---
title: "GenEst - 3. Command Line Walkthrough"
author: "Juniper L. Simonis"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{GenEst - 3. Command Line Walkthrough}
  %\VignetteEngine{knitr::rmarkdown}
  %\usepackage[utf8]{inputenc}
---
```{r setup, include=FALSE}
require(rmarkdown)
require(knitr)
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r, include=FALSE}
library(GenEst)
vers <- packageVersion("GenEst")
today <- Sys.Date()
```

This vignette walks through an example of **GenEst** at the command line and
was constructed using **GenEst** version `r vers` on `r today`.


## Installation

To obtain the most recent version of **GenEst**, download the most recent
version build from
[USGS](https://code.usgs.gov/ecosystems/GenEst/-/releases) or CRAN.

## Data

For this vignette, we will be using a completely generic, mock dataset provided
with the **GenEst** package, which contains Searcher Efficiency (SE), Carcass
Persistence (CP), Search Schedule (SS), Density Weighted Proportion (DWP), and
Carcass Observation (CO) Data.

```{r}
data(mock)
names(mock)
```

## Searcher Efficiency

### Single Searcher Efficiency Model

The central function for searcher efficiency analyses is `pkm`, which, in its
most basic form, conducts a singular searcher efficiency analysis (*i.e.*, a
singular set of $p$ and $k$ formulae and a singular size classification of
carcasses). As a first example, we will ignore the size category and use
intercept-only models for both $p$ and $k$:

```{r}
data_SE <- mock$SE
pkModel <- pkm(formula_p = p ~ 1, formula_k = k ~ 1, data = data_SE)
```

Here, we have taken advantage of `pkm`'s default behavior of selecting
observation columns (see `?pkm` for details).

```{r}
head(data_SE)
```

If we wanted to explicitly control the observations, we would use the `obsCol`
argument:

```{r}
pkModel <- pkm(formula_p = p ~ 1, formula_k = k ~ 1, data = data_SE,
             obsCol = c("Search1", "Search2", "Search3", "Search4")
           )
```

Note that the search observations must be entered in order such that no
carcasses have non-detected observations (*i.e.*, `0`) after detected
observations (*i.e.*, `1`). Further, no carcasses can be detected more than
once.

If successfully fit, a `pkm` model output contains a number of elements,
some printed automatically:

```{r}
pkModel
```

and others available upon request:

```{r}
names(pkModel)
pkModel$cells
```

The `plot` function has been defined for `pkm` objects, such that one can
simply run

```{r, fig.show = "hold", fig.width = 7, fig.height = 7, fig.align = 'center'}
plot(pkModel)
```

to visualize the model's output.

You can generate random draws of the $p$ and $k$ parameters for each cell
grouping (in `pkModel` there are no predictors, so there is one cell grouping
called "all") using the `rpk` function which, like other `r*` functions in
**R** (*e.g.*, `rnorm`, `runif`) takes the number of random draws (`n`) as the
first argument:

```{r}
rpk(n = 10, pkModel)
```

You can complicate the $p$ and $k$ formulae independently

```{r}
pkm(formula_p = p ~ Visibility, formula_k = k ~ HabitatType, data = data_SE,
  obsCol = c("Search1", "Search2", "Search3", "Search4")
)
```

And you can fix $k$ at a nominal value between 0 and 1 (inclusive) using the
`kFixed` argument

```{r}
pkm(formula_p = p ~ Visibility, kFixed = 0.7, data = data_SE,
  obsCol = c("Search1", "Search2", "Search3", "Search4"))
```

### Set of Searcher Efficiency Models

If the arg `allCombos = TRUE` is provided, `pkm` fits a set of `pkm` models
defined as all allowable models simpler than, and including, the provided model
for both formulae (where "allowable" means that any interaction terms have all
component terms included in the model).

Consider the following model set analysis, where visibility and habitat type
are included in the $p$ formula but only habitat type is in the $k$ formula.
This generates a set of 10 models:

```{r}
pkmModSet <- pkm(formula_p = p ~ Visibility*HabitatType,
               formula_k = k ~ HabitatType, data = data_SE,
               obsCol = c("Search1", "Search2", "Search3", "Search4"),
               allCombos = TRUE
             )
class(pkmModSet)
names(pkmModSet)
```

The `plot` function is defined for the `pkmSet` class, and by default,
creates a new plot window on command for each sub-model. If we want to only
plot a specific single (or subset) of models from the full set, we can utilize
the `specificModel` argument:

```{r, eval = F, fig.show = "hold", fig.width = 7, fig.height = 7, fig.align = 'center'}
plot(pkmModSet, specificModel = "p ~ Visibility + HabitatType; k ~ 1")
```

The resulting model outputs can be compared in an AICc table

```{r}
aicc(pkmModSet)
```


### Multiple Sizes of Animals and Sets of Searcher Efficiency Models

Often, carcasses are grouped in multiple size classes, and we are interested
in analyzing a set of models separately for each size class. To do so, we
use the `sizeCol` arg to tell `pkm` which column in `data_CP` gives the carcass
size class. If, in addition, `allCombos = TRUE`, `pkm` will fit a `pkmSet` that
runs for each unique size class in the column identified by the `sizeCol`
argument:

```{r}
pkmModSetSize <- pkm(formula_p = p ~ Visibility*HabitatType,
                   formula_k = k ~ HabitatType, data = data_SE,
                   obsCol = c("Search1", "Search2", "Search3", "Search4"),
                   sizeCol = "Size", allCombos = TRUE)
class(pkmModSetSize)
```

The `pkmSetSize` object is a list where each element corresponds to a
different unique size class, and contains the associated `pkmSet`object, which
itself is a list of `pkm` outputs:

```{r}
names(pkmModSetSize)
names(pkmModSetSize[[1]])
```


## Carcass Persistence

### Single Carcass Persistence Model

The central function for carcass persistence analyses is `cpm`, which, in its
simplest form, conducts a singular carcass persistence analysis (*i.e.*, a
singular set of $l$ and $s$ formulae and a singular size classification of
carcasses). Note that we use $l$ and $s$ to reference $location$ and $scale$
as the parameters for survival models, following `survreg`, however we also
provide an alternative parameterization (using parameters $a$ and $b$,
referred to as "`ab`" or "ppersist"). As a first example, we will ignore the
size category, use intercept-only models for both $l$ and $s$, and use the
Weibull distribution:

```{r}
data_CP <- mock$CP
cpModel <- cpm(formula_l = l ~ 1, formula_s = s ~ 1, data = data_CP,
             left = "LastPresentDecimalDays",
             right = "FirstAbsentDecimalDays", dist = "weibull"
           )
```


If successfully fit, a `cpm` model output contains a number of elements,
some printed automatically:

```{r}
cpModel
```

and others available upon request:

```{r}
names(cpModel)
cpModel$cells
```

The `plot` function has been defined for `cpm` objects, such that one can
simply run

```{r, fig.show = "hold", fig.width = 6, fig.height = 6, fig.align = 'center'}
plot(cpModel)
```

to visualize the model's output.

You can generate random draws of the $l$ and $s$ (or $a$ and $b$) parameters
for each cell grouping (in `cpModel` there are no predictors, so there is one
cell grouping called "all") using the `rcp` function which, like other `r*`
functions in **R** (*e.g.*, `rnorm`) takes the number of random draws (`n`)
as the first argument:

```{r}
rcp(n = 10, cpModel)
rcp(n = 10, cpModel, type = "ppersist")
```

You can complicate the $l$ and $s$ formulae independently

```{r}
cpm(formula_l = l ~ Visibility * GroundCover, formula_s = s ~ 1, data = data_CP,
  left = "LastPresentDecimalDays", right = "FirstAbsentDecimalDays",
  dist = "weibull"
)
```

Given that the exponential only has one parameter ($l$, location), a model
for scale (`formula_s`) is not required:

```{r}
cpModExp <- cpm(formula_l = l ~ Visibility * GroundCover, data = data_CP,
              left = "LastPresentDecimalDays",
              right = "FirstAbsentDecimalDays", dist = "exponential"
            )
```

### Set of Carcass Persistence Models

If the arg `allCombos = TRUE` is provided, `cpm` fits a set of `cpm` models
defined as all allowable models simpler than, and including, the provided model
formulae (where "allowable" means that any interaction terms have all component
terms included in the model).

In addition, `cpm` with `allCombos` can include any subset of the four base
distributions (exponential, weibull, lognormal, loglogistic) and crosses them
with the predictor models.

Consider the following model set analysis, where `Visibility` and `Season` are
included in the $l$ formula but only `Visibility` is in the $s$ formula, and
only the exponential and lognormal distributions are included. This generates a
set of 15 models:

```{r}
cpmModSet <- cpm(formula_l = l ~ Visibility * Season,
               formula_s = s ~ Visibility, data = data_CP,
               left = "LastPresentDecimalDays",
               right = "FirstAbsentDecimalDays",
               dist = c("exponential", "lognormal"), allCombos = TRUE
             )
class(cpmModSet)
names(cpmModSet)
```

The resulting model outputs can be compared in an AICc table

```{r}
aicc(cpmModSet)
```

The `plot` function is defined for the `cpmSet` class, and by default,
creates a new plot window on command for each sub-model. If we want to only
plot a specific single (or subset) of models from the full set, we can utilize
the `specificModel` argument:

```{r, fig.show = "hold", fig.width = 7, fig.height = 7, fig.align = 'center'}
plot(cpmModSet,
  specificModel = "dist: lognormal; l ~ Visibility * Season; s ~ Visibility"
)
```

### Multiple Sizes of Animals and Sets of Carcass Persistence Models

Often, carcasses are grouped in multiple size classes, and we are interested
in analyzing a set of models separately for each size class. To do so, we
furnish `cpm` with `sizeCol`, which is the name of the column in `data_CP` that
gives the size classes of the carcasses. If, in addition, `allCombos = TRUE`,
then `cpm` returns a `cpmSet` for each unique size class in the column
identified by the `sizeCol` argument:

```{r}
cpmModSetSize <- cpm(formula_l = l ~ Visibility * Season,
                   formula_s = s ~ Visibility, data = data_CP,
                   left = "LastPresentDecimalDays",
                   right = "FirstAbsentDecimalDays",
                   dist = c("exponential", "lognormal"),
                   sizeCol = "Size", allCombos = TRUE)
class(cpmModSetSize)
```

The `cpmSetSize` object is a list where each element corresponds to a
different unique size class, and contains the associated `cpmSet`o bject, which
itself is a list of `cpm` outputs:

```{r}
names(cpmModSetSize)
names(cpmModSetSize[[1]])
class(cpmModSetSize[[1]])
```

## Generic Detection Probability

For the purposes of mortality estimation, we calculate carcass-specific
detection probabilities (see below), which may be difficult to generalize,
given the specific history of each observed carcass. Thus, we also provide
a simple means to calculate generic detection probabilities that are
cell-specific, rather than carcass-specific.

For any estimation of detection probability ($\hat{g}$), we need to have
singular SE and CP models to use for each of the size classes. Here, we use
the best-fit of the models for each size class:

```{r}
pkMods <- c("S" = "p ~ 1; k ~ 1", "L" = "p ~ 1; k ~ 1",
            "M" = "p ~ 1; k ~ 1", "XL" = "p ~ 1; k ~ HabitatType"
          )
cpMods <- c("S" = "dist: exponential; l ~ Season; NULL",
            "L" = "dist: exponential; l ~ 1; NULL",
            "M" = "dist: exponential; l ~ 1; NULL",
            "XL" = "dist: exponential; l ~ 1; NULL"
          )
```

The `estgGenericSize` function produces `n` random draws of generic (i.e.,
cell-specific, not carcass-sepecific) detection probabilities for
each of the possible carcass cell combinations across the selected SE and CP
models across the size classes. `estgGeneric` is a single-size-class
version of function and `estgGenericSize` actually loops over
`estgGeneric`. The generic $\hat{g}$ is estimated according to a particular
search schedule. When we pass `averageSS` a full `data_SS` table like we have
here, it will assume that columns filled exclusively with 0s and 1s represent
search schedules for units and will create the average search schedule across
the units.

```{r}
data_SS <- mock$SS
avgSS <- averageSS(data_SS)

gsGeneric <- estgGenericSize(nsim = 1000, days = avgSS,
               modelSetSize_SE = pkmModSetSize,
               modelSetSize_CP = cpmModSetSize,
               modelSizeSelections_SE = pkMods,
               modelSizeSelections_CP = cpMods
             )
```

The output from `estgGeneric` can be simply summarized
```{r}
summary(gsGeneric)
```

or plotted.

```{r, fig.show = "hold", fig.width = 4, fig.height = 14, fig.align = 'center'}
plot(gsGeneric)
```


## Mortality Estimation

When estimating mortality, detection probability is determined for
individual carcasses based on the dates when they are observed, size class
values, associated covariates, the searcher efficiency and carcass persistence
models, and the search schedule. The carcass-specific detection probabilities
(as opposed to the generic/cell-specific detection probabilities above) are
therefore calculated before estimating the total mortality.
Although it is possible to estimate these detection probabilities separately,
they are best interpreted in the context of a full mortality estimation.

The `estM` function is the general wrapper function for estimating `M`,
whether for a single size class or multiple size classes. Prior to estimation,
we need to reduce the model-set-size complexed to just a single chosen
model per size class, corresponding to the `pkMods` and `cpMods` vectors
given above. To reduce the model set complexity, we can use the `trimSetSize`
function:

```{r}
pkmModSize <- trimSetSize(pkmModSetSize, pkMods)
cpmModSize <- trimSetSize(cpmModSetSize, cpMods)
```

In addition to the models and search schedule data, `estM` requires
density-weighted proportion (DWP) and carcass observation (CO) data. If more
than one size class is represented in the data, a required input is also the
column names associated with the DWP value for each size class (argument
`DWPCol` in `estM`):

```{r}
data_CO <- mock$CO
data_DWP <- mock$DWP
head(data_DWP)
DWPcolnames <- names(pkmModSize)

eM <- estM(data_CO = data_CO, data_SS = data_SS, data_DWP = data_DWP,
        frac = 1, model_SE = pkmModSize, model_CP = cpmModSize,
        unitCol = "Unit", COdate = "DateFound",
        SSdate = "DateSearched", sizeCol = "Size", nsim = 1000)
```

`estM` returns an object that contains the random draws of `pkm` and `cpm`
parameters (named `pk` and `ab`, respectively) and the estimated carcass-level
detection parameters (`g`), arrival intervals (`Aj`), and associated total
mortality (`Mhat`) values for each simulation. These `Mhat` values should be
considered in combination, and can be summarized and plotted simply:

```{r, fig.show = "hold", fig.width = 6, fig.height = 6, fig.align = 'center'}
summary(eM)
plot(eM)
```

### Splitting Mortality Estimations

It is possible to split the resulting mortality estimation into components
that are denoted according to covariates in either the search schedule or
carcass observation data sets.

First, a temporal split:

```{r, fig.show = "hold", fig.width = 4, fig.height = 6, fig.align = 'center'}
M_season <- calcSplits(M = eM, split_SS = "Construction",
                 split_CO = NULL, data_SS = data_SS, data_CO = data_CO
             )
summary(M_season)
plot(M_season)
```

Next, a carcass split:

```{r, fig.show = "hold", fig.width = 4, fig.height = 6, fig.align = 'center'}
M_class <- calcSplits(M = eM, split_SS = NULL,
             split_CO = "Split", data_SS = data_SS, data_CO = data_CO
           )
summary(M_class)
plot(M_class)
```

And finally, if two splits are included, the mortality estimation is expanded
fully factorially:

```{r, fig.show = "hold", fig.width = 4, fig.height = 8, fig.align = 'center'}
M_SbyC <- calcSplits(M = eM, split_SS = "Construction",
            split_CO = "Split", data_SS = data_SS, data_CO = data_CO
          )
summary(M_SbyC)
plot(M_SbyC)
```
