diff --git a/NAMESPACE b/NAMESPACE
index 2c152dab..bf213995 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -40,6 +40,7 @@ export(is.egret)
export(logPretty1)
export(logPretty3)
export(makeAnnualSeries)
+export(makeAugmentedSample)
export(mergeReport)
export(modelEstimation)
export(monthInfo)
diff --git a/R/EGRET.R b/R/EGRET.R
index 51cbcaec..f92359d1 100644
--- a/R/EGRET.R
+++ b/R/EGRET.R
@@ -34,12 +34,19 @@ NULL
#' Data is a named list of the Daily, Sample, INFO dataframes, and the surface matrix.
#'
#' @name Choptank_eList
+#' @rdname sampleData
#' @docType data
#' @keywords water quality data
#' @examples
#' head(Choptank_eList$Daily)
NULL
+#' @name Arkansas_eList
+#' @rdname sampleData
+#' @examples
+#' head(Arkansas_eList$Daily)
+NULL
+
#' Constants included with EGRET
#'
#'\itemize{
diff --git a/R/fluxBiasStat.R b/R/fluxBiasStat.R
index a0b3afc9..03093b05 100644
--- a/R/fluxBiasStat.R
+++ b/R/fluxBiasStat.R
@@ -16,8 +16,8 @@
#' fluxBias <- fluxBiasStat(Sample)
fluxBiasStat<-function(localSample) {
sumLow<-sum(localSample$ConcLow*localSample$Q,na.rm=TRUE)
- sumHigh<-sum(localSample$ConcHigh*localSample$Q)
- sumEst<-sum(localSample$ConcHat*localSample$Q)
+ sumHigh<-sum(localSample$ConcHigh*localSample$Q,na.rm=TRUE)
+ sumEst<-sum(localSample$ConcHat*localSample$Q,na.rm=TRUE)
bias1<-(sumEst-sumHigh)/sumEst
bias2<-(sumEst-sumLow)/sumEst
bias3<-(bias1+bias2)/2
diff --git a/R/makeRandomResiduals.R b/R/makeRandomResiduals.R
index e504413a..273d0dd2 100644
--- a/R/makeRandomResiduals.R
+++ b/R/makeRandomResiduals.R
@@ -7,6 +7,7 @@
#' @param eList named list with at least the Daily dataframe
#' @keywords water-quality statistics
#' @importFrom truncnorm rtruncnorm
+#' @export
#' @return eList named list with modified Daily data frame.
makeAugmentedSample <- function(eList){
diff --git a/data/Arkansas_eList.RData b/data/Arkansas_eList.RData
new file mode 100644
index 00000000..4f5dea3d
Binary files /dev/null and b/data/Arkansas_eList.RData differ
diff --git a/inst/doc/EGRET.pdf b/inst/doc/EGRET.pdf
index 72e495ca..a0deeac0 100644
Binary files a/inst/doc/EGRET.pdf and b/inst/doc/EGRET.pdf differ
diff --git a/inst/doc/rResid.R b/inst/doc/rResid.R
new file mode 100644
index 00000000..db3ee959
--- /dev/null
+++ b/inst/doc/rResid.R
@@ -0,0 +1,28 @@
+## ------------------------------------------------------------------------
+library(EGRET)
+eList <- Arkansas_eList
+plotConcTime(eList)
+
+## ------------------------------------------------------------------------
+plotConcQ(eList,qUnit=4)
+
+## ---- eval=FALSE---------------------------------------------------------
+# eList <- makeAugmentedSample(eList)
+# plotConcQ(eList, qUnit = 4, rResid = TRUE)
+# # now do it all over again
+# eList <- makeAugmentedSample(eList)
+# plotConcQ(eList, qUnit = 4, rResid = TRUE)
+
+## ------------------------------------------------------------------------
+plotResidTime(eList, rResid = TRUE)
+plotResidQ(eList, qUnit = 4, rResid = TRUE)
+
+## ----eval=FALSE----------------------------------------------------------
+# eList <- makeAugmentedSample(eList)
+
+## ---- eval=FALSE---------------------------------------------------------
+# multiPlotDataOverview(eList, qUnit = 4, rResid = TRUE)
+
+## ----fig.height=10, fig.width=8------------------------------------------
+fluxBiasMulti(eList, qUnit = 4, fluxUnit = 9, rResid = TRUE)
+
diff --git a/inst/doc/rResid.Rmd b/inst/doc/rResid.Rmd
new file mode 100644
index 00000000..b989ef0f
--- /dev/null
+++ b/inst/doc/rResid.Rmd
@@ -0,0 +1,103 @@
+---
+title: "Using Random Residuals for Censored Data in EGRET"
+author: "Robert M. Hirsch"
+date: "`r format(Sys.time(), '%d %B, %Y')`"
+output:
+ rmarkdown::html_vignette:
+ toc: true
+ number_sections: true
+ fig_caption: yes
+ fig_height: 7
+ fig_width: 7
+vignette: >
+ %\VignetteEngine{knitr::rmarkdown}
+ %\VignetteIndexEntry{gsplot Intro}
+ \usepackage[utf8]{inputenc}
+---
+
+# Introduction
+
+When censored data are present in a water quality data set, depicting them in any type of scatter plot is a challenge. This applies to the problem of plotting the actual data values or plotting the residuals. What follows is an example that shows the problem.
+
+```{r}
+library(EGRET)
+eList <- Arkansas_eList
+plotConcTime(eList)
+```
+
+The solid vertical lines, which represent the range of values that a given censored value could be, is very distracting in terms of getting a picture of the overall behavior of the data. We can see this even more if we try to look at the relationship of concentration to discharge.
+
+```{r}
+plotConcQ(eList,qUnit=4)
+```
+
+It is difficult to see the relationship between ammonia concentration and discharge. If we look at residuals from a fitted WRTDS model and discharge we also find it difficult to see if the pattern looks reasonable (a horizontal cloud of points centered on the zero residual line) or if there is some substantial curvature to the relationship.
+
+```{}
+plotResidQ(eList,qUnit=4)
+```
+
+Here again, the plot is not very informative. What solutions might exist to resolve this problem of the graphical representation of the censored data?
+
+# The concept of randomized estimates of censored values
+
+If we think about a fitted WRTDS model, what it is telling us is this: For some particular date and some particular discharge the model estimates a unique conditional probability distribution of concentration. That distribution is always a log normal distribution (that means that the log of concentration is normal) and that distribution of the log concentration has a particular mean (which in the EGRET package is always called `yHat`) and a particular standard deviation (which is always called `SE`). The `Daily` data frame has columns with these names, showing their value for each day of the record. However, for days on which there was a sample taken but that sample was reported as a "less than" value, we also know that there is an upper bound to what the concentration could have been. It is the reporting limit. *As an aside, all of the following discussion would hold for an interval censored value. EGRET allows for these but they are not common. For simplicity of the discussion we will only consider left censored data, but the code being used here considers interval censored data as well.*
+
+So, what we can say about some particular censored value is that the log of the true value has a mean of `yHat` and a standard deviation of `SE`, it is normally distributed, but is constrained to be in the part of the normal distribution which is less than the log of the reporting limit. Such a random variable is known as a truncated normal random variable. Fortunately there is an R package entirely focused on the truncated normal distribution. It is called `truncnorm`. We can use `truncnorm` to generate a random number for each of the censored values and this random number will be drawn from the lower portion of normal distribution with the correct mean, standard deviation, and upper bound. The idea is to create these random values to substitute for the censored observations. We call them the `rObserved` values and they reside in an augmented version of the `Sample` data frame in a column called `Sample$rObserved`. What is most important to understand is that these randomly generated values are never used in any of the WRTDS computations that result in estimates of daily concentrations or fluxes, or annual average concentrations or fluxes, or any trends. These randomly generated values are created strictly to provide a more-easily interpreted set of diagonstic graphics. Here is an example of a plot of concentration versus time using this approach.
+
+The solid circles are the uncensored observations and the open circles are these `rObserved` values. One thing to note is that if these values were to be generated a second time the graph would look slightly different. There is no unique set of values that will be plotted. The random numbers used will be different if we go back to the same data set and generate them again. Below we show such a figure and then redo the graphic with a second set of random numbers. The code is shown with the graphics.
+
+```{r, eval=FALSE}
+eList <- makeAugmentedSample(eList)
+plotConcQ(eList, qUnit = 4, rResid = TRUE)
+# now do it all over again
+eList <- makeAugmentedSample(eList)
+plotConcQ(eList, qUnit = 4, rResid = TRUE)
+```
+
+Careful examination of these two figures reveals that the black dots are exactly the same in both, but the open circles are different between the two. In looking at these kinds of plots we are not necessarily looking to see what actually happened on a particular day, but rather to understand the pattern of the relationship between the two variables being plotted.
+
+# Randomized residuals
+
+Many of the diagnostics we use in EGRET are plots of residuals (on the y-axis) versus predicted value, or time, or discharge (on the x-axis). Once we have this `rObserved` value, we can compute a randomized residual which is called `rResid` and is stored as `Sample$rResid` in EGRET. The computation is this:
+
+rResid = rObserved - predicted value
+
+All three variables in this equation are in log concentration units.
+
+We can look at our residuals plots in the following manner (using the second set of rObserved values computed above).
+
+```{r}
+plotResidTime(eList, rResid = TRUE)
+plotResidQ(eList, qUnit = 4, rResid = TRUE)
+```
+
+# Details for how to include random residuals in your computations
+
+In order to use the `rObserved` and `rResid` in making graphs in EGRET the process is the following.
+
+1. Bring in your data and create the `eList` in the usual way: `eList <- mergeReport(INFO,Daily,Sample)`
+2. Run `modelEstimation` in the usual way: `eList <- modelEstimation(eList)`
+3. Then augment the `Sample` data frame that is inside of the `eList` with the command:
+
+```{r eval=FALSE}
+eList <- makeAugmentedSample(eList)
+```
+
+4. To produce any one of the following graphics, using the `rObserved` or `rResid` values simply add the argument `rResid = TRUE` to the call to the graphical function. Note that it doesn't matter if what is being plotted is an observed value or a residual, the argument is always `rResid = TRUE`. The original option of showing the vertical lines for censored values remains available as the default for any of these functions. The call can either say `rResid = FALSE` or just not include `rResid` in the argument list and the graphs will appear without these random values and without the open circle/closed circle symbology. The functions where this approach applies are these: `plotConcPred, plotConcQ, plotConcTime, plotConcTimeDaily, plotFluxPred, plotFluxQ, plotFluxTImeDaily, plotResidPred, plotResidQ, plotResidTime`. It is also available in the two multiple plot functions: `multiPlotOverview`, and `fluxBiasMulti`.
+
+For example.
+
+```{r, eval=FALSE}
+multiPlotDataOverview(eList, qUnit = 4, rResid = TRUE)
+```
+
+```{r fig.height=10, fig.width=8}
+fluxBiasMulti(eList, qUnit = 4, fluxUnit = 9, rResid = TRUE)
+```
+
+# A final thought
+
+In the EGRET User Guide (http://pubs.usgs.gov/tm/04/a10/) the distinction is made between the graphical methods that are used to simply descirbe the data (and these graphics shown in `multiPlotDataOverview`) as distinct from graphical methods that are used to describe the WRTDS model of the system (such as the graphs in `fluxBiasMulti`). If the `rResid = TRUE` option is used with `multiPlotDataOverview`, or other graphical functions that normally don't depend on the WRTDS model, they now become a hybrid, because they are using the WRTDS model to generate the random values used in the graphs. Take a graph such as `plotConcQ`. With `rResid = FALSE` it is a pure representation of the data. No assumptions are being made. But, when `rResid = TRUE`, it is now a representation of the data which is partly based on an assumption that the fitted WRTDS model is indeed a correct model. The fitted WRTDS model is partly determining the placement of the random values that are less than the reporting limit. If the analyst wants a "pure" representation of the data without any assumed model for graphing, then the `rResid` option should be set to `FALSE`.
+
+Also, with figures such as shown in `fluxBiasMulti`, there is a kind of circularity in the logic. The circularity is this: we are using the graphs to assesses the adequacy of the model fit, but we are using the model to estimate some of the observations. This circularity is not a fatal flaw to the approach, but is a reality that the user should consider. On balance, the authors think that using `rResid = TRUE` in all of the plots to which it applies is a beneficial approach because it enhances the ability of the analyst to interpret the figures. But, we reiterate here, the choice of using the random approach or not has no bearing whatsoever on the quantitative outputs that the WRTDS method in the EGRET package produces.
diff --git a/inst/doc/rResid.html b/inst/doc/rResid.html
new file mode 100644
index 00000000..11244713
--- /dev/null
+++ b/inst/doc/rResid.html
@@ -0,0 +1,159 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Using Random Residuals for Censored Data in EGRET
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
When censored data are present in a water quality data set, depicting them in any type of scatter plot is a challenge. This applies to the problem of plotting the actual data values or plotting the residuals. What follows is an example that shows the problem.
The solid vertical lines, which represent the range of values that a given censored value could be, is very distracting in terms of getting a picture of the overall behavior of the data. We can see this even more if we try to look at the relationship of concentration to discharge.
+
plotConcQ(eList,qUnit=4)
+
+
It is difficult to see the relationship between ammonia concentration and discharge. If we look at residuals from a fitted WRTDS model and discharge we also find it difficult to see if the pattern looks reasonable (a horizontal cloud of points centered on the zero residual line) or if there is some substantial curvature to the relationship.
+
plotResidQ(eList,qUnit=4)
+
Here again, the plot is not very informative. What solutions might exist to resolve this problem of the graphical representation of the censored data?
+
+
+
2 The concept of randomized estimates of censored values
+
If we think about a fitted WRTDS model, what it is telling us is this: For some particular date and some particular discharge the model estimates a unique conditional probability distribution of concentration. That distribution is always a log normal distribution (that means that the log of concentration is normal) and that distribution of the log concentration has a particular mean (which in the EGRET package is always called yHat) and a particular standard deviation (which is always called SE). The Daily data frame has columns with these names, showing their value for each day of the record. However, for days on which there was a sample taken but that sample was reported as a “less than” value, we also know that there is an upper bound to what the concentration could have been. It is the reporting limit. As an aside, all of the following discussion would hold for an interval censored value. EGRET allows for these but they are not common. For simplicity of the discussion we will only consider left censored data, but the code being used here considers interval censored data as well.
+
So, what we can say about some particular censored value is that the log of the true value has a mean of yHat and a standard deviation of SE, it is normally distributed, but is constrained to be in the part of the normal distribution which is less than the log of the reporting limit. Such a random variable is known as a truncated normal random variable. Fortunately there is an R package entirely focused on the truncated normal distribution. It is called truncnorm. We can use truncnorm to generate a random number for each of the censored values and this random number will be drawn from the lower portion of normal distribution with the correct mean, standard deviation, and upper bound. The idea is to create these random values to substitute for the censored observations. We call them the rObserved values and they reside in an augmented version of the Sample data frame in a column called Sample$rObserved. What is most important to understand is that these randomly generated values are never used in any of the WRTDS computations that result in estimates of daily concentrations or fluxes, or annual average concentrations or fluxes, or any trends. These randomly generated values are created strictly to provide a more-easily interpreted set of diagonstic graphics. Here is an example of a plot of concentration versus time using this approach.
+
The solid circles are the uncensored observations and the open circles are these rObserved values. One thing to note is that if these values were to be generated a second time the graph would look slightly different. There is no unique set of values that will be plotted. The random numbers used will be different if we go back to the same data set and generate them again. Below we show such a figure and then redo the graphic with a second set of random numbers. The code is shown with the graphics.
+
eList <-makeAugmentedSample(eList)
+plotConcQ(eList, qUnit =4, rResid =TRUE)
+# now do it all over again
+eList <-makeAugmentedSample(eList)
+plotConcQ(eList, qUnit =4, rResid =TRUE)
+
Careful examination of these two figures reveals that the black dots are exactly the same in both, but the open circles are different between the two. In looking at these kinds of plots we are not necessarily looking to see what actually happened on a particular day, but rather to understand the pattern of the relationship between the two variables being plotted.
+
+
+
3 Randomized residuals
+
Many of the diagnostics we use in EGRET are plots of residuals (on the y-axis) versus predicted value, or time, or discharge (on the x-axis). Once we have this rObserved value, we can compute a randomized residual which is called rResid and is stored as Sample$rResid in EGRET. The computation is this:
+
rResid = rObserved - predicted value
+
All three variables in this equation are in log concentration units.
+
We can look at our residuals plots in the following manner (using the second set of rObserved values computed above).
+
plotResidTime(eList, rResid =TRUE)
+
+
plotResidQ(eList, qUnit =4, rResid =TRUE)
+
+
+
+
4 Details for how to include random residuals in your computations
+
In order to use the rObserved and rResid in making graphs in EGRET the process is the following.
+
+
Bring in your data and create the eList in the usual way: eList <- mergeReport(INFO,Daily,Sample)
+
Run modelEstimation in the usual way: eList <- modelEstimation(eList)
+
Then augment the Sample data frame that is inside of the eList with the command:
+
+
eList <-makeAugmentedSample(eList)
+
+
To produce any one of the following graphics, using the rObserved or rResid values simply add the argument rResid = TRUE to the call to the graphical function. Note that it doesn’t matter if what is being plotted is an observed value or a residual, the argument is always rResid = TRUE. The original option of showing the vertical lines for censored values remains available as the default for any of these functions. The call can either say rResid = FALSE or just not include rResid in the argument list and the graphs will appear without these random values and without the open circle/closed circle symbology. The functions where this approach applies are these: plotConcPred, plotConcQ, plotConcTime, plotConcTimeDaily, plotFluxPred, plotFluxQ, plotFluxTImeDaily, plotResidPred, plotResidQ, plotResidTime. It is also available in the two multiple plot functions: multiPlotOverview, and fluxBiasMulti.
In the EGRET User Guide (http://pubs.usgs.gov/tm/04/a10/) the distinction is made between the graphical methods that are used to simply descirbe the data (and these graphics shown in multiPlotDataOverview) as distinct from graphical methods that are used to describe the WRTDS model of the system (such as the graphs in fluxBiasMulti). If the rResid = TRUE option is used with multiPlotDataOverview, or other graphical functions that normally don’t depend on the WRTDS model, they now become a hybrid, because they are using the WRTDS model to generate the random values used in the graphs. Take a graph such as plotConcQ. With rResid = FALSE it is a pure representation of the data. No assumptions are being made. But, when rResid = TRUE, it is now a representation of the data which is partly based on an assumption that the fitted WRTDS model is indeed a correct model. The fitted WRTDS model is partly determining the placement of the random values that are less than the reporting limit. If the analyst wants a “pure” representation of the data without any assumed model for graphing, then the rResid option should be set to FALSE.
+
Also, with figures such as shown in fluxBiasMulti, there is a kind of circularity in the logic. The circularity is this: we are using the graphs to assesses the adequacy of the model fit, but we are using the model to estimate some of the observations. This circularity is not a fatal flaw to the approach, but is a reality that the user should consider. On balance, the authors think that using rResid = TRUE in all of the plots to which it applies is a beneficial approach because it enhances the ability of the analyst to interpret the figures. But, we reiterate here, the choice of using the random approach or not has no bearing whatsoever on the quantitative outputs that the WRTDS method in the EGRET package produces.
+
+
+
+
+
+
+
+
+
diff --git a/man/Choptank_eList.Rd b/man/sampleData.Rd
similarity index 89%
rename from man/Choptank_eList.Rd
rename to man/sampleData.Rd
index c15f6e11..6106d9d7 100644
--- a/man/Choptank_eList.Rd
+++ b/man/sampleData.Rd
@@ -2,6 +2,7 @@
% Please edit documentation in R/EGRET.R
\docType{data}
\name{Choptank_eList}
+\alias{Arkansas_eList}
\alias{Choptank_eList}
\title{Example eList}
\description{
@@ -10,6 +11,7 @@ Data is a named list of the Daily, Sample, INFO dataframes, and the surface matr
}
\examples{
head(Choptank_eList$Daily)
+head(Arkansas_eList$Daily)
}
\keyword{data}
\keyword{quality}
diff --git a/vignettes/rResid.Rmd b/vignettes/rResid.Rmd
new file mode 100644
index 00000000..b989ef0f
--- /dev/null
+++ b/vignettes/rResid.Rmd
@@ -0,0 +1,103 @@
+---
+title: "Using Random Residuals for Censored Data in EGRET"
+author: "Robert M. Hirsch"
+date: "`r format(Sys.time(), '%d %B, %Y')`"
+output:
+ rmarkdown::html_vignette:
+ toc: true
+ number_sections: true
+ fig_caption: yes
+ fig_height: 7
+ fig_width: 7
+vignette: >
+ %\VignetteEngine{knitr::rmarkdown}
+ %\VignetteIndexEntry{gsplot Intro}
+ \usepackage[utf8]{inputenc}
+---
+
+# Introduction
+
+When censored data are present in a water quality data set, depicting them in any type of scatter plot is a challenge. This applies to the problem of plotting the actual data values or plotting the residuals. What follows is an example that shows the problem.
+
+```{r}
+library(EGRET)
+eList <- Arkansas_eList
+plotConcTime(eList)
+```
+
+The solid vertical lines, which represent the range of values that a given censored value could be, is very distracting in terms of getting a picture of the overall behavior of the data. We can see this even more if we try to look at the relationship of concentration to discharge.
+
+```{r}
+plotConcQ(eList,qUnit=4)
+```
+
+It is difficult to see the relationship between ammonia concentration and discharge. If we look at residuals from a fitted WRTDS model and discharge we also find it difficult to see if the pattern looks reasonable (a horizontal cloud of points centered on the zero residual line) or if there is some substantial curvature to the relationship.
+
+```{}
+plotResidQ(eList,qUnit=4)
+```
+
+Here again, the plot is not very informative. What solutions might exist to resolve this problem of the graphical representation of the censored data?
+
+# The concept of randomized estimates of censored values
+
+If we think about a fitted WRTDS model, what it is telling us is this: For some particular date and some particular discharge the model estimates a unique conditional probability distribution of concentration. That distribution is always a log normal distribution (that means that the log of concentration is normal) and that distribution of the log concentration has a particular mean (which in the EGRET package is always called `yHat`) and a particular standard deviation (which is always called `SE`). The `Daily` data frame has columns with these names, showing their value for each day of the record. However, for days on which there was a sample taken but that sample was reported as a "less than" value, we also know that there is an upper bound to what the concentration could have been. It is the reporting limit. *As an aside, all of the following discussion would hold for an interval censored value. EGRET allows for these but they are not common. For simplicity of the discussion we will only consider left censored data, but the code being used here considers interval censored data as well.*
+
+So, what we can say about some particular censored value is that the log of the true value has a mean of `yHat` and a standard deviation of `SE`, it is normally distributed, but is constrained to be in the part of the normal distribution which is less than the log of the reporting limit. Such a random variable is known as a truncated normal random variable. Fortunately there is an R package entirely focused on the truncated normal distribution. It is called `truncnorm`. We can use `truncnorm` to generate a random number for each of the censored values and this random number will be drawn from the lower portion of normal distribution with the correct mean, standard deviation, and upper bound. The idea is to create these random values to substitute for the censored observations. We call them the `rObserved` values and they reside in an augmented version of the `Sample` data frame in a column called `Sample$rObserved`. What is most important to understand is that these randomly generated values are never used in any of the WRTDS computations that result in estimates of daily concentrations or fluxes, or annual average concentrations or fluxes, or any trends. These randomly generated values are created strictly to provide a more-easily interpreted set of diagonstic graphics. Here is an example of a plot of concentration versus time using this approach.
+
+The solid circles are the uncensored observations and the open circles are these `rObserved` values. One thing to note is that if these values were to be generated a second time the graph would look slightly different. There is no unique set of values that will be plotted. The random numbers used will be different if we go back to the same data set and generate them again. Below we show such a figure and then redo the graphic with a second set of random numbers. The code is shown with the graphics.
+
+```{r, eval=FALSE}
+eList <- makeAugmentedSample(eList)
+plotConcQ(eList, qUnit = 4, rResid = TRUE)
+# now do it all over again
+eList <- makeAugmentedSample(eList)
+plotConcQ(eList, qUnit = 4, rResid = TRUE)
+```
+
+Careful examination of these two figures reveals that the black dots are exactly the same in both, but the open circles are different between the two. In looking at these kinds of plots we are not necessarily looking to see what actually happened on a particular day, but rather to understand the pattern of the relationship between the two variables being plotted.
+
+# Randomized residuals
+
+Many of the diagnostics we use in EGRET are plots of residuals (on the y-axis) versus predicted value, or time, or discharge (on the x-axis). Once we have this `rObserved` value, we can compute a randomized residual which is called `rResid` and is stored as `Sample$rResid` in EGRET. The computation is this:
+
+rResid = rObserved - predicted value
+
+All three variables in this equation are in log concentration units.
+
+We can look at our residuals plots in the following manner (using the second set of rObserved values computed above).
+
+```{r}
+plotResidTime(eList, rResid = TRUE)
+plotResidQ(eList, qUnit = 4, rResid = TRUE)
+```
+
+# Details for how to include random residuals in your computations
+
+In order to use the `rObserved` and `rResid` in making graphs in EGRET the process is the following.
+
+1. Bring in your data and create the `eList` in the usual way: `eList <- mergeReport(INFO,Daily,Sample)`
+2. Run `modelEstimation` in the usual way: `eList <- modelEstimation(eList)`
+3. Then augment the `Sample` data frame that is inside of the `eList` with the command:
+
+```{r eval=FALSE}
+eList <- makeAugmentedSample(eList)
+```
+
+4. To produce any one of the following graphics, using the `rObserved` or `rResid` values simply add the argument `rResid = TRUE` to the call to the graphical function. Note that it doesn't matter if what is being plotted is an observed value or a residual, the argument is always `rResid = TRUE`. The original option of showing the vertical lines for censored values remains available as the default for any of these functions. The call can either say `rResid = FALSE` or just not include `rResid` in the argument list and the graphs will appear without these random values and without the open circle/closed circle symbology. The functions where this approach applies are these: `plotConcPred, plotConcQ, plotConcTime, plotConcTimeDaily, plotFluxPred, plotFluxQ, plotFluxTImeDaily, plotResidPred, plotResidQ, plotResidTime`. It is also available in the two multiple plot functions: `multiPlotOverview`, and `fluxBiasMulti`.
+
+For example.
+
+```{r, eval=FALSE}
+multiPlotDataOverview(eList, qUnit = 4, rResid = TRUE)
+```
+
+```{r fig.height=10, fig.width=8}
+fluxBiasMulti(eList, qUnit = 4, fluxUnit = 9, rResid = TRUE)
+```
+
+# A final thought
+
+In the EGRET User Guide (http://pubs.usgs.gov/tm/04/a10/) the distinction is made between the graphical methods that are used to simply descirbe the data (and these graphics shown in `multiPlotDataOverview`) as distinct from graphical methods that are used to describe the WRTDS model of the system (such as the graphs in `fluxBiasMulti`). If the `rResid = TRUE` option is used with `multiPlotDataOverview`, or other graphical functions that normally don't depend on the WRTDS model, they now become a hybrid, because they are using the WRTDS model to generate the random values used in the graphs. Take a graph such as `plotConcQ`. With `rResid = FALSE` it is a pure representation of the data. No assumptions are being made. But, when `rResid = TRUE`, it is now a representation of the data which is partly based on an assumption that the fitted WRTDS model is indeed a correct model. The fitted WRTDS model is partly determining the placement of the random values that are less than the reporting limit. If the analyst wants a "pure" representation of the data without any assumed model for graphing, then the `rResid` option should be set to `FALSE`.
+
+Also, with figures such as shown in `fluxBiasMulti`, there is a kind of circularity in the logic. The circularity is this: we are using the graphs to assesses the adequacy of the model fit, but we are using the model to estimate some of the observations. This circularity is not a fatal flaw to the approach, but is a reality that the user should consider. On balance, the authors think that using `rResid = TRUE` in all of the plots to which it applies is a beneficial approach because it enhances the ability of the analyst to interpret the figures. But, we reiterate here, the choice of using the random approach or not has no bearing whatsoever on the quantitative outputs that the WRTDS method in the EGRET package produces.
