Further formatting improvement of benchmark vignette

Also, use .rmd extension instead of .Rmd for vignettes.

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----
-title: "Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance"
-author: "Johannes Ranke"
-date: "`r Sys.Date()`"
-output:
-  html_document:
-    toc: true
-    toc_float:
-      collapsed: false
-    mathjax: null
-    fig_retina: null
-references:
-- id: usepa2015
-  title: Standard Operating Procedure for Using the NAFTA
-    Guidance to Calculate Representative Half-life Values and Characterizing
-    Pesticide Degradation
-  author:
-    - family: US EPA
-  type: report
-  issued:
-    year: 2015
-  url: https://www.epa.gov/pesticide-science-and-assessing-pesticide-risks/standard-operating-procedure-using-nafta-guidance
-vignette: >
-  %\VignetteIndexEntry{Example evaluation of FOCUS Laboratory Data L1 to L3}
-  %\VignetteEngine{knitr::rmarkdown}
-  %\VignetteEncoding{UTF-8}
----
-
-# Introduction
-
-In this document, the example evaluations provided in Attachment 1 to the SOP
-of US EPA for using the NAFTA guidance [@usepa2015] are repeated using mkin.
-The original evaluations reported in the attachment were performed using PestDF
-in version 0.8.4. Note that PestDF 0.8.13 is the version distributed at the US
-EPA website today (2019-02-26).
-
-The datasets are now distributed with the mkin package.
-
-```{r, include = FALSE}
-library(knitr)
-opts_chunk$set(tidy = FALSE, cache = FALSE, fig.height = 7)
-library("mkin", quietly = TRUE)
-```
-
-# Examples where DFOP did not converge with PestDF 0.8.4
-
-In attachment 1, it is reported that the DFOP model does not converge for these
-datasets when PestDF 0.8.4 was used. For all four datasets, the DFOP model can
-be fitted with mkin (see below). The negative half-life given by PestDF 0.8.4
-for these fits appears to be the result of a bug. The results for the other
-two models (SFO and IORE) are the same.
-
-## Example on page 5, upper panel
-
-```{r p5a}
-p5a <- nafta(NAFTA_SOP_Attachment[["p5a"]])
-plot(p5a)
-print(p5a)
-```
-
-## Example on page 5, lower panel
-
-```{r p5b}
-p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]])
-plot(p5b)
-print(p5b)
-```
-
-## Example on page 6
-
-```{r p6}
-p6 <- nafta(NAFTA_SOP_Attachment[["p6"]])
-plot(p6)
-print(p6)
-```
-
-## Example on page 7
-
-```{r p7}
-p7 <- nafta(NAFTA_SOP_Attachment[["p7"]])
-plot(p7)
-print(p7)
-```
-
-# Examples where the representative half-life deviates from the observed DT50
-
-## Example on page 8
-
-For this dataset, the IORE fit does not converge when the default starting values
-used by mkin for the IORE model are used. Therefore, a lower value for the rate
-constant is used here.
-
-```{r p8}
-p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent_sink = 1e-3))
-plot(p8)
-print(p8)
-```
-
-# Examples where SFO was not selected for an abiotic study
-
-## Example on page 9, upper panel
-
-```{r p9a}
-p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]])
-plot(p9a)
-print(p9a)
-```
-
-In this example, the residuals of the SFO indicate a lack of fit of this model,
-so even if it was an abiotic experiment, the data do not suggest a simple
-exponential decline.
-
-## Example on page 9, lower panel
-
-```{r p9b}
-p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]])
-plot(p9b)
-print(p9b)
-```
-
-Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) than
-PestDF (13.5 days). Presumably, this is related to the fact that
-PestDF gives a negative value for the proportion of the fast degradation
-which should be between 0 and 1, inclusive. This parameter is called
-f in PestDF and g in mkin. In mkin, it is restricted to the interval from
-0 to 1.
-
-## Example on page 10
-
-```{r p10}
-p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
-plot(p10)
-print(p10)
-```
-
-Here, a value below N is given for the IORE model, because the data
-suggests a faster decline towards the end of the experiment, which
-appears physically rather unlikely in the case of a photolysis study.
-It seems PestDF does not constrain N to values above zero, thus
-the slight difference in IORE model parameters between PestDF and
-mkin.
-
-# The DT50 was not observed during the study
-
-## Example on page 11
-
-```{r p11}
-p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])
-plot(p11)
-print(p11)
-```
-
-In this case, the DFOP fit reported for PestDF resulted
-in a negative value for the slower rate constant, which is
-not possible in mkin. The other results are in agreement.
-
-# N is less than 1 and the DFOP rate constants are like the SFO rate constant
-
-In the following three examples, the same results are obtained with mkin as
-reported for PestDF. As in the case on page 10, the N values below 1 are deemed
-unrealistic and appear to be the result of an overparameterisation.
-
-
-## Example on page 12, upper panel
-
-```{r p12a}
-p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])
-plot(p12a)
-print(p12a)
-```
-
-## Example on page 12, lower panel
-
-```{r p12b}
-p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
-plot(p12b)
-print(p12b)
-```
-
-## Example on page 13
-
-```{r p13}
-p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])
-plot(p13)
-print(p13)
-```
-
-# DT50 not observed in the study and DFOP problems in PestDF
-
-```{r p14}
-p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])
-plot(p14)
-print(p14)
-```
-
-The slower rate constant reported by PestDF is negative, which is not
-physically realistic, and not possible in mkin. The other fits give the same
-results in mkin and PestDF.
-
-# N is less than 1 and DFOP fraction parameter is below zero
-
-```{r p15a}
-p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
-plot(p15a)
-print(p15a)
-```
-
-```{r p15b}
-p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
-plot(p15b)
-print(p15b)
-```
-
-In mkin, only the IORE fit is affected (deemed unrealistic), as the fraction
-parameter of the DFOP model is restricted to the interval between 0 and 1 in
-mkin. The SFO fits give the same results for both mkin and PestDF.
-
-# The DFOP fraction parameter is greater than 1
-
-```{r p16}
-p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])
-plot(p16)
-print(p16)
-```
-
-In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds
-a solution with a much lower $\chi^2$ error level. As the half-life from the
-slower rate constant of the DFOP model is larger than the IORE derived half-life,
-the NAFTA recommendation obtained with mkin is to use the DFOP representative
-half-life of 8.9 days.
-
-# Conclusions
-
-The results obtained with mkin deviate from the results obtained with PestDF
-either in cases where one of the interpretive rules would apply, i.e. the
-IORE parameter N is less than one or the DFOP k values obtained with PestDF are
-equal to the SFO k values, or in cases where the DFOP model did not converge,
-which often lead to negative rate constants returned by PestDF.
-
-Therefore, mkin appears to suitable for kinetic evaluations according to the
-NAFTA guidance.
-
-# References