sbd

Non-negative size biased distributions and models. Developed for estimating animal speed from camera trap observations, where slower speeds are less likely to be observed. Includes a simple harmonic mean function.

https://github.com/marcusrowcliffe/sbd

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Non-negative size biased distributions and models. Developed for estimating animal speed from camera trap observations, where slower speeds are less likely to be observed. Includes a simple harmonic mean function.

README.Rmd

---
title: "sbd"
output: github_document
always_allow_html: true
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Size Biased Distributions

An R package for fitting and plotting size-biased non-negative distributions. Size-biased distributions occur when the probability of observing something is proportional to its size. The example motivating this package is observations of animal speeds made by camera traps, where faster moving animals are more likely to encounter camera traps and hence be recorded, with probability of observation expected to be proportional to speed ([Rowcliffe et al. 2016](https://zslpublications.onlinelibrary.wiley.com/doi/full/10.1002/rse2.17)).

The core function is `sbm`, which performs model fitting and estimates the underlying average of a set of size biased data, given a model formula and a dataframe containing the variables named in the formula. Default usage is non-parametric, providing the harmonic mean as the estimator of underlying average:

```{r}
library(sbd)
data("BCI_speed_data")
agoutiData <- subset(BCI_speed_data, species=="agouti")
mod <- sbm(speed~1, agoutiData)
mod
```

The distribution can be plotted using the `hist` method:

```{r}
hist(mod)
```

Three parametric distributions are also available - log-normal, gamma, and Weibull. These can be selected using the `pdf` argument, and model support can be evaluated using the `AIC` method:

```{r}
lmod <- sbm(speed~1, agoutiData, pdf = "lnorm")
gmod <- sbm(speed~1, agoutiData, pdf = "gamma")
wmod <- sbm(speed~1, agoutiData, pdf = "weibull")
AIC(lmod, gmod, wmod)
```

For parametric models without covariates, a fitted probability density function is added to the data distribution when it is plotted:

```{r}
hist(lmod)
```

Parametric models can accept covariates, for example, testing the effect of species body mass on average speed:

```{r}
lmod_null <- sbm(speed~1, BCI_speed_data, "lnorm")
lmod_mass <- sbm(speed~mass, BCI_speed_data, "lnorm")
AIC(lmod_null, lmod_mass)
```

The parameters of the underlying linear model can be inspected using the `summary` method, where `lmean` is the natural log of the underlying mean, and `lsig` is the natural log of the underlying standard deviation:

```{r}
summary(lmod_mass)
```

The `predict` method can be used to calculate estimated averages and their standard errors for any desired predictor value, for example:

```{r}
nd <- data.frame(mass = c(1,10,100))
predict(lmod_mass, newdata = nd)
```

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