that quantify the paths to each of the compounds formed from a
+specific parent compound, and no such 1:1 relation exists.
+
+Therefore, parameter confidence intervals for formation fractions obtained with
+this method only appear valid for the case of a single transformation product, where 
+only one formation fraction is to be estimated, directly corresponding to one
+component of the ilr transformed parameter.
+
+The confidence intervals obtained by backtransformation for the cases where a 
+1:1 relation between transformed and original parameter exist are considered by 
+the author of this vignette to be more accurate than those obtained using a
+re-estimation of the Hessian matrix after backtransformation, as implemented 
+in the FME package.
 
 \bibliographystyle{plainnat}
 \bibliography{references}
diff --git a/vignettes/mkin.pdf b/vignettes/mkin.pdf
index 0e4d1be8..12293506 100644
--- a/vignettes/mkin.pdf
+++ b/vignettes/mkin.pdf
diff --git a/vignettes/references.bib b/vignettes/references.bib
index e069daf2..88caea60 100644
--- a/vignettes/references.bib
+++ b/vignettes/references.bib
@@ -1,7 +1,7 @@
 % This file was originally created with JabRef 2.7b.
 % Encoding: ISO8859_1
 
-@BOOK{bates88,
+@BOOK{bates1988,
   title = {Nonlinear regression and its applications},
   publisher = {Wiley-Interscience},
   year = {1988},
@@ -29,12 +29,12 @@
   url = {http://focus.jrc.ec.europa.eu/dk}
 }
 
-@MANUAL{rcore2013,
+@MANUAL{rcore2014,
   title = {\textsf{R}: A Language and Environment for Statistical Computing},
   author = {{R Development Core Team}},
   organization = {R Foundation for Statistical Computing},
   address = {Vienna, Austria},
-  year = {2013},
+  year = {2014},
   note = {{ISBN} 3-900051-07-0},
   url = {http://www.R-project.org}
 }
@@ -52,21 +52,20 @@
 	variables to chemical degradation data},
   author = {Johannes Ranke},
   year = {2013},
-  url = {http://CRAN.R-project.org/package/kinfit}
+  url = {http://CRAN.R-project.org/package=mkin}
 }
 
-@INPROCEEDINGS{schaefer2007,
-  author = {D. Sch\"{a}fer and M. Mikolasch and P. Rainbird and B. Harvey},
-  title = {{KinGUI}: a new kinetic software tool for evaluations according to
-	FOCUS degradation kinetics},
-  booktitle = {Proceedings of the XIII Symposium Pesticide Chemistry},
-  year = {2007},
-  editor = {Del Re A. A. M. and Capri E. and Fragoulis G. and Trevisan M.},
-  pages = {916--923},
-  address = {Piacenza}
+@Inproceedings{   schaefer2007,
+  title         = {{KinGUI}: a new kinetic software tool for evaluations according to {FOCUS} degradation kinetics},
+  author       = {D. Sch\"{a}fer and B. Mikolasch and P. Rainbird and B. Harvey},
+  booktitle    = {Proceedings of the XIII Symposium Pesticide Chemistry},
+  editor       = {Del Re A. A. M. and Capri E. and Fragoulis G. and Trevisan M.},
+  year          = {2007},
+  address       = {Piacenza},
+  pages         = {916--923}
 }
 
-@ARTICLE{soetaert10,
+@ARTICLE{soetaert2010,
   author = {Karline Soetaert and Thomas Petzoldt},
   title = {Inverse Modelling, Sensitivity and Monte Carlo Analysis in {R} Using
 	Package {FME}},
@@ -77,3 +76,11 @@
   number = {3},
   url = {http://www.jstatsoft.org/v33/i03/}
 }
+
+@Inproceedings{   ranke2012,
+  title         = {Parameter reliability in kinetic evaluation of environmental metabolism data - Assessment and the influence of model specification},
+  author       = {J. Ranke and R. Lehmann},
+  booktitle    = {SETAC World 20-24 May},
+  year          = {2012},
+  address       = {Berlin}
+}