In jaroyle/oSCR: Multi-Session Sex-Structured Spatial Capture-Recapture Models
library(knitr)
library(oSCR)
#library(scrbook)
options(width=120)
options(width.cutoff=80)
opts_chunk$set(prompt = FALSE, comment = NA, mysize=TRUE, size="\\scriptsize")
hook1 <- function(x){ gsub("```\n*```r*\n*", "", x) }
hook2 <- function(x){ gsub("```\n+```\n", "", x) }
knit_hooks$set(document = hook2)
knitr::knit_hooks$set(mysize = function(before, options, envir) {
if (before)
return(options$size)
})
What is \texttt{oSCR}?
The \textcolor{mLightBrown}{\texttt{o}} is for open
\begin{itemize}
\item<1-> built upon various functions in \texttt{scrbook}
\item<2-> an editable and evolving code base
\item<3-> a community of contributors
\begin{itemize}
\item<3-> \textcolor{gray}{\textit{contributing}} ideas
\item<3-> \textcolor{gray}{\textit{contributing}} problems
\item<3-> \textcolor{gray}{\textit{contributing}} solutions
\item<3-> \textcolor{gray}{\textit{contributing}} code
\end{itemize}
\item<4-> a philosophy of 'parallel publishing'
\begin{itemize}
\item<4-> \textcolor{gray}{\textit{increase}} transparency
\item<4-> \textcolor{gray}{\textit{increase}} accessibility
\end{itemize}
\end{itemize}
\begin{tikzpicture}[overlay]
\node[inner sep=0pt] (one) at (10,4) {\includegraphics[height=1.2in]{scrbook.png}};
\node[inner sep=0pt] (one) at (10,0.91) {\includegraphics[height=0.8in]{oSCR.png}};
\end{tikzpicture}
What is \texttt{oSCR}?
$\ldots$ more about \texttt{oSCR}
\begin{itemize}
\item<1-> one of several ways to analyze SCR data
\begin{itemize}
\item<1-> alternative (\textit{not} substitute) to \texttt{secr}
\item<1-> (see Dan's lecture tomorrow)
\item<1-> alternative to Bayesian analysis
\end{itemize}
\item<2-> likelihood based - has advantages
\begin{itemize}
\item<2-> \textcolor{gray}{\textit{advantage}} speed
\item<2-> \textcolor{gray}{\textit{advantage}} model selection methods
\item<2-> \textcolor{gray}{\textit{advantage}} cost surface modeling
\item<2-> \textcolor{gray}{\textit{advantage}} user friendly
\end{itemize}
\end{itemize}
\begin{tikzpicture}[overlay]
\node[inner sep=0pt] (one) at (10,0.175) {\includegraphics[height=0.8in]{oSCR.png}};
\end{tikzpicture}
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories
traps, # trap coordinates
trapCovs, # trap level covariates
indCovs, # sex data
trapOperation, # binary operation indicator
type) # data format type
\normalsize
\texttt{?make.scrFrame}
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories
traps, # trap coordinates
trapCovs, # trap level covariates
indCovs, # sex data
trapOperation, # binary operation indicator
type) # data format type
\normalsize
\texttt{caphist} ($y_{ijk}$):
- spatial capture history object
- array with dimensions n x J x K (ind-by-trap-by-occasion)
- binary (detected or not) $\rightarrow$ Binomial encounter model
- counts (no. of detecteds) $\rightarrow$ Poisson encounter model
\texttt{caphist}
- schematically:
\scalebox{0.6}{
\begin{tikzpicture}[overlay]
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{
3 \& 2 \& 0 \& 0 \& \cdots \& \& \& \& \
1 \& 0 \& 1 \& \cdots \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
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\& \& \& \& \& \& \& \vdots \& 4 \
\& \& \& \& \& \& \& 3 \& 0 \
\& \& \& \& \& \& \& 1 \& 1 \
};
\fill[gray,opacity=.2] (C-2-1.south west) -- (C-1-1.north west) -- (C-1-9.north east) -- (C-11-9.south east) -- (C-11-8.south west) -- (C-3-8.north west) -- (C-2-1.south west);
\draw[opacity=0.2] (C-2-1.south west) -- (C-1-1.north west)--(C-1-9.north east)--(C-11-9.south east)--(C-11-8.south west);
\matrix[draw=none,inner sep=0pt] (D) at (4,-4)[matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=0.35,text height=1ex,nodes in empty cells]
{
2 \& 2 \& 1 \& 0 \& \cdots \& \& \& \& \
4 \& 0 \& 0 \& \cdots \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
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\& \& \& \& \& \& \& \& \vdots \
\& \& \& \& \& \& \& \vdots \& 0 \
\& \& \& \& \& \& \& 0 \& 2 \
\& \& \& \& \& \& \& 1 \& 0 \ %%%%%% 8
};
\fill[gray,opacity=.35] (D-3-1.south west) -- (D-1-1.north west) -- (D-1-9.north east) -- (D-11-9.south east) -- (D-11-8.south west) -- (D-4-8.north west) -- (D-3-1.south west);
\draw[opacity=0.35] (D-3-1.south west) -- (D-1-1.north west)--(D-1-9.north east)--(D-11-9.south east)--(D-11-8.south west);
\matrix[draw,inner sep=0pt] (E) at (3,-5) [matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=1,fill=gray,text height=1ex,nodes in empty cells]
{
1 \& 3 \& 0\& 1\& \cdots \& \& \& \& \
6 \& 1 \& 2\& \& \& \& \& \& \
0 \& 0 \& \& \& \& \& \& \& \
3 \& \& \& \& \& \& \& \& \
\vdots \& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \&\vdots \
\& \& \& \& \& \& \& \& 3 \
\& \& \& \& \& \& \& 0 \& 0 \
\& \& \& \& \& \cdots \& 0 \& 0 \& 0 \
};%
\draw[] (E-6-5) node {\large\textcolor{green}{$\boldsymbol{y_{i,j,r}}$}};
\draw[] (E-7-5) node {\large\textcolor{green}{counts}};
%Trap
\draw[] (C-1-1.north east) node[above left] {\textbf{Trap = 1}};
\draw[] (C-1-9.north) node[above] {\textbf{$J$}};
\draw[->, thick] ([yshift=7.5]C-1-1.north east) -- ([yshift=7.5]C-1-9.north west);
%Ind
\draw[] (E-1-1.west) node[left, yshift=2] {\textbf{Ind. = 1}};
\draw[] (E-11-1.west) node[left, yshift=2] {\textbf{$n_{obs}$}};
\draw[->, thick] ([xshift=-7.5]E-2-1.west) -- ([xshift=-7.5]E-10-1.west);
\draw[] (E-11-9.south) node[below] {\textbf{Occassion = 1}};
\draw[] (C-11-9.east) node[right, xshift=2ex] {\textbf{$K$}};
\draw[->, thick] ([xshift=2ex]E-11-9.south east) -- ([xshift=2ex]C-11-9.south east);
\matrix[draw=none,inner sep=0pt] (C) at (15,-3)[matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=0.2,text height=1ex,nodes in empty cells]
{
1\& 1\& 0\& 0 \& \cdots \& \& \& \& \
1\& 0\& 1\& \cdots \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
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\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \vdots \
\& \& \& \& \& \& \& \vdots \& 1 \
\& \& \& \& \& \& \& 1 \& 0 \
\& \& \& \& \& \& \& 1 \& 1 \ %%%%%% 11
};
\fill[gray,opacity=.2] (C-2-1.south west) -- (C-1-1.north west) -- (C-1-9.north east) -- (C-11-9.south east) -- (C-11-8.south west) -- (C-3-8.north west) -- (C-2-1.south west);
\draw[opacity=0.2] (C-2-1.south west) -- (C-1-1.north west)--(C-1-9.north east)--(C-11-9.south east)--(C-11-8.south west);
\matrix[draw=none,inner sep=0pt] (D) at (14,-4)[matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=0.35,text height=1ex,nodes in empty cells]
{
1 \& 1\& 1\& 0 \& \cdots \& \& \& \& \
1 \& 0\& 0\& \cdots \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \vdots \
\& \& \& \& \& \& \& \vdots \& 0 \
\& \& \& \& \& \& \& 0 \& 1 \
\& \& \& \& \& \& \& 1 \& 0 \ %%%%%% 8
};
\fill[gray,opacity=.35] (D-3-1.south west) -- (D-1-1.north west) -- (D-1-9.north east) -- (D-11-9.south east) -- (D-11-8.south west) -- (D-4-8.north west) -- (D-3-1.south west);
\draw[opacity=0.35] (D-3-1.south west) -- (D-1-1.north west)--(D-1-9.north east)--(D-11-9.south east)--(D-11-8.south west);
\matrix[draw,inner sep=0pt] (E) at (13,-5) [matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=1,fill=gray,text height=1ex,nodes in empty cells]
{
1 \& 1 \& 0 \& 1\& \cdots \& \& \& \& \
1 \& 1 \& 1 \& \& \& \& \& \& \
0 \& 0 \& \& \& \& \& \& \& \
1 \& \& \& \& \& \& \& \& \
\vdots \& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \
\& \& \& \& \& \& \& \& \vdots \
\& \& \& \& \& \& \& \& 1 \
\& \& \& \& \& \& \& 0 \& 0 \
\& \& \& \& \& \cdots \& 0 \& 0 \& 0 \
};%
\draw[] (E-6-5) node {\large\textcolor{green}{$\boldsymbol{y_{i,j,r}}$}};
\draw[] (E-7-5) node {\large\textcolor{green}{detections}};
%Trap
\draw[] (C-1-1.north east) node[above left] {\textbf{Trap = 1}};
\draw[] (C-1-9.north) node[above] {\textbf{$J$}};
\draw[->, thick] ([yshift=7.5]C-1-1.north east) -- ([yshift=7.5]C-1-9.north west);
%Ind
\draw[] (E-1-1.west) node[left, yshift=2] {\textbf{Ind. = 1}};
\draw[] (E-11-1.west) node[left, yshift=2] {\textbf{$n_{obs}$}};
\draw[->, thick] ([xshift=-7.5]E-2-1.west) -- ([xshift=-7.5]E-10-1.west);
\draw[] (E-11-9.south) node[below] {\textbf{Occassion = 1}};
\draw[] (C-11-9.east) node[right, xshift=2ex] {\textbf{$K$}};
\draw[->, thick] ([xshift=2ex]E-11-9.south east) -- ([xshift=2ex]C-11-9.south east);
\end{tikzpicture}
}
\texttt{caphist}
- in
R:
yarr <- array(rbinom(3*10*3,1,0.4),c(3,10,3))
yarr
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories
traps, # trap coordinates
trapCovs, # trap level covariates
indCovs, # sex data
trapOperation, # binary operation indicator
type) # data format type
\normalsize
\texttt{traps}:
- a trap coordinate data frame
- coordinates must be named
X and Y (upper case)
- all traps operational at least once (see
trapOperation)
- know your units!
- spatial units must be consistent throughout
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories
traps, # trap coordinates
trapCovs, # trap level covariates
indCovs, # sex data
trapOperation, # binary operation indicator
type) # data format type
\normalsize
\texttt{trapCovs}:
- a $k$-length list of trap covariate data frames
- can model occassion-specific variation in $p$, i.e. $p_k$
- temperature
- Julian day, etc$\ldots$
NA's allowed
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories
traps, # trap coordinates
trapCovs, # trap level covariates
indCovs, # sex data
trapOperation, # binary operation indicator
type) # data format type
\normalsize
\texttt{indCovs}:
- a data frame containing individual-level data
- currently only with a two-class categorical variables
- typically male/female (male = 1)
- can accomodate missing data
- if provided, 2-class mixture model always fitted
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories
traps, # trap coordinates
trapCovs, # trap level covariates
indCovs, # sex data
trapOperation, # binary operation indicator
type) # data format type
\normalsize
\texttt{trapOperation}:
- binary J x K (trap-by-occasion) matrix
- denotes whether a trap was operational (1) or not (0), in each occasion
- unoperational traps get discarded from any calculations
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories
traps, # trap coordinates
trapCovs, # trap level covariates
indCovs, # sex data
trapOperation, # binary operation indicator
type) # data format type
\normalsize
\texttt{type}:
- for now always set to
SCR
- in the future will allow for alternative formats
- secr
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
- each object must be supplied as a list
make.scrFrame() does internal checks for consistencies- the resulting data object (
sf) is ready for use
- list structure makes multi-session data formatting easy
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
- each object must be supplied as a list
make.scrFrame() does internal checks for consistencies- the resulting data object (
sf) is ready for use
- list structure makes multi-session data formatting easy
- \textcolor{mLightBrown}{{\it single}} session data:
sf <- make.scrFrame(caphist = list(ch),
traps = list(tr),
trapCovs = list(list(tc1,tc2,tc3)), #k=3
indCovs = list(ic),
trapOperation = list(to),
type = "SCR")
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
- each object must be supplied as a list
make.scrFrame() does internal checks for consistencies- the resulting data object (
sf) is ready for use
- list structure makes multi-session data formatting easy
- \textcolor{mLightBrown}{{\it two}} session data:
sf <- make.scrFrame(caphist = list(ch1, ch2),
traps = list(tr1, tr1),
trapCovs = list(list(tc1.1,tc1.2,tc1.3),
list(tc2.1,tc2.2,tc2.3)), #k=3
indCovs = list(ic1, ic2),
trapOperation = list(to1,to2),
type = "SCR")
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
- each object must be supplied as a list
make.scrFrame() does internal checks for consistencies- the resulting data object (
sf) is ready for use
- list structure makes multi-session data formatting easy
- \textcolor{mLightBrown}{{\it three}} session data:
sf <- make.scrFrame(caphist = list(ch1, ch2, ch3),
traps = list(tr1, tr1, tr3),
trapCovs = list(list(tc1.1,tc1.2,tc1.3),
list(tc2.1,tc2.2,tc2.3),
list(tc3.1,tc3.2,tc3.3)), #k=3
indCovs = list(ic1, ic2, ic3),
trapOperation = list(to1,to2, to3),
type = "SCR")
\normalsize
$\ldots$ and so on and so forth
\texttt{oSCR} - Data organization and structure
Data formats:
- data collection and storage formats vary widely
secr format is a common format
- row per observation
- e.g., individual, trap, occasion, session
- function to convert
secr to oSCR format
data2oscr()
- can use work session to format personal data
Exploring the \texttt{scrFrame}
Lets look at some real data
- redback salamnders Plethodon cinereus
- 4 sampling grids withing a single forest
- 5 $\times$ 10 cover boards spaced 1m apart
\begin{tikzpicture}[overlay]
\node[inner sep=0pt] (one) at (9,-1) {\includegraphics[height=2.8in]{sampling.png}};
\node[inner sep=0pt] (one) at (4,-2) {\includegraphics[height=1.75in]{mark.png}};
\end{tikzpicture}
Exploring the \texttt{scrFrame}
- you can run this code!
library(oSCR)
data(rbs)
ls()
[1] "rbs.sf" "rbs.ss"
library(oSCR)
data(rbs)
\normalsize
rbs.sf is the redback salander scrFrame object
Exploring the \texttt{scrFrame}
- you can run this code!
library(oSCR)
data(rbs)
rbs.sf
Subsetting the \texttt{scrFrame}
subFrame() can be used to efficiently subset the scrFrame
sf.sub <- subFrame(scrFrame, # the scrFrame to be subsetted
subs) # the index/indices to be kept
Subsetting the \texttt{scrFrame}
subFrame() can be used to efficiently subset the scrFrame
sf.sub <- subFrame(scrFrame = rbs.sf,
subs = c(2,4))
sf.sub
Subsetting the \texttt{scrFrame}
- let's try that with the
rbs data:
sf.sub <- subFrame(scrFrame = rbs.sf,
subs = c(2,4))
sf.sub
\texttt{oSCR} - Data organization and structure
State space definition is extremely important
- part of the model
- an approximation of activity centers (ac)
- resolution should be $\le \hat{\sigma}$
- should represent all ac of detectable individuals
- buffer of at least $2\hat{\sigma}$ around traps
\begin{tikzpicture}[overlay]
\node[inner sep=0pt] (one) at (5,-1.5) {\includegraphics[height=1.2in]{sbuf.png}};
\end{tikzpicture}
\texttt{oSCR} - Data organization and structure
ssDF: the state space data object (\textbf{s}tate \textbf{s}pace {\textbf{d}ata \textbf{f}rame):
- a list of data frames (one per session)
- coordinates of each pixel
- named
X and Y (upper case)
- each coordinate represents a pixel
- named columns of pixel-specific covariate values
- used for modelling spatially varying density
- can be continuous or categorical
- non-habitat can be removed
- coordinates should be same units as
traps
\texttt{oSCR} - Data organization and structure
Making the ssDF object requires constructing a list of data frames
ssDF <- list(ss1, # dataframe for session 1
ss2, # dataframe for session 2
ss3, # dataframe for session 3
ss4) # dataframe for session 4
Exploring the \texttt{ssDF}
Let's work with the salamander state space object:
str(rbs.ss, give.attr=FALSE)
Exploring the \texttt{ssDF}
Sub setting ssDF is easily done:
# sub setting ssDF is easy:
ss.sub <- rbs.ss[c(1,2)]
Exploring the \texttt{ssDF}
Sub setting ssDF is easily done:
# sub setting ssDF is easy:
ss.sub <- rbs.ss[c(1,2)]
str(ss.sub, give.attr=FALSE)
Exploring the \texttt{ssDF}
We can plot the object
par(mfrow=c(2,2), oma=c(0,0,0,0),mar=c(4,4,2,2))
par(mfrow=c(1,4)) #4 sessions
plot.ssDF(rbs.ss)
Exploring the \texttt{ssDF}
We can plot the object with the traps
par(mfrow=c(1,4)) #4 sessions
plot.ssDF(rbs.ss, scrFrame=rbs.sf)
Constructing a \texttt{ssDF}
If no interest in assessing spatial variation in density
- the state space is somewhat arbitrary
- no covariates
- we can make an
ssDF object: make.ssDF()
ssDF <- make.ssDF(scrFrame, # an scrFRame objects
buffer, # a buffer witdh (around traps!)
res) # the distance between S points
Constructing a \texttt{ssDF}
par(mfrow=c(1,2))
ssDF <- make.ssDF(scrFrame = sf.sub,
buffer = 1,
res = 1)
plot(ssDF, sf.sub)
Constructing a \texttt{ssDF}
ssDF <- make.ssDF(scrFrame = sf.sub,
buffer = 5,
res = 0.5)
plot(ssDF, sf.sub)
\texttt{oSCR} - Model fitting
With an scrFrame and ssDF object, we can start fitting models uning the fitting function oSCR.fit()
mod <- oSCR.fit(model, # model formulation
scrFrame, # the scrFrame object
ssDF, # the ssDF object
encmod, # the detection function model
trimS, # local evaluation distance
start.vals, # parameter starting values
predict, # predict desnity
...) # a few other options
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation
scrFrame, # the scrFrame object
ssDF, # the ssDF object
encmod, # the detection function model
trimS, # local evaluation distance
start.vals, # parameter starting values
predict, # predict desnity
...) # a few other options
\normalsize
\texttt{model}:
- a list with 4 model formulations
list(D ~ 1, p0 ~ 1, sig ~ 1, asu ~ 1)
D ~: model describing variation in densityp0 ~: model describing variation in baseline encounter prob/ratesig ~: model describibg variation in sigmaasu ~: model for a cost surface
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation
scrFrame, # the scrFrame object
ssDF, # the ssDF object
encmod, # the detection function model
trimS, # local evaluation distance
start.vals, # parameter starting values
predict, # predict desnity
...) # a few other options
\normalsize
\texttt{model}:
- a list with 3 model formulations
list(D ~ 1, p0 ~ 1, sig ~ 1)
D ~: model describing variation in densityp0 ~: model describing variation in baseline encounter prob/ratesig ~: model describibg variation in sigma
\texttt{oSCR} - model choices
Varaition in \textcolor{blue}{density} (D ~)
D ~ 1 # null model, constant density
D ~ session # density varies by session
D ~ "covariate" # density varies by spatially indexed covariates
\normalsize
- includes additive and interaction models
- includes all combinations
"covariate" must match column names in ssDFD ~ 1 is the default
\texttt{oSCR} - model choices
Varaition in \textcolor{blue}{detection} (p0 ~)
p0 ~ 1 # null model, constant p (M0)
p0 ~ t # occasion specific p (Mt)
p0 ~ b # behavioural response (Mb)
p0 ~ sex # p varies by sex
p0 ~ session # p varies by session
p0 ~ "covariate" # p varies by trap level covariates
\normalsize
- includes additive and interaction models
- includes most combinations
"covariate" must match column names in trapCovsp0 ~ 1 is the default
\texttt{oSCR} - model choices
Varaition in \textcolor{blue}{sigma} (sig ~)
sig ~ 1 # null model, constant sigma
sig ~ sex # sex-specific sigma
sig ~ session # session-specific sigma
\normalsize
- includes additive and interaction models
- includes all combinations
sig ~ 1 is the default
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation
scrFrame, # the scrFrame object
ssDF, # the ssDF object
encmod, # the detection function model
trimS, # local evaluation distance
start.vals, # parameter starting values
predict, # predict desnity
...) # a few other options
\normalsize
\texttt{scrFrame} and \texttt{ssDF}:
- we know what these are now!
scrFame is the encounter data objectssDF is the state space data object
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation
scrFrame, # the scrFrame object
ssDF, # the ssDF object
encmod, # the detection function model
trimS, # local evaluation distance
start.vals, # parameter starting values
predict, # predict desnity
...) # a few other options
\normalsize
\texttt{encmod}:
A character defining which enccounter model to be used
-
"B": Binomial model (default)
- response is binary (detection/non-detection)
-
"P": Poisson model
- response is counts (frequancy of encounters)
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation
scrFrame, # the scrFrame object
ssDF, # the ssDF object
encmod, # the detection function model
trimS, # local evaluation distance
start.vals, # parameter starting values
predict, # predict desnity
...) # a few other options
\normalsize
\texttt{trimS}:
- a distance value used to restrict the integration area
- remove implausible ($>3\sigma$) activity centers
- points with practically zero capture probability
- more computationally effcient for large spatial problems
- 'trimming' to within 3$\sigma$ produces unbiased estimates
\textit{trimming} the state space
sf1 <- subFrame(rbs.sf,1)
ss1 <- rbs.ss[1]
par(ask=TRUE)
mod <- oSCR.fit(scrFrame=sf1, ssDF=ss1, trimS=2, plotit=TRUE)
mod <- oSCR.fit(scrFrame=sf1, ssDF=ss1, trimS=4, plotit=TRUE)
mod <- oSCR.fit(scrFrame=sf1, ssDF=ss1, trimS=6, plotit=TRUE)
mod <- oSCR.fit(scrFrame=sf1, ssDF=ss1, trimS=NULL, plotit=TRUE) #DEFAULT
\begin{tikzpicture}[overlay]
\node[inner sep=0pt] (one) at (5.5,-2) {\includegraphics[height=1.5in]{trim.png}};
\end{tikzpicture}
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation
scrFrame, # the scrFrame object
ssDF, # the ssDF object
encmod, # the detection function model
trimS, # local evaluation distance
start.vals, # parameter starting values
predict, # predict desnity
...) # a few other options
\normalsize
\texttt{start.vals}:
- starting values for the parameters to be estimated
- a preliminary model run can give ball park values
- models can be sensitive to starting values
- use
getStarts=TRUE to get parameters and order
Getting starting values
For example:
sf1 <- subFrame(rbs.sf,1)
ss1 <- rbs.ss[1]
(oSCR.fit(model=list(D~1, p0~1, sig~1), scrFrame = sf1,
ssDF = ss1, getStarts = T))
(oSCR.fit(model=list(D~1, p0~t, sig~1), scrFrame = sf1,
ssDF = ss1, getStarts = T))
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation
scrFrame, # the scrFrame object
ssDF, # the ssDF object
encmod, # the detection function model
trimS, # local evaluation distance
start.vals, # parameter starting values
predict, # predict desnity
...) # a few other options
\normalsize
\texttt{predict}:
- compute a predicted density surface
- supply mle's as
start.vals
- (we'll see this in action later!)
\texttt{oSCR} - Model fitting with the \textit{rbs} data
Takes $\sim$ 7 mins, can get the model fits here: data(rbs.mods))
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4))
ss.sub <- rbs.ss[c(2,4)]
st <- c(-3.4, 0.04, 0.08, -1, -0.08)
#NULL model (SCR0)
m0 <- oSCR.fit(model=list(D~1,p0~1, sig~1), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4)])
\texttt{oSCR} - Model fitting with the \textit{rbs} data
Takes $\sim$ 7 mins, can get the model fits here: data(rbs.mods))
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4))
ss.sub <- rbs.ss[c(2,4)]
st <- c(-3.4, 0.04, 0.08, -1, -0.08)
#NULL model (SCR0)
m0 <- oSCR.fit(model=list(D~1,p0~1, sig~1), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4)])
#session-specific desnsity
m1 <- oSCR.fit(model=list(D~session,p0~1, sig~1), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4,5)])
\texttt{oSCR} - Model fitting with the \textit{rbs} data
Takes $\sim$ 7 mins, can get the model fits here: data(rbs.mods))
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4))
ss.sub <- rbs.ss[c(2,4)]
st <- c(-3.4, 0.04, 0.08, -1, -0.08)
#NULL model (SCR0)
m0 <- oSCR.fit(model=list(D~1,p0~1, sig~1), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4)])
#session-specific desnsity
m1 <- oSCR.fit(model=list(D~session,p0~1, sig~1), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4,5)])
#session-specific sigma
m2 <- oSCR.fit(model=list(D~1,p0~1, sig~session), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,2,3,4)])
\texttt{oSCR} - Model fitting with the \textit{rbs} data
Takes $\sim$ 7 mins, can get the model fits here: data(rbs.mods))
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4))
ss.sub <- rbs.ss[c(2,4)]
st <- c(-3.4, 0.04, 0.08, -1, -0.08)
#NULL model (SCR0)
m0 <- oSCR.fit(model=list(D~1,p0~1, sig~1), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4)])
#session-specific desnsity
m1 <- oSCR.fit(model=list(D~session,p0~1, sig~1), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4,5)])
#session-specific sigma
m2 <- oSCR.fit(model=list(D~1,p0~1, sig~session), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,2,3,4)])
#session-specific density & sigma
m3 <- oSCR.fit(model=list(D~session,p0~1, sig~session), scrFrame=sf.sub,
ssDF=ss.sub, trim=4, start.vals = st[c(1,2,3,4,5)])
\texttt{oSCR} - Model output
data(rbs.mods)
#NULL model (SCR0)
m0
\texttt{oSCR} - Model output
#session-specific desnsity
m1
\texttt{oSCR} - Model output
#session-specific sigma
m2
\texttt{oSCR} - Model output
#session-specific density & sigma
m3
\texttt{oSCR} - Model output
#session-specific density & sigma
m3
\normalsize
- so which model is the right model?
- how could we discriminate betweem models?
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
fitList.oSCR()modSel.oSCR()ma.coef()
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
fitList.oSCR()
- a list of models fitted in
oSCR
- can apply other summarizing functions to that list
(fl <- fitList.oSCR(x, # list of fitted models
rename)) # if TRUE models given sensible names
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
fitList.oSCR()
- a list of models fitted in
oSCR
- can apply other summarizing functions to that list
(fl <- fitList.oSCR(list(m0,m1,m2,m3),
rename=T))
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
modSel.oSCR()
- compare multiple models in a
fitList.oSCR list
- generates an AIC table (
aic.tab)
- generates an coeficient table (
coef.tab)
ms <- modSel.oSCR(fl)
ms$aic.tab
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
modSel.oSCR()
- compare multiple models in a
fitList.oSCR list
- generates an AIC table (
aic.tab)
- generates an coeficient table (
coef.tab)
ms <- modSel.oSCR(fl)
ms$coef.tab
\texttt{oSCR} - Model selection
modSel.oSCR()
ms
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
ma.coef()
- takes a
modSel.oSCR object
- generates model averaged coeficients (standard and shrinkage)
- generates unconditional standard errors
- generates relative variable importance
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
ma.coef()
- takes a
modSel.oSCR object
- generates model averaged coeficients (standard and shrinkage)
- generates unconditional standard errors
- generates relative variable importance
(ma <- ma.coef(ms))
In class exercise: Ocelot data
\vspace{2.5cm}
\begin{center}
\Huge The \textcolor{mLightBrown}{Ocelot} data
\footnotesize photo: http://felid-tag.org/ocelot/
\end{center}
\begin{tikzpicture}[overlay]
\node[inner sep=0pt] (one) at (0.5, 4.01) {\includegraphics[height=1.5in]{Ocelot_area.png}};
\node[inner sep=0pt] (one) at (10.1,-1.5) {\includegraphics[height=0.8in]{ocelot.jpg}};
\end{tikzpicture}
In class exercise: Ocelot data
\small
Access the ocelot data (data(ocelot)) and, in small groups:
-
Make an scrFrame for the 2-session ocelot data
data2oscr(), make.scrFrame()
-
Make a state space with a 2000m buffer and 500m resolution
make.ssDF(), plot.ssDF()
-
Estimate density (/100 km^2) and sigma for the simplest SCR model
oSCR.fit()
-
Fit 4 models to assess variation in density and/or sigma by session
-
Which of theses 4 models is better supported by AIC
fitList.oSCR(), modSel.oSCR(), ma.coef()
In class exercise: Ocelot data
- Make an
scrFrame for the 2-session ocelot data
data(ocelot)
# convert 'secr' format to objects for oSCR
ocelot <-data2oscr(rbind(edf1,edf2), # encounter data file
K=c(44,96), # occasions per session
ntraps=c(23,23), # traps per session
tdf=list(tdf1,tdf2), # trap deployment files (a list)
remove.zeros=TRUE, # remove uncaptured inds
remove.extracaps=TRUE) # turn >1 to 1
# make the scrFrame
ocelot.sf <- make.scrFrame(caphist = ocelot$y3d,
traps = ocelot$traplocs,
trapOperation = ocelot$trapopp,
type="scr")
In class exercise: Ocelot data
- Make an
scrFrame for the 2-session ocelot data
par(mfrow=c(1,2), oma=c(0,0,0,0),mar=c(1,1,1,1))
plot(ocelot.sf, ax=FALSE)
In class exercise: Ocelot data
- Make a state space with a 2000m buffer and 500m resolution
# make a state-space
ocelot.ss <- make.ssDF(ocelot.sf, buffer=2000, res = 500)
par(mfrow=c(1,2))
plot(ocelot.ss,ocelot.sf)
In class exercise: Ocelot data
- Estimate density (/100 km^2) and sigma for the simplest SCR model
data(ocelot.mods)
# fit the null (default!) model
m0 <- oSCR.fit(model=list(D ~ 1, p0 ~ 1, sig~1), # model
scrFrame = ocelot.sf, # scrFrame
ssDF = ocelot.ss, # ssDF
trimS = 1000, se=FALSE))
m0
In class exercise: Ocelot data
- Fit 4 models to assess variation in density and/or sigma by session
# NULL
m0 <- oSCR.fit(model=list(D ~ 1, p0 ~ 1, sig~1), scrFrame = ocelot.sf,
ssDF = ocelot.ss, trimS = 1000)
# D ~ session only
m1 <- oSCR.fit(model=list(D ~ session, p0 ~ 1, sig~1), scrFrame = ocelot.sf,
ssDF = ocelot.ss, trimS = 1000)
# sig ~ session only
m2 <- oSCR.fit(model=list(D ~ 1, p0 ~ 1, sig~session), scrFrame = ocelot.sf,
ssDF = ocelot.ss, trimS = 1000)
# D ~ sesison AND sig ~ session
m3 <- oSCR.fit(model=list(D ~ session, p0 ~ 1, sig~session), scrFrame = ocelot.sf,
ssDF = ocelot.ss, trimS = 1000)
In class exercise: Ocelot data
- Which of theses 4 models is better supported by AIC
# make a 'fit list'
ocelot.fl <- fitList.oSCR(list(m0,m1,m2,m3), rename = TRUE)
# compare models using AIC
ocelot.ms <- modSel.oSCR(ocelot.fl)
ocelot.ms$aic.tab
jaroyle/oSCR documentation built on Sept. 23, 2023, 12:46 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
library(knitr) library(oSCR) #library(scrbook) options(width=120) options(width.cutoff=80) opts_chunk$set(prompt = FALSE, comment = NA, mysize=TRUE, size="\\scriptsize") hook1 <- function(x){ gsub("```\n*```r*\n*", "", x) } hook2 <- function(x){ gsub("```\n+```\n", "", x) } knit_hooks$set(document = hook2) knitr::knit_hooks$set(mysize = function(before, options, envir) { if (before) return(options$size) })
What is \texttt{oSCR}?
The \textcolor{mLightBrown}{\texttt{o}} is for open
\begin{itemize}
\item<1-> built upon various functions in \texttt{scrbook}
\item<2-> an editable and evolving code base
\item<3-> a community of contributors
\begin{itemize}
\item<3-> \textcolor{gray}{\textit{contributing}} ideas
\item<3-> \textcolor{gray}{\textit{contributing}} problems
\item<3-> \textcolor{gray}{\textit{contributing}} solutions
\item<3-> \textcolor{gray}{\textit{contributing}} code
\end{itemize}
\item<4-> a philosophy of 'parallel publishing'
\begin{itemize}
\item<4-> \textcolor{gray}{\textit{increase}} transparency
\item<4-> \textcolor{gray}{\textit{increase}} accessibility
\end{itemize}
\end{itemize}
\begin{tikzpicture}[overlay] \node[inner sep=0pt] (one) at (10,4) {\includegraphics[height=1.2in]{scrbook.png}}; \node[inner sep=0pt] (one) at (10,0.91) {\includegraphics[height=0.8in]{oSCR.png}}; \end{tikzpicture}
What is \texttt{oSCR}?
$\ldots$ more about \texttt{oSCR}
\begin{itemize} \item<1-> one of several ways to analyze SCR data \begin{itemize} \item<1-> alternative (\textit{not} substitute) to \texttt{secr} \item<1-> (see Dan's lecture tomorrow) \item<1-> alternative to Bayesian analysis \end{itemize} \item<2-> likelihood based - has advantages \begin{itemize} \item<2-> \textcolor{gray}{\textit{advantage}} speed \item<2-> \textcolor{gray}{\textit{advantage}} model selection methods \item<2-> \textcolor{gray}{\textit{advantage}} cost surface modeling \item<2-> \textcolor{gray}{\textit{advantage}} user friendly \end{itemize} \end{itemize} \begin{tikzpicture}[overlay] \node[inner sep=0pt] (one) at (10,0.175) {\includegraphics[height=0.8in]{oSCR.png}}; \end{tikzpicture}
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories traps, # trap coordinates trapCovs, # trap level covariates indCovs, # sex data trapOperation, # binary operation indicator type) # data format type
\normalsize \texttt{?make.scrFrame}
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories traps, # trap coordinates trapCovs, # trap level covariates indCovs, # sex data trapOperation, # binary operation indicator type) # data format type
\normalsize \texttt{caphist} ($y_{ijk}$):
- spatial capture history object
- array with dimensions n x J x K (ind-by-trap-by-occasion)
- binary (detected or not) $\rightarrow$ Binomial encounter model
- counts (no. of detecteds) $\rightarrow$ Poisson encounter model
\texttt{caphist}
- schematically:
\scalebox{0.6}{ \begin{tikzpicture}[overlay] \matrix[draw=none,inner sep=0pt] (C) at (5,-3)[matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=0.2,text height=1ex,nodes in empty cells] { 3 \& 2 \& 0 \& 0 \& \cdots \& \& \& \& \ 1 \& 0 \& 1 \& \cdots \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \vdots \ \& \& \& \& \& \& \& \vdots \& 4 \ \& \& \& \& \& \& \& 3 \& 0 \ \& \& \& \& \& \& \& 1 \& 1 \ }; \fill[gray,opacity=.2] (C-2-1.south west) -- (C-1-1.north west) -- (C-1-9.north east) -- (C-11-9.south east) -- (C-11-8.south west) -- (C-3-8.north west) -- (C-2-1.south west); \draw[opacity=0.2] (C-2-1.south west) -- (C-1-1.north west)--(C-1-9.north east)--(C-11-9.south east)--(C-11-8.south west);
\matrix[draw=none,inner sep=0pt] (D) at (4,-4)[matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=0.35,text height=1ex,nodes in empty cells] { 2 \& 2 \& 1 \& 0 \& \cdots \& \& \& \& \ 4 \& 0 \& 0 \& \cdots \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \vdots \ \& \& \& \& \& \& \& \vdots \& 0 \ \& \& \& \& \& \& \& 0 \& 2 \ \& \& \& \& \& \& \& 1 \& 0 \ %%%%%% 8 }; \fill[gray,opacity=.35] (D-3-1.south west) -- (D-1-1.north west) -- (D-1-9.north east) -- (D-11-9.south east) -- (D-11-8.south west) -- (D-4-8.north west) -- (D-3-1.south west); \draw[opacity=0.35] (D-3-1.south west) -- (D-1-1.north west)--(D-1-9.north east)--(D-11-9.south east)--(D-11-8.south west);
\matrix[draw,inner sep=0pt] (E) at (3,-5) [matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=1,fill=gray,text height=1ex,nodes in empty cells] { 1 \& 3 \& 0\& 1\& \cdots \& \& \& \& \ 6 \& 1 \& 2\& \& \& \& \& \& \ 0 \& 0 \& \& \& \& \& \& \& \ 3 \& \& \& \& \& \& \& \& \ \vdots \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \&\vdots \ \& \& \& \& \& \& \& \& 3 \ \& \& \& \& \& \& \& 0 \& 0 \ \& \& \& \& \& \cdots \& 0 \& 0 \& 0 \ };%
\draw[] (E-6-5) node {\large\textcolor{green}{$\boldsymbol{y_{i,j,r}}$}}; \draw[] (E-7-5) node {\large\textcolor{green}{counts}};
%Trap \draw[] (C-1-1.north east) node[above left] {\textbf{Trap = 1}}; \draw[] (C-1-9.north) node[above] {\textbf{$J$}}; \draw[->, thick] ([yshift=7.5]C-1-1.north east) -- ([yshift=7.5]C-1-9.north west);
%Ind \draw[] (E-1-1.west) node[left, yshift=2] {\textbf{Ind. = 1}}; \draw[] (E-11-1.west) node[left, yshift=2] {\textbf{$n_{obs}$}}; \draw[->, thick] ([xshift=-7.5]E-2-1.west) -- ([xshift=-7.5]E-10-1.west);
\draw[] (E-11-9.south) node[below] {\textbf{Occassion = 1}}; \draw[] (C-11-9.east) node[right, xshift=2ex] {\textbf{$K$}}; \draw[->, thick] ([xshift=2ex]E-11-9.south east) -- ([xshift=2ex]C-11-9.south east);
\matrix[draw=none,inner sep=0pt] (C) at (15,-3)[matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=0.2,text height=1ex,nodes in empty cells] { 1\& 1\& 0\& 0 \& \cdots \& \& \& \& \ 1\& 0\& 1\& \cdots \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \vdots \ \& \& \& \& \& \& \& \vdots \& 1 \ \& \& \& \& \& \& \& 1 \& 0 \ \& \& \& \& \& \& \& 1 \& 1 \ %%%%%% 11 }; \fill[gray,opacity=.2] (C-2-1.south west) -- (C-1-1.north west) -- (C-1-9.north east) -- (C-11-9.south east) -- (C-11-8.south west) -- (C-3-8.north west) -- (C-2-1.south west); \draw[opacity=0.2] (C-2-1.south west) -- (C-1-1.north west)--(C-1-9.north east)--(C-11-9.south east)--(C-11-8.south west);
\matrix[draw=none,inner sep=0pt] (D) at (14,-4)[matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=0.35,text height=1ex,nodes in empty cells] { 1 \& 1\& 1\& 0 \& \cdots \& \& \& \& \ 1 \& 0\& 0\& \cdots \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \vdots \ \& \& \& \& \& \& \& \vdots \& 0 \ \& \& \& \& \& \& \& 0 \& 1 \ \& \& \& \& \& \& \& 1 \& 0 \ %%%%%% 8 }; \fill[gray,opacity=.35] (D-3-1.south west) -- (D-1-1.north west) -- (D-1-9.north east) -- (D-11-9.south east) -- (D-11-8.south west) -- (D-4-8.north west) -- (D-3-1.south west); \draw[opacity=0.35] (D-3-1.south west) -- (D-1-1.north west)--(D-1-9.north east)--(D-11-9.south east)--(D-11-8.south west);
\matrix[draw,inner sep=0pt] (E) at (13,-5) [matrix of math nodes,ampersand replacement=\&,nodes={outer sep=0pt,minimum width=5mm,minimum height=5mm, anchor=center,},opacity=1,fill=gray,text height=1ex,nodes in empty cells] { 1 \& 1 \& 0 \& 1\& \cdots \& \& \& \& \ 1 \& 1 \& 1 \& \& \& \& \& \& \ 0 \& 0 \& \& \& \& \& \& \& \ 1 \& \& \& \& \& \& \& \& \ \vdots \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \ \& \& \& \& \& \& \& \& \vdots \ \& \& \& \& \& \& \& \& 1 \ \& \& \& \& \& \& \& 0 \& 0 \ \& \& \& \& \& \cdots \& 0 \& 0 \& 0 \ };%
\draw[] (E-6-5) node {\large\textcolor{green}{$\boldsymbol{y_{i,j,r}}$}}; \draw[] (E-7-5) node {\large\textcolor{green}{detections}};
%Trap \draw[] (C-1-1.north east) node[above left] {\textbf{Trap = 1}}; \draw[] (C-1-9.north) node[above] {\textbf{$J$}}; \draw[->, thick] ([yshift=7.5]C-1-1.north east) -- ([yshift=7.5]C-1-9.north west);
%Ind \draw[] (E-1-1.west) node[left, yshift=2] {\textbf{Ind. = 1}}; \draw[] (E-11-1.west) node[left, yshift=2] {\textbf{$n_{obs}$}}; \draw[->, thick] ([xshift=-7.5]E-2-1.west) -- ([xshift=-7.5]E-10-1.west);
\draw[] (E-11-9.south) node[below] {\textbf{Occassion = 1}}; \draw[] (C-11-9.east) node[right, xshift=2ex] {\textbf{$K$}}; \draw[->, thick] ([xshift=2ex]E-11-9.south east) -- ([xshift=2ex]C-11-9.south east); \end{tikzpicture} }
\texttt{caphist}
- in
R:
yarr <- array(rbinom(3*10*3,1,0.4),c(3,10,3))
yarr
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories traps, # trap coordinates trapCovs, # trap level covariates indCovs, # sex data trapOperation, # binary operation indicator type) # data format type
\normalsize \texttt{traps}:
- a trap coordinate data frame
- coordinates must be named
XandY(upper case) - all traps operational at least once (see
trapOperation) - know your units!
- spatial units must be consistent throughout
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories traps, # trap coordinates trapCovs, # trap level covariates indCovs, # sex data trapOperation, # binary operation indicator type) # data format type
\normalsize \texttt{trapCovs}:
- a $k$-length list of trap covariate data frames
- can model occassion-specific variation in $p$, i.e. $p_k$
- temperature
- Julian day, etc$\ldots$
NA's allowed
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories traps, # trap coordinates trapCovs, # trap level covariates indCovs, # sex data trapOperation, # binary operation indicator type) # data format type
\normalsize \texttt{indCovs}:
- a data frame containing individual-level data
- currently only with a two-class categorical variables
- typically male/female (male = 1)
- can accomodate missing data
- if provided, 2-class mixture model always fitted
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories traps, # trap coordinates trapCovs, # trap level covariates indCovs, # sex data trapOperation, # binary operation indicator type) # data format type
\normalsize \texttt{trapOperation}:
- binary J x K (trap-by-occasion) matrix
- denotes whether a trap was operational (1) or not (0), in each occasion
- unoperational traps get discarded from any calculations
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
sf <- make.scrFrame(caphist, # spatial encounter histories traps, # trap coordinates trapCovs, # trap level covariates indCovs, # sex data trapOperation, # binary operation indicator type) # data format type
\normalsize \texttt{type}:
- for now always set to
SCR - in the future will allow for alternative formats
- secr
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
- each object must be supplied as a list
make.scrFrame()does internal checks for consistencies- the resulting data object (
sf) is ready for use - list structure makes multi-session data formatting easy
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
- each object must be supplied as a list
make.scrFrame()does internal checks for consistencies- the resulting data object (
sf) is ready for use - list structure makes multi-session data formatting easy
- \textcolor{mLightBrown}{{\it single}} session data:
sf <- make.scrFrame(caphist = list(ch), traps = list(tr), trapCovs = list(list(tc1,tc2,tc3)), #k=3 indCovs = list(ic), trapOperation = list(to), type = "SCR")
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
- each object must be supplied as a list
make.scrFrame()does internal checks for consistencies- the resulting data object (
sf) is ready for use - list structure makes multi-session data formatting easy
- \textcolor{mLightBrown}{{\it two}} session data:
sf <- make.scrFrame(caphist = list(ch1, ch2), traps = list(tr1, tr1), trapCovs = list(list(tc1.1,tc1.2,tc1.3), list(tc2.1,tc2.2,tc2.3)), #k=3 indCovs = list(ic1, ic2), trapOperation = list(to1,to2), type = "SCR")
\texttt{oSCR} - Data organization and structure
scrFrame: the main data object for model fitting:
- each object must be supplied as a list
make.scrFrame()does internal checks for consistencies- the resulting data object (
sf) is ready for use - list structure makes multi-session data formatting easy
- \textcolor{mLightBrown}{{\it three}} session data:
sf <- make.scrFrame(caphist = list(ch1, ch2, ch3), traps = list(tr1, tr1, tr3), trapCovs = list(list(tc1.1,tc1.2,tc1.3), list(tc2.1,tc2.2,tc2.3), list(tc3.1,tc3.2,tc3.3)), #k=3 indCovs = list(ic1, ic2, ic3), trapOperation = list(to1,to2, to3), type = "SCR")
\normalsize
$\ldots$ and so on and so forth
\texttt{oSCR} - Data organization and structure
Data formats:
- data collection and storage formats vary widely
secrformat is a common format- row per observation
- e.g., individual, trap, occasion, session
- function to convert
secrtooSCRformatdata2oscr()
- can use work session to format personal data
Exploring the \texttt{scrFrame}
Lets look at some real data
- redback salamnders Plethodon cinereus
- 4 sampling grids withing a single forest
- 5 $\times$ 10 cover boards spaced 1m apart
\begin{tikzpicture}[overlay] \node[inner sep=0pt] (one) at (9,-1) {\includegraphics[height=2.8in]{sampling.png}}; \node[inner sep=0pt] (one) at (4,-2) {\includegraphics[height=1.75in]{mark.png}}; \end{tikzpicture}
Exploring the \texttt{scrFrame}
- you can run this code!
library(oSCR) data(rbs) ls() [1] "rbs.sf" "rbs.ss"
library(oSCR) data(rbs)
\normalsize
rbs.sfis the redback salanderscrFrameobject
Exploring the \texttt{scrFrame}
- you can run this code!
library(oSCR) data(rbs) rbs.sf
Subsetting the \texttt{scrFrame}
subFrame()can be used to efficiently subset thescrFrame
sf.sub <- subFrame(scrFrame, # the scrFrame to be subsetted subs) # the index/indices to be kept
Subsetting the \texttt{scrFrame}
subFrame()can be used to efficiently subset thescrFrame
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4)) sf.sub
Subsetting the \texttt{scrFrame}
- let's try that with the
rbsdata:
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4)) sf.sub
\texttt{oSCR} - Data organization and structure
State space definition is extremely important
- part of the model
- an approximation of activity centers (ac)
- resolution should be $\le \hat{\sigma}$
- should represent all ac of detectable individuals
- buffer of at least $2\hat{\sigma}$ around traps
\begin{tikzpicture}[overlay] \node[inner sep=0pt] (one) at (5,-1.5) {\includegraphics[height=1.2in]{sbuf.png}}; \end{tikzpicture}
\texttt{oSCR} - Data organization and structure
ssDF: the state space data object (\textbf{s}tate \textbf{s}pace {\textbf{d}ata \textbf{f}rame):
- a list of data frames (one per session)
- coordinates of each pixel
- named
XandY(upper case) - each coordinate represents a pixel
- named
- named columns of pixel-specific covariate values
- used for modelling spatially varying density
- can be continuous or categorical
- non-habitat can be removed
- coordinates should be same units as
traps
\texttt{oSCR} - Data organization and structure
Making the ssDF object requires constructing a list of data frames
ssDF <- list(ss1, # dataframe for session 1 ss2, # dataframe for session 2 ss3, # dataframe for session 3 ss4) # dataframe for session 4
Exploring the \texttt{ssDF}
Let's work with the salamander state space object:
str(rbs.ss, give.attr=FALSE)
Exploring the \texttt{ssDF}
Sub setting ssDF is easily done:
# sub setting ssDF is easy: ss.sub <- rbs.ss[c(1,2)]
Exploring the \texttt{ssDF}
Sub setting ssDF is easily done:
# sub setting ssDF is easy: ss.sub <- rbs.ss[c(1,2)] str(ss.sub, give.attr=FALSE)
Exploring the \texttt{ssDF}
We can plot the object
par(mfrow=c(2,2), oma=c(0,0,0,0),mar=c(4,4,2,2))
par(mfrow=c(1,4)) #4 sessions plot.ssDF(rbs.ss)
Exploring the \texttt{ssDF}
We can plot the object with the traps
par(mfrow=c(1,4)) #4 sessions plot.ssDF(rbs.ss, scrFrame=rbs.sf)
Constructing a \texttt{ssDF}
If no interest in assessing spatial variation in density
- the state space is somewhat arbitrary
- no covariates
- we can make an
ssDFobject:make.ssDF()
ssDF <- make.ssDF(scrFrame, # an scrFRame objects buffer, # a buffer witdh (around traps!) res) # the distance between S points
Constructing a \texttt{ssDF}
par(mfrow=c(1,2))
ssDF <- make.ssDF(scrFrame = sf.sub, buffer = 1, res = 1) plot(ssDF, sf.sub)
Constructing a \texttt{ssDF}
ssDF <- make.ssDF(scrFrame = sf.sub, buffer = 5, res = 0.5) plot(ssDF, sf.sub)
\texttt{oSCR} - Model fitting
With an scrFrame and ssDF object, we can start fitting models uning the fitting function oSCR.fit()
mod <- oSCR.fit(model, # model formulation scrFrame, # the scrFrame object ssDF, # the ssDF object encmod, # the detection function model trimS, # local evaluation distance start.vals, # parameter starting values predict, # predict desnity ...) # a few other options
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation scrFrame, # the scrFrame object ssDF, # the ssDF object encmod, # the detection function model trimS, # local evaluation distance start.vals, # parameter starting values predict, # predict desnity ...) # a few other options
\normalsize \texttt{model}:
- a list with 4 model formulations
list(D ~ 1, p0 ~ 1, sig ~ 1, asu ~ 1)D ~: model describing variation in densityp0 ~: model describing variation in baseline encounter prob/ratesig ~: model describibg variation in sigmaasu ~: model for a cost surface
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation scrFrame, # the scrFrame object ssDF, # the ssDF object encmod, # the detection function model trimS, # local evaluation distance start.vals, # parameter starting values predict, # predict desnity ...) # a few other options
\normalsize \texttt{model}:
- a list with 3 model formulations
list(D ~ 1, p0 ~ 1, sig ~ 1)D ~: model describing variation in densityp0 ~: model describing variation in baseline encounter prob/ratesig ~: model describibg variation in sigma
\texttt{oSCR} - model choices
Varaition in \textcolor{blue}{density} (D ~)
D ~ 1 # null model, constant density D ~ session # density varies by session D ~ "covariate" # density varies by spatially indexed covariates
\normalsize
- includes additive and interaction models
- includes all combinations
"covariate"must match column names inssDFD ~ 1is the default
\texttt{oSCR} - model choices
Varaition in \textcolor{blue}{detection} (p0 ~)
p0 ~ 1 # null model, constant p (M0) p0 ~ t # occasion specific p (Mt) p0 ~ b # behavioural response (Mb) p0 ~ sex # p varies by sex p0 ~ session # p varies by session p0 ~ "covariate" # p varies by trap level covariates
\normalsize
- includes additive and interaction models
- includes most combinations
"covariate"must match column names intrapCovsp0 ~ 1is the default
\texttt{oSCR} - model choices
Varaition in \textcolor{blue}{sigma} (sig ~)
sig ~ 1 # null model, constant sigma sig ~ sex # sex-specific sigma sig ~ session # session-specific sigma
\normalsize
- includes additive and interaction models
- includes all combinations
sig ~ 1is the default
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation scrFrame, # the scrFrame object ssDF, # the ssDF object encmod, # the detection function model trimS, # local evaluation distance start.vals, # parameter starting values predict, # predict desnity ...) # a few other options
\normalsize \texttt{scrFrame} and \texttt{ssDF}:
- we know what these are now!
scrFameis the encounter data objectssDFis the state space data object
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation scrFrame, # the scrFrame object ssDF, # the ssDF object encmod, # the detection function model trimS, # local evaluation distance start.vals, # parameter starting values predict, # predict desnity ...) # a few other options
\normalsize \texttt{encmod}:
A character defining which enccounter model to be used
-
"B": Binomial model (default)- response is binary (detection/non-detection)
-
"P": Poisson model- response is counts (frequancy of encounters)
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation scrFrame, # the scrFrame object ssDF, # the ssDF object encmod, # the detection function model trimS, # local evaluation distance start.vals, # parameter starting values predict, # predict desnity ...) # a few other options
\normalsize \texttt{trimS}:
- a distance value used to restrict the integration area
- remove implausible ($>3\sigma$) activity centers
- points with practically zero capture probability
- more computationally effcient for large spatial problems
- 'trimming' to within 3$\sigma$ produces unbiased estimates
\textit{trimming} the state space
sf1 <- subFrame(rbs.sf,1) ss1 <- rbs.ss[1] par(ask=TRUE) mod <- oSCR.fit(scrFrame=sf1, ssDF=ss1, trimS=2, plotit=TRUE) mod <- oSCR.fit(scrFrame=sf1, ssDF=ss1, trimS=4, plotit=TRUE) mod <- oSCR.fit(scrFrame=sf1, ssDF=ss1, trimS=6, plotit=TRUE) mod <- oSCR.fit(scrFrame=sf1, ssDF=ss1, trimS=NULL, plotit=TRUE) #DEFAULT
\begin{tikzpicture}[overlay] \node[inner sep=0pt] (one) at (5.5,-2) {\includegraphics[height=1.5in]{trim.png}}; \end{tikzpicture}
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation scrFrame, # the scrFrame object ssDF, # the ssDF object encmod, # the detection function model trimS, # local evaluation distance start.vals, # parameter starting values predict, # predict desnity ...) # a few other options
\normalsize \texttt{start.vals}:
- starting values for the parameters to be estimated
- a preliminary model run can give ball park values
- models can be sensitive to starting values
- use
getStarts=TRUEto get parameters and order
Getting starting values
For example:
sf1 <- subFrame(rbs.sf,1) ss1 <- rbs.ss[1] (oSCR.fit(model=list(D~1, p0~1, sig~1), scrFrame = sf1, ssDF = ss1, getStarts = T))
(oSCR.fit(model=list(D~1, p0~t, sig~1), scrFrame = sf1, ssDF = ss1, getStarts = T))
\texttt{oSCR} - Model fitting
mod <- oSCR.fit(model, # model formulation scrFrame, # the scrFrame object ssDF, # the ssDF object encmod, # the detection function model trimS, # local evaluation distance start.vals, # parameter starting values predict, # predict desnity ...) # a few other options
\normalsize \texttt{predict}:
- compute a predicted density surface
- supply mle's as
start.vals - (we'll see this in action later!)
\texttt{oSCR} - Model fitting with the \textit{rbs} data
Takes $\sim$ 7 mins, can get the model fits here: data(rbs.mods))
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4)) ss.sub <- rbs.ss[c(2,4)] st <- c(-3.4, 0.04, 0.08, -1, -0.08) #NULL model (SCR0) m0 <- oSCR.fit(model=list(D~1,p0~1, sig~1), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4)])
\texttt{oSCR} - Model fitting with the \textit{rbs} data
Takes $\sim$ 7 mins, can get the model fits here: data(rbs.mods))
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4)) ss.sub <- rbs.ss[c(2,4)] st <- c(-3.4, 0.04, 0.08, -1, -0.08) #NULL model (SCR0) m0 <- oSCR.fit(model=list(D~1,p0~1, sig~1), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4)]) #session-specific desnsity m1 <- oSCR.fit(model=list(D~session,p0~1, sig~1), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4,5)])
\texttt{oSCR} - Model fitting with the \textit{rbs} data
Takes $\sim$ 7 mins, can get the model fits here: data(rbs.mods))
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4)) ss.sub <- rbs.ss[c(2,4)] st <- c(-3.4, 0.04, 0.08, -1, -0.08) #NULL model (SCR0) m0 <- oSCR.fit(model=list(D~1,p0~1, sig~1), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4)]) #session-specific desnsity m1 <- oSCR.fit(model=list(D~session,p0~1, sig~1), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4,5)]) #session-specific sigma m2 <- oSCR.fit(model=list(D~1,p0~1, sig~session), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,2,3,4)])
\texttt{oSCR} - Model fitting with the \textit{rbs} data
Takes $\sim$ 7 mins, can get the model fits here: data(rbs.mods))
sf.sub <- subFrame(scrFrame = rbs.sf, subs = c(2,4)) ss.sub <- rbs.ss[c(2,4)] st <- c(-3.4, 0.04, 0.08, -1, -0.08) #NULL model (SCR0) m0 <- oSCR.fit(model=list(D~1,p0~1, sig~1), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4)]) #session-specific desnsity m1 <- oSCR.fit(model=list(D~session,p0~1, sig~1), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,3,4,5)]) #session-specific sigma m2 <- oSCR.fit(model=list(D~1,p0~1, sig~session), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,2,3,4)]) #session-specific density & sigma m3 <- oSCR.fit(model=list(D~session,p0~1, sig~session), scrFrame=sf.sub, ssDF=ss.sub, trim=4, start.vals = st[c(1,2,3,4,5)])
\texttt{oSCR} - Model output
data(rbs.mods)
#NULL model (SCR0)
m0
\texttt{oSCR} - Model output
#session-specific desnsity
m1
\texttt{oSCR} - Model output
#session-specific sigma
m2
\texttt{oSCR} - Model output
#session-specific density & sigma
m3
\texttt{oSCR} - Model output
#session-specific density & sigma
m3
\normalsize
- so which model is the right model?
- how could we discriminate betweem models?
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
fitList.oSCR()modSel.oSCR()ma.coef()
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
fitList.oSCR()- a list of models fitted in
oSCR - can apply other summarizing functions to that list
- a list of models fitted in
(fl <- fitList.oSCR(x, # list of fitted models rename)) # if TRUE models given sensible names
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
fitList.oSCR()- a list of models fitted in
oSCR - can apply other summarizing functions to that list
- a list of models fitted in
(fl <- fitList.oSCR(list(m0,m1,m2,m3), rename=T))
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
modSel.oSCR()- compare multiple models in a
fitList.oSCRlist - generates an AIC table (
aic.tab) - generates an coeficient table (
coef.tab)
- compare multiple models in a
ms <- modSel.oSCR(fl) ms$aic.tab
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
modSel.oSCR()- compare multiple models in a
fitList.oSCRlist - generates an AIC table (
aic.tab) - generates an coeficient table (
coef.tab)
- compare multiple models in a
ms <- modSel.oSCR(fl) ms$coef.tab
\texttt{oSCR} - Model selection
modSel.oSCR()
ms
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
ma.coef()- takes a
modSel.oSCRobject - generates model averaged coeficients (standard and shrinkage)
- generates unconditional standard errors
- generates relative variable importance
- takes a
\texttt{oSCR} - Model selection
oSCR has some post processing and model selection functions:
ma.coef()- takes a
modSel.oSCRobject - generates model averaged coeficients (standard and shrinkage)
- generates unconditional standard errors
- generates relative variable importance
- takes a
(ma <- ma.coef(ms))
In class exercise: Ocelot data
\vspace{2.5cm}
\begin{center} \Huge The \textcolor{mLightBrown}{Ocelot} data
\footnotesize photo: http://felid-tag.org/ocelot/ \end{center}
\begin{tikzpicture}[overlay] \node[inner sep=0pt] (one) at (0.5, 4.01) {\includegraphics[height=1.5in]{Ocelot_area.png}}; \node[inner sep=0pt] (one) at (10.1,-1.5) {\includegraphics[height=0.8in]{ocelot.jpg}}; \end{tikzpicture}
In class exercise: Ocelot data
\small
Access the ocelot data (data(ocelot)) and, in small groups:
-
Make an
scrFramefor the 2-session ocelot datadata2oscr(),make.scrFrame()
-
Make a state space with a 2000m buffer and 500m resolution
make.ssDF(),plot.ssDF()
-
Estimate density (/100 km^2) and sigma for the simplest SCR model
oSCR.fit()
-
Fit 4 models to assess variation in density and/or sigma by session
-
Which of theses 4 models is better supported by AIC
fitList.oSCR(),modSel.oSCR(),ma.coef()
In class exercise: Ocelot data
- Make an
scrFramefor the 2-session ocelot data
data(ocelot) # convert 'secr' format to objects for oSCR ocelot <-data2oscr(rbind(edf1,edf2), # encounter data file K=c(44,96), # occasions per session ntraps=c(23,23), # traps per session tdf=list(tdf1,tdf2), # trap deployment files (a list) remove.zeros=TRUE, # remove uncaptured inds remove.extracaps=TRUE) # turn >1 to 1 # make the scrFrame ocelot.sf <- make.scrFrame(caphist = ocelot$y3d, traps = ocelot$traplocs, trapOperation = ocelot$trapopp, type="scr")
In class exercise: Ocelot data
- Make an
scrFramefor the 2-session ocelot data
par(mfrow=c(1,2), oma=c(0,0,0,0),mar=c(1,1,1,1)) plot(ocelot.sf, ax=FALSE)
In class exercise: Ocelot data
- Make a state space with a 2000m buffer and 500m resolution
# make a state-space ocelot.ss <- make.ssDF(ocelot.sf, buffer=2000, res = 500) par(mfrow=c(1,2)) plot(ocelot.ss,ocelot.sf)
In class exercise: Ocelot data
- Estimate density (/100 km^2) and sigma for the simplest SCR model
data(ocelot.mods)
# fit the null (default!) model m0 <- oSCR.fit(model=list(D ~ 1, p0 ~ 1, sig~1), # model scrFrame = ocelot.sf, # scrFrame ssDF = ocelot.ss, # ssDF trimS = 1000, se=FALSE))
m0
In class exercise: Ocelot data
- Fit 4 models to assess variation in density and/or sigma by session
# NULL m0 <- oSCR.fit(model=list(D ~ 1, p0 ~ 1, sig~1), scrFrame = ocelot.sf, ssDF = ocelot.ss, trimS = 1000) # D ~ session only m1 <- oSCR.fit(model=list(D ~ session, p0 ~ 1, sig~1), scrFrame = ocelot.sf, ssDF = ocelot.ss, trimS = 1000) # sig ~ session only m2 <- oSCR.fit(model=list(D ~ 1, p0 ~ 1, sig~session), scrFrame = ocelot.sf, ssDF = ocelot.ss, trimS = 1000) # D ~ sesison AND sig ~ session m3 <- oSCR.fit(model=list(D ~ session, p0 ~ 1, sig~session), scrFrame = ocelot.sf, ssDF = ocelot.ss, trimS = 1000)
In class exercise: Ocelot data
- Which of theses 4 models is better supported by AIC
# make a 'fit list' ocelot.fl <- fitList.oSCR(list(m0,m1,m2,m3), rename = TRUE) # compare models using AIC ocelot.ms <- modSel.oSCR(ocelot.fl)
ocelot.ms$aic.tab
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