# NeuralNetTools 1.0.0 now on CRAN

After successfully navigating the perilous path of CRAN submission, I’m pleased to announce that NeuralNetTools is now available!  From the description file, the package provides visualization and analysis tools to aid in the interpretation of neural networks, including functions for plotting, variable importance, and sensitivity analyses. I’ve written at length about each of these functions (see here, here, and here), so I’ll only provide an overview in this post. Most of these functions have remained unchanged since I initially described them, with one important change for the Garson function. Rather than reporting variable importance as -1 to 1 for each variable, I’ve returned to the original method that reports importance as 0 to 1. I was getting inconsistent results after toying around with some additional examples and decided the original method was a safer approach for the package. The modified version can still be installed from my GitHub gist. The development version of the package is also available on GitHub. Please use the development page to report issues.

The package is fairly small but I think the functions that have been included can help immensely in evaluating neural network results. The main functions include:

• plotnet: Plot a neural interpretation diagram for a neural network object, original blog post here
# install, load package
install.packages(NeuralNetTools)
library(NeuralNetTools)

# create model
library(neuralnet)
AND <- c(rep(0, 7), 1)
OR <- c(0, rep(1, 7))
binary_data <- data.frame(expand.grid(c(0, 1), c(0, 1), c(0, 1)), AND, OR)
mod <- neuralnet(AND + OR ~ Var1 + Var2 + Var3, binary_data,
hidden = c(6, 12, 8), rep = 10, err.fct = 'ce', linear.output = FALSE)

# plotnet
par(mar = numeric(4), family = 'serif')
plotnet(mod, alpha = 0.6)


• garson: Relative importance of input variables in neural networks using Garson’s algorithm, original blog post here
# create model
library(RSNNS)
data(neuraldat)
x <- neuraldat[, c('X1', 'X2', 'X3')]
y <- neuraldat[, 'Y1']
mod <- mlp(x, y, size = 5)

# garson
garson(mod, 'Y1')


• lekprofile: Conduct a sensitivity analysis of model responses in a neural network to input variables using Lek’s profile method, original blog post here
# create model
library(nnet)
data(neuraldat)
mod <- nnet(Y1 ~ X1 + X2 + X3, data = neuraldat, size = 5)

# lekprofile
lekprofile(mod)


A few other functions are available that are helpers to the main functions. See the documentation for a full list.

All the functions have S3 methods for most of the neural network classes available in R, making them quite flexible. This includes methods for nnet models from the nnet package, mlp models from the RSNNS package, nn models from the neuralnet package, and train models from the caret package. The functions also have methods for numeric vectors if the user prefers inputting raw weight vectors for each function, as for neural network models created outside of R.

Huge thanks to Hadley Wickham for his packages that have helped immensely with this process, namely devtools and roxygen2. I also relied extensively on his new web book for package development. Any feedback regarding NeuralNetTools or its further development is appreciated!

Cheers,

Marcus

# Back to square one – R and RStudio installation

I remember my first experience installing R. Basic installation can be humbling for someone not familiar with mirror networks or file binaries. I remember not knowing the difference between base and contrib… which one to select? The concept of CRAN and mirrors was also new to me. Which location do I choose and are they all the same? What the hell is a tar ball?? Simple challenges like these can be discouraging to first-time users that have never experienced the world of open-source software. Although these challenges seem silly now, they were very real at the time. Additionally, help documentation is not readily accessible for the novice. This month I decided to step back and present a simple guide to installing R and RStudio. Surprisingly, a quick Google search was unable to locate comparable guides. I realize that most people don’t have any problem installing R, but I can remember a time when step-by-step installation instructions would have been very appreciated. Also, I made this guide for a workshop and I’m presenting it here so I don’t have to create a different blog post for this month… I am lazy. Files for creating the guide are available here.

.

Cheers,

Marcus

# Some love for ggplot2

With all the recent buzz about ggvis (this, this, and this) it’s often easy to forget all that ggplot2 offers as a graphics package. True, ggplot is a static approach to graphing unlike ggvis but it has fundamentally changed the way we think about plots in R. I recently spent some time thinking about some of the more useful features of ggplot2 to answer the question ‘what is offered by ggplot2 that one can’t do with the base graphics functions?’ First-time users of ggplot2 are often confused by the syntax, yet it is precisely this syntax built on the philosophy of the grammar of graphics that makes ggplot2 so powerful. Adding content layers to mapped objects are central to this idea, which allows linking of map aesthetics through a logical framework. Additionally, several packages have been developed around this philosophy to extend the functionality of ggplot2 in alternative applications (e.g., ggmap, GGally, ggthemes).

I recently gave a presentation to describe some of my favorite features of ggplot2 and other packages building on its core concepts. I describe the use of facets for multi-panel plots, default and custom themes, ggmap for spatial mapping with ggplot2, and GGally for generalized pairs plots. Although this is certainly a subjective and incomplete list, my workflows have become much more efficient (and enjoyable) by using these tools. Below is a link to the presentation. Note that this will not load using internet explorer and you may have to reload if using Chrome to get the complete slide deck. This is my first time hosting a Slidify presentation on RPubs, so please bear with me. The presentation materials are also available at Github.

.

What are some of your favorite features of ggplot2??

Cheers,

Marcus

# Average dissertation and thesis length, take two

About a year ago I wrote a post describing average length of dissertations at the University of Minnesota. I've been meaning to expand that post by adding data from masters theses since the methods for gathering/parsing the records are transferable. This post provides some graphics and links to R code for evaluating dissertation (doctorate) and thesis (masters) data from an online database at the University of Minnesota. In addition to describing data from masters theses, I've collected the most recent data on dissertations to provide an update on my previous post. I've avoided presenting the R code for brevity, but I invite interested readers to have a look at my Github repository where all source code and data are stored. Also, please, please, please note that I've since tried to explain that dissertation length is a pretty pointless metric of quality (also noted here), so interpret the data only in the context that they’re potentially descriptive of the nature of each major.

Feel free to fork/clone the repository to recreate the plots. The parsed data for theses and dissertations are saved as .RData files, 'thes_parse.RData' and 'diss_parse.RData', respectively. Plots were created in 'thes_plot.r' and 'diss_plot.r'. The plots comparing the two were created in 'all_plo.r'. To briefly summarize, the dissertation data includes 3037 records from 2006 to present. This differs from my previous blog by including all majors with at least five records, in addition to the most current data. The masters thesis data contains 930 records from 2009 to present. You can get an idea of the relative page ranges for each by taking a look at the plots. I've truncated all plots to maximum page ranges of 500 and 250 for the dissertation and thesis data, as only a handful of records exceeded these values. I'm not sure if these extremes are actually real data or entered in error, and to be honest, I'm too lazy to verify them myself. Just be cautious that there are some errors in the data and all plots are for informational purposes only, as they say…

-Marcus

# A simple workflow for using R with Microsoft Office products

The challenge of integrating Microsoft products with R software has been an outstanding issue for several years. Reasons for these issues are complicated and related to fundamental differences in developing proprietary vs open-source products. To date, I don’t believe there has been a satisfactory solution but I present this blog as my attempt to work around at least some of the issues using the two. As a regular contributor to R-bloggers, I stress that one should use MS products as little as possible given the many issues that have been described (for example, here, here, and here). It’s not my intent to pick on Microsoft. In fact, I think Excel is a rather nifty program that has its place in specific situations. However, most of my work is not conducive to the point-and-click style of spreadsheet analysis and the surprising limited number of operations available in Excel prevent all but the simplest analyses. I try my best to keep my work within the confines of RStudio, given its integration with multiple document preparation systems.

I work with several talented researchers that have different philosophies than my own on the use of Microsoft products. It’s inevitable that we’re occasionally at odds. Our difficulties go both directions — my insistence on using pdfs for creating reports or manuscripts and the other party’s inclination towards the spreadsheet style of analysis. It seems silly that we’re limited by the types of medium we prefer. I’ve recently been interested in developing a workflow that addresses some of the issues of using end-products from different sources under the notion of reproducibility. To this end, I used Pandoc and relevant R packages (namely gdata and knitr) to develop a stand-alone workflow that allows integration of Microsoft products with my existing workflows. The idea is simple. I want to import data sent to me in .xlsx format, conduct the analysis and report generation entirely within RStudio, and convert the output to .docx format on completion. This workflow allows all tasks to be completed within RStudio, provided the supporting documents, software, and packages work correctly.

Of course, I don’t propose this workflow as a solution to all issues related to Office products and R. I present this material as a conceptual and functional design that could be used by others with similar ideas. I’m quite happy with this workflow for my personal needs, although I’m sure it could be improved upon. I describe this workflow using the pdf below and provide all supporting files on Github: https://github.com/fawda123/pan_flow.

\documentclass[xcolor=svgnames]{beamer}
\usecolortheme[named=SeaGreen]{structure}
\usepackage{graphicx}
\usepackage{breqn}
\usepackage{xcolor}
\usepackage{booktabs}
\usepackage{verbatim}
\usepackage{tikz}
\usepackage{pgfpages}

\tikzstyle{block} = [rectangle, draw, text width=9em, text centered, rounded corners, minimum height=3em, minimum width=7em, top color = white, bottom color=brown!30,  drop shadow]

\newcommand{\ShowSexpr}[1]{\texttt{{\char\\}Sexpr\{#1\}}}

\begin{document}

\title[R with Microsoft]{A simple workflow for using R with Microsoft products}
\author[M. Beck]{Marcus W. Beck}

\institute[USEPA NHEERL]{USEPA NHEERL Gulf Ecology Division, Gulf Breeze, FL\\
Email: \href{mailto:beck.marcus@epa.gov}{beck.marcus@epa.gov}, Phone: 850 934 2480}

\date{May 21, 2014}

%%%%%%
\begin{frame}
\vspace{-0.3in}
\titlepage
\end{frame}

%%%%%%
\begin{frame}{The problem...}
\begin{itemize}
\item R is great and has an increasing user base\\~\\
\item RStudio is integrated with multiple document preparation systems \\~\\
\item Output documents are not in a format that facilitates collaboration with
non R users, e.g., pdf, html \\~\\
\item Data coming to you may be in a proprietary format, e.g., xls spreadsheet
\end{itemize}
\end{frame}

%%%%%%
\begin{frame}{The solution?}
\begin{itemize}
\item Solution one - Make liberal use of projects' within RStudio \\~\\
\item Solution two - Use \texttt{gdata} package to import excel data \\~\\
\item Solution three - Get pandoc to convert document formats - \href{http://johnmacfarlane.net/pandoc/}{http://johnmacfarlane.net/pandoc/} \\~\\
\end{itemize}
\onslide<2->
\large
\centerline{\textit{Not recommended for simple tasks unless you really, really love R}}
\end{frame}

%%%%%
\begin{frame}{An example workflow}
\begin{itemize}
\item I will present a workflow for integrating Microsoft products within RStudio as an approach to working with non R users \\~\\
\item Idea is to never leave the RStudio environment - dynamic documents! \\~\\
\item General workflow... \\~\\
\end{itemize}
\small
\begin{center}
\begin{tikzpicture}[node distance=2.5cm, auto, >=stealth]
\onslide<2->{
\node[block] (a) {1. Install necessary software and packages};}
\onslide<3->{
\node[block] (b)  [right of=a, node distance=4.2cm] {2. Create project in RStudio};
\draw[->] (a) -- (b);}
\onslide<4->{
\node[block] (c)  [right of=b, node distance=4.2cm]  {3. Setup supporting docs/functions};
\draw[->] (b) -- (c);}
\onslide<5->{
\node[block] (d)  [below of=a, node distance=2.5cm]  {4. Import with \texttt{gdata}, summarize};
\draw[->] (c) -- (d);}
\onslide<6->{
\node[block] (e)  [right of=d, node distance=4.2cm]  {5. Create HTML document using knitr Markdown};
\draw[->] (d) -- (e);}
\onslide<7->{
\node[block] (f)  [right of=e, node distance=4.2cm]  {6. Convert HTML doc to Word with Pandoc};
\draw[->] (e) -- (f);}
\end{tikzpicture}
\end{center}
\end{frame}

%%%%%%
\begin{frame}[shrink]{The example}
You are sent an Excel file of data to summarize and report but you love R and want to do everything in RStudio...
<<echo = F, results = 'asis', message = F>>=
library(gdata)
library(xtable)

prl_pth <- 'C:/strawberry/perl/bin/perl.exe'
url <- 'https://beckmw.files.wordpress.com/2014/05/my_data.xlsx'
dat <- read.xls(xls = url, sheet = 'Sheet1', perl = prl_pth)
out.tab <- xtable(dat, digits=4)
print.xtable(out.tab, type = 'latex', include.rownames = F,
size = 'scriptsize')
@
\end{frame}

%%%%%%
\begin{frame}{Step 1}
Install necessary software and Packages \\~\\
\onslide<1->
\begin{itemize}
\onslide<2->
\item R and RStudio (can do with other R editors)\\~\\
\item Microsoft Office\\~\\
\onslide<3->
\item Strawberry Perl for using \texttt{gdata} package\\~\\
\item Pandoc\\~\\
\onslide<4->
\item Packages: \texttt{gdata}, \texttt{knitr}, \texttt{utils}, \texttt{xtable}, others as needed...
\end{itemize}
\end{frame}

%%%%%%
\begin{frame}{Step 2}
Create a project in RStudio \\~\\
\begin{itemize}
\item Create a folder or use existing on local machine \\~\\
\item Add .Rprofile file to the folder for custom startup \\~\\
\item Move all data you are working with to the folder \\~\\
\item Literally create project in RStudio \\~\\
\item Set options within RStudio \\~\\
\end{itemize}
\end{frame}

%%%%%%
\begin{frame}[fragile]{Step 3}
Setup supporting docs/functions, i.e., .Rprofile, functions, report, master
\scriptsize
\begin{block}{.Rprofile}
<<echo = T, eval = F, results = 'markup'>>=
# library path
.libPaths('C:\\Users\\mbeck\\R\\library')

# startup message
cat('My project...\n')

# packages to use
library(utils) # for system commands
library(knitr) # for markdown
library(gdata) # for import xls
library(reshape2) # data format conversion
library(xtable) # easy tables
library(ggplot2) # plotting

# perl path for gdata
prl_pth <- 'C:/strawberry/perl/bin/perl.exe'

# functions to use
source('my_funcs.r')
@
\end{block}
\end{frame}

%%%%%%
\begin{frame}[t, fragile]{Step 3}
Setup supporting docs/functions, i.e., .Rprofile, functions, report, master
\scriptsize
\begin{block}{my\_funcs.r}
<<echo = T, eval = F, results = 'markup'>>=
######
# functions for creating report,
# created May 2014, M. Beck

######
# processes data for creating output in report,
# 'dat_in' is input data as data frame,
# output is data frame with converted variables
proc_fun<-function(dat_in){

# convert temp to C
dat_in$Temperature <- round((dat_in$Temperature - 32) * 5/9)

#  convert data to long format
dat_in <- melt(dat_in, measure.vars = c('Restoration', 'Reference'))

return(dat_in)

}

######
# creates linear model for data,
# 'proc_dat' is processed data returned from 'proc_fun',
# output is linear model object
mod_fun <- function(proc_in) lm(value ~ variable + Year, dat = proc_in)
@
\end{block}
\end{frame}

%%%%%%
\begin{frame}[fragile,shrink]{Step 3}
Setup supporting docs/functions, i.e., .Rprofile, functions, report, master
\scriptsize
\begin{block}{report.Rmd}
\begin{verbatim}
======================
Here's a report I made for r gsub('/|.xlsx','',name)
----------------------

{r echo=F, include=F}
# import data
url <- paste0('https://beckmw.files.wordpress.com/2014/05', name)
dat <- read.xls(xls = url, sheet = 'Sheet1', perl = prl_pth)

# process data for tables/figs
dat <- proc_fun(dat)

# model of data
mod <- mod_fun(dat)


### Model summary
{r results='asis', echo=F}
print.xtable(xtable(mod, digits = 2), type = 'html')


### Figure of restoration and reference by year
{r reg_fig, echo = F, fig.width = 5, fig.height = 3, dpi=200}
ggplot(dat, aes(x = Year, y = value, colour = variable)) +
geom_point() +
stat_smooth(method = 'lm')

\end{verbatim}
\end{block}
\end{frame}

%%%%%%
\begin{frame}[t, fragile]{Step 3}
Setup supporting docs/functions, i.e., .Rprofile, functions, report, master
\scriptsize
\begin{block}{master.r}
<<echo = T, eval = F, results = 'markup'>>=
# file to process
name <- '/my_data.xlsx'

# rmd to html
knit2html('report.Rmd')

# pandoc conversion of html to word doc
system(paste0('pandoc -o report.docx report.html'))
@
\end{block}
\end{frame}

%%%%%%
\begin{frame}[fragile]{Steps 4 - 6}
\small
After creating supporting documents in Project directory, final steps are completed by running master.r'
\begin{itemize}
\item Step 4 - xls file imported using \texttt{gdata} package, implemented in report.Rmd'
\item Step 5 - HTML document created by converting report.Rmd' with \texttt{knit2html} in master.r'
\item Step 6 - HTML document converted to Word with Pandoc by invoking system command
\end{itemize}
\begin{block}{master.r}
<<echo = T, eval = F, results = 'markup'>>=
# file to process
name <- '/my_data.xlsx'

# rmd to html
knit2html('report.Rmd')

# pandoc conversion of html to word doc
system(paste0('pandoc -o report.docx report.html'))
@
\end{block}
\end{frame}

\end{document}


To use the workflow, start a new version control project through Git in RStudio, pull the files from the repository, and run the master file. An excellent introduction for using RStudio with Github can be found here. I’ve also included two excel files that can be used to generate the reports. You can try using each one by changing the name variable in the master file and then running the commands:

name <- 'my_data.xlsx'
knit2html('report.Rmd')
system(paste0('pandoc -o report.docx report.html'))


or…

name <- 'my_data_2.xlsx'
knit2html('report.Rmd')
system(paste0('pandoc -o report.docx report.html'))


The output .docx file should be different depending on which Excel file you use as input. As the pdf describes, none of this will work if you don’t have the required software/packages, i.e., R/RStudio, Strawberry Perl, Pandoc, MS Office, knitr, gdata, etc. You’ll also need Git installed if you are pulling the files for local use (again, see here). I’d be interested to hear if anyone finds this useful or any general comments on improvements/suggestions for the workflow.

Cheers,

Marcus

# How much code have you written?

This past week I attended the National Water Quality Monitoring Conference in Cincinnati. Aside from spending my time attending talks, workshops, and meeting like-minded individuals, I spent an unhealthy amount of time in the hotel bar working on this blog post. My past experiences mixing coding and beer have suggested the two don’t mix, but I was partly successful in writing a function that will be the focus of this post.

I’ve often been curious how much code I’ve written over the years since most of my professional career has centered around using R in one form or another. In the name of ridiculous self-serving questions, I wrote a function for quantifying code lengths by file type. I would describe myself as somewhat of a hoarder with my code in that nothing ever gets deleted. Getting an idea of the total amount was a simple exercise in finding the files, enumerating the file contents, and displaying the results in a sensible manner.

I was not surprised that several functions in R already exist for searching for file paths in directory trees. The list.files function can be used to locate files using regular expression matching, whereas the file.info function can be used to get descriptive information for each file. I used both in my function to find files in a directory tree through recursive searching of paths with a given extension name. The date the files was last modified is saved, and the file length, as lines or number of characters, is saved after reading the file with readLines. The output is a data frame for each file with the file name, type, length, cumulative length by file type, and date. The results can be easily plotted, as shown below.

The function, obtained here, has the following arguments:

 root Character string of root directory to search file_typs Character vector of file types to search, file types must be compatible with readLines omit_blank Logical indicating of blank lines are counted, default TRUE recursive Logical indicating if all directories within root are searched, default TRUE lns Logical indicating if lines in each file are counted, default TRUE, otherwise characters are counted trace Logical for monitoring progress, default TRUE

Here’s an example using the function to search a local path on my computer.

# import function from Github
library(devtools)

# https://gist.github.com/fawda123/20688ace86604259de4e
source_gist('20688ace86604259de4e')

# path to search and file types
root <- 'C:/Projects'
file_typs <- c('r','py', 'tex', 'rnw')

# get data from function
my_fls <- file.lens(root, file_typs)

##                               fl Length       Date cum_len Type
## 1                 buffer loop.py     29 2010-08-12      29   py
## 2                  erase loop.py     22 2010-08-12      51   py
## 3 remove selection and rename.py     26 2010-08-16      77   py
## 4              composite loop.py     32 2010-08-18     109   py
## 5                extract loop.py     61 2010-08-18     170   py
## 6         classification loop.py     32 2010-08-19     202   py


In this example, I’ve searched for R, Python, LaTeX, and Sweave files in the directory ‘C:/Projects/’. The output from the function is shown using the head command.

Here’s some code for plotting the data. I’ve created four plots with ggplot and combined them using grid.arrange from the gridExtra package. The first plot shows the number of files by type, the second shows file length by date and type, the third shows a frequency distribution of file lengths by type, and the fourth shows a cumulative distribution of file lengths by type and date.

# plots
library(ggplot2)
library(gridExtra)

# number of files by type
p1 <- ggplot(my_fls, aes(x = Type, fill = Type)) +
geom_bar() +
ylab('Number of files') +
theme_bw()

# file length by type and date
p2 <- ggplot(my_fls, aes(x = Date, y = Length, group = Type,
colour = Type)) +
geom_line() +
ylab('File length') +
geom_point() +
theme_bw() +
theme(legend.position = 'none')

# density of file length by type
p3 <- ggplot(my_fls, aes(x = Length, y = ..scaled.., group = Type,
colour = Type, fill = Type)) +
geom_density(alpha = 0.25, size = 1) +
xlab('File length') +
ylab('Density (scaled)') +
theme_bw() +
theme(legend.position = 'none')

# cumulative length by file type and date
p4 <- ggplot(my_fls, aes(x = Date, y = cum_len, group = Type,
colour = Type)) +
geom_line() +
geom_point() +
ylab('Cumulative file length') +
theme_bw() +
theme(legend.position = 'none')

# function for common legend
g_legend<-function(a.gplot){
tmp <- ggplot_gtable(ggplot_build(a.gplot))
leg <- which(sapply(tmp$grobs, function(x) x$name) == "guide-box")
legend <- tmp$grobs[[leg]] return(legend)} # get common legend, remove from p1 mylegend <- g_legend(p1) p1 <- p1 + theme(legend.position = 'none') # final plot grid.arrange( arrangeGrob(p1, p2, p3, p4, ncol = 2), mylegend, ncol = 2, widths = c(10,1))  Clearly, most of my work has been done in R, with most files being less than 200-300 lines. There seems to be a lull of activity in Mid 2013 after I finished my dissertation, which is entirely expected. I was surprised to see that the Sweave (.rnw) and LaTeX files weren’t longer until I remembered that paragraphs in these files are interpreted as single lines of text. I re-ran the function using characters as my unit of my measurement. # get file lengths by character my_fls <- file.lens(root, file_typs, lns = F) # re-run plot functions above  Now there are clear differences in lengths for the Sweave and LaTeX files, with the longest file topping out at 181256 characters. I know others might be curious to see how much code they’ve written so feel free to use/modify the function as needed. These figures represent all of my work, fruitful or not, in six years of graduate school. It goes without saying that all of your code has to be in the root directory. The totals will obviously be underestimates if you have code elsewhere, such as online. The function could be modified for online sources but I think I’m done for now. Cheers, Marcus # Process and observation uncertainty explained with R Once upon a time I had grand ambitions of writing blog posts outlining all of the examples in the Ecological Detective.1 A few years ago I participated in a graduate seminar series where we went through many of the examples in this book. I am not a population biologist by trade but many of the concepts were useful for not only helping me better understand core concepts of statistical modelling, but also for developing an appreciation of the limits of your data. Part of this appreciation stems from understanding sources and causes of uncertainty in estimates. Perhaps in the future I will focus more blog topics on other examples from The Ecological Detective, but for now I’d like to discuss an example that has recently been of interest in my own research. Over the past few months I have been working with some colleagues to evaluate statistical power of biological indicators. These analyses are meant to describe the certainty within which a given level of change in an indicator is expected over a period of time. For example, what is the likelihood of detecting a 50% decline over twenty years considering that our estimate of the indicators are influenced by uncertainty? We need reliable estimates of the uncertainty to answer these types of questions and it is often useful to categorize sources of variation. Hilborn and Mangel describe process and observation uncertainty as two primary categories of noise in a data measurement. Process uncertainty describes noise related to actual or real variation in a measurement that a model does not describe. For example, a model might describe response of an indicator to changing pollutant loads but we lack an idea of seasonal variation that occurs naturally over time. Observation uncertainty is often called sampling uncertainty and describes our ability to obtain a precise data measurement. This is a common source of uncertainty in ecological data where precision of repeated surveys may be affected by several factors, such as skill level of the field crew, precision of sampling devices, and location of survey points. The effects of process and observation uncertainty on data measurements are additive such that the magnitude of both can be separately estimated. The example I’ll focus on is described on pages 59–61 (the theory) and 90–92 (an example with pseudocode) in The Ecological Detective. This example describes an approach for conceptualizing the effects of uncertainty on model estimates, as opposed to methods for quantifying uncertainty from actual data. For the most part, this blog is an exact replica of the example, although I have tried to include some additional explanation where I had difficulty understanding some of the concepts. Of course, I’ll also include R code since that’s the primary motivation for my blog. We start with a basic population model that describes population change over time. This is a theoretical model that, in practice, should describe some actual population, but is very simple for the purpose of learning about sources of uncertainty. From this basic model, we simulate sources of uncertainty to get an idea of their exact influence on our data measurements. The basic model without imposing uncertainty is as follows: $\displaystyle N_{t+1}=sN_t + b_t$ where the population at time $t + 1$ is equal to the population at time $t$ multiplied by the survival probability $s$ plus the number of births at time $t$. We call this the process model because it’s meant to describe an actual population process, i.e., population growth over time given birth and survival. We can easily create a function to model this process over a time series. As in the book example, we’ll use a starting population of fifty individuals, add 20 individuals from births at each time step, and use an 80% survival rate. # simple pop model proc_mod <- function(N_0 = 50, b = 20, s = 0.8, t = 50){ N_out <- numeric(length = t) N_out[1] <- N_0 for(step in 1:t) N_out[step + 1] <- s*N_out[step] + b out <- data.frame(steps = 1:t, Pop = N_out[-1]) return(out) } est <- proc_mod()  The model is pretty straightforward. A for loop is used to estimate the population for time steps one to fifty with a starting population size of fifty at time zero. Each time step multiplies the population estimate from the previous time step and adds twenty new individuals. You may notice that the function could easily be vectorized, but I’ve used a for loop to account for sources of uncertainty that are dependent on previous values in the time series. This will be explained below but for now the model only describes the actual process. The results are assigned to the est object and then plotted. library(ggplot2) ggplot(est, aes(steps, Pop)) + geom_point() + theme_bw() + ggtitle('N_0 = 50, s = 0.8, b = 20\n')  In a world with absolute certainty, an actual population would follow this trend if our model accurately described the birth and survivorship rates. Suppose our model provided an incomplete description of the population. Hilborn and Mangel (p. 59) suggest that birth rates, for example, may fluctuate from year to year. This fluctuation is not captured by our model and represents a source of process uncertainty, or uncertainty caused by an incomplete description of the process. We can assume that the effect of this process uncertainty is additive to the population estimate at each time step: $\displaystyle N_{t+1}=sN_t + b_t + W_t$ where the model remains the same but we’ve included an additional term, $W_t$, to account for uncertainty. This uncertainty is random in the sense that we don’t know exactly how it will influence our estimate but we can describe it as a random variable from a known distribution. Suppose we expect random variation in birth rates for each time step to be normally distributed with mean zero and a given standard deviation. Population size at $t+1$ is the survivorship of the population at time $t$ plus the births accounting for random variation. An important point is that the random variation is additive throughout the time series. That is, if more births were observed for a given year due to random chance, the population would be larger the next year such that additional random variation at $t+1$ is added to the larger population. This is why a for loop is used because we can’t simulate uncertainty by adding a random vector all at once to the population estimates. The original model is modified to include process uncertainty. # simple pop model with process uncertainty proc_mod2 <- function(N_0 = 50, b = 20, s = 0.8, t = 50, sig_w = 5){ N_out <- numeric(length = t + 1) N_out[1] <- N_0 sig_w <- rnorm(t, 0, sig_w) for(step in 1:t) N_out[step + 1] <- s*N_out[step] + b + sig_w[step] out <- data.frame(steps = 1:t, Pop = N_out[-1]) return(out) } set.seed(2) est2 <- proc_mod2() # plot the estimates ggt <- paste0('N_0 = 50, s = 0.8, b = 20, sig_w = ',formals(proc_mod)$sig_w,'\n')
ggplot(est2, aes(steps, Pop)) +
geom_point() +
theme_bw() +
ggtitle(ggt)


We see considerable variation from the original model now that we’ve included process uncertainty. Note that the process uncertainty in each estimate is dependent on the estimate prior, as described above. This creates uncertainty that, although random, follows a pattern throughout the time series. We can look at an auto-correlation plot of the new estimates minus the actual population values to get an idea of this pattern. Observations that are closer to one another in the time series are correlated, as expected.

Adding observation uncertainty is simpler in that the effect is not propagated throughout the time steps. Rather, the uncertainty is added after the time series is generated. This makes intuitive because the observation uncertainty describes sampling error. For example, if we have an instrument malfunction one year that creates an unreliable estimate we can fix the instrument to get a more accurate reading the next year. However, suppose we have a new field crew the following year that contributes to uncertainty (e.g., wrong species identification). This uncertainty is not related to the year prior. Computationally, the model is as follows:

$\displaystyle N_{t+1}=sN_t + b_t$

$\displaystyle N^{*} = N + V$

where the model is identical to the deterministic model with the addition of observation uncertainty $V$ after the time series is calculated for fifty time steps. $N$ is the population estimate for the whole time series and $N^{*}$ is the estimate including observation uncertainty. We can simulate observation uncertainty using a random normal variable with assumed standard deviation as we did with process uncertainty, e.g., $V$ has length fifty with mean zero and standard deviation equal to five.

# model with observation uncertainty
proc_mod3 <- function(N_0 = 50, b = 20, s = 0.8, t = 50, sig_v = 5){

N_out <- numeric(length = t)
N_out[1] <- N_0

sig_v <- rnorm(t, 0, sig_v)

for(step in 1:t)
N_out[step + 1] <- s*N_out[step] + b

N_out <- N_out + c(NA,sig_v)

out <- data.frame(steps = 1:t, Pop = N_out[-1])

return(out)

}

# get estimates
set.seed(3)
est3 <- proc_mod3()

# plot
ggt <- paste0('N_0 = 50, s = 0.8, b = 20, sig_v = ',
formals(proc_mod3)$sig_v,'\n') ggplot(est3, aes(steps, Pop)) + geom_point() + theme_bw() + ggtitle(ggt)  We can confirm that the observations are not correlated between the time steps, unlike the model with process uncertainty. Now we can create a model that includes both process and observation uncertainty by combining the above functions. The function is slightly tweaked to return include a data frame with all estimates: process model only, process model with process uncertainty, process model with observation uncertainty, process model with process and observation uncertainty. # combined function proc_mod_all <- function(N_0 = 50, b = 20, s = 0.8, t = 50, sig_w = 5, sig_v = 5){ N_out <- matrix(NA, ncol = 4, nrow = t + 1) N_out[1,] <- N_0 sig_w <- rnorm(t, 0, sig_w) sig_v <- rnorm(t, 0, sig_v) for(step in 1:t){ N_out[step + 1, 1] <- s*N_out[step] + b N_out[step + 1, 2] <- N_out[step, 1] + sig_w[step] } N_out[1:t + 1, 3] <- N_out[1:t + 1, 1] + sig_v N_out[1:t + 1, 4] <- N_out[1:t + 1, 2] + sig_v out <- data.frame(1:t,N_out[-1,]) names(out) <- c('steps', 'mod_act', 'mod_proc', 'mod_obs', 'mod_all') return(out) } # create data set.seed(2) est_all <- proc_mod_all() # plot the data library(reshape2) to_plo <- melt(est_all, id.var = 'steps') # re-assign factor labels for plotting to_plo$variable <- factor(to_plo$variable, levels = levels(to_plo$variable),
labels = c('Actual','Pro','Obs','Pro + Obs'))

ggplot(to_plo, aes(steps, value)) +
geom_point() +
facet_wrap(~variable) +
ylab('Pop. estimate') +
theme_bw()


On the surface, the separate effects of process and observation uncertainty on the estimates is similar, whereas the effects of adding both maximizes the overall uncertainty. We can quantify the extent to which the sources of uncertainty influence the estimates by comparing observations at time $t$ to observations at $t - 1$. In other words, we can quantify the variance for each model by regressing observations separated by one time lag. We would expect the model that includes both sources of uncertainty to have the highest variance.

# comparison of mods
# create vectors for pop estimates at time t (t_1) and t - 1 (t_0)
t_1 <- est_all[2:nrow(est_all),-1]
t_1 <- melt(t_1, value.name = 'val_1')
t_0 <- est_all[1:(nrow(est_all)-1),-1]
t_0 <- melt(t_0, value.name = 'val_0')

#combine for plotting
to_plo2 <- cbind(t_0,t_1[,!names(t_1) %in% 'variable',drop = F])
##   variable   val_0    val_1
## 1  mod_act 60.0000 68.00000
## 2  mod_act 68.0000 74.40000
## 3  mod_act 74.4000 79.52000
## 4  mod_act 79.5200 83.61600
## 5  mod_act 83.6160 86.89280
## 6  mod_act 86.8928 89.51424

# re-assign factor labels for plotting
to_plo2$variable <- factor(to_plo2$variable, levels = levels(to_plo2$variable), labels = c('Actual','Pro','Obs','Pro + Obs')) # we don't want to plot the first process model sub_dat <- to_plo2$variable == 'Actual'
ggplot(to_plo2[!sub_dat,], aes(val_0, val_1)) +
geom_point() +
facet_wrap(~variable) +
theme_bw() +
scale_y_continuous('Population size at time t') +
scale_x_continuous('Population size at time t - 1') +
geom_abline(slope = 0.8, intercept = 20)


A tabular comparison of the regressions for each plot provides a quantitative measure of the effect of uncertainty on the model estimates.

library(stargazer)
mods <- lapply(
split(to_plo2,to_plo2$variable), function(x) lm(val_1~val_0, data = x) ) stargazer(mods, omit.stat = 'f', title = 'Regression of population estimates at time$t$against time$t - 1\$ for each process model.  Each model except the first simulates different sources of uncertainty.', column.labels = c('Actual','Pro','Obs','Pro + Obs'), model.numbers = F)


The table tells us exactly what we would expect. Based on the r-squared values, adding more uncertainty decreases the explained variance of the models. Also note the changes in the parameter estimates. The actual model provides slope and intercept estimates identical to those we specified in the beginning ($s = 0.8$ and $b = 20$). Adding more uncertainty to each model contributes to uncertainty in the parameter estimates such that survivorship is under-estimated and birth contributions are over-estimated.

It’s nice to use an arbitrary model where we can simulate effects of uncertainty, unlike situations with actual data where sources of uncertainty are not readily apparent. This example from The Ecological Detective is useful for appreciating the effects of uncertainty on parameter estimates in simple process models. I refer the reader to the actual text for more discussion regarding the implications of these analyses. Also, check out Ben Bolker’s text2 (chapter 11) for more discussion with R examples.

Cheers,

Marcus

1Hilborn R, Mangel M. 1997. The Ecological Detective: Confronting Models With Data. Monographs in Population Biology 28. Princeton University Press. Princeton, New Jersey. 315 pages.
2Bolker B. 2007. Ecological Models and Data in R. Princeton University Press. Princeton, New Jersey. 508 pages.