Family options in sdmTMB

class: center, middle, inverse, title-slide

.title[
# Family options in sdmTMB
]
.subtitle[
## DFO TESA sdmTMB workshop
]
.author[
### 
]
.date[
### January 16–19 2023
]

---

# Families

Many of the same families used in `glm()`, `glmmTMB()`, `mgcv::gam()` can be used here

Includes:
  `gaussian()`, `Gamma()`, 
  `binomial()`, `poisson()`, `Beta()`, 
  `student()`, `tweedie()`, 
  `nbinom1()`, `nbinom2()`,
  `truncated_nbinom1()`, `truncated_nbinom2()`,
  `delta_gamma()`, `delta_lognormal()`, `delta_beta()`, and more...
  
All have `link` arguments
  
See `?sdmTMB::Families`

---

.center[
<img src="images/family_diagram.png" width="800px" height = "450px"/>
 
*New distributions continue to be added

]

---

# An aside on the Tweedie

.small[
Useful for positive continuous data with zeros (e.g., biomass density per unit effort)

Dispersion ( `\(\phi\)` ) and power ( `\(p\)` ) parameters allow for a wide variety of shapes including many zeros

Also known as compound Poisson-Gamma distribution
]

---

# Delta models

* Delta/hurdle model has 2 sub-models:
- presence/absence (binomial, logit link)  
- positive model (link varies by family)

* `family` argument to sdmTMB can be a list()  
- for convenience, many delta- families implemented: `delta_gamma`, `delta_lognormal`, `delta_truncated_nbinom2` etc

---

# Delta models

* Some arguments can be a list, e.g.

```r
fit <- sdmTMB(
  list(
    density ~ 1, 
    density ~ depth
  ),
  spatial = list('on', 'off'),  
  spatiotemporal = list('off', 'ar1'), 
  share_range = list(TRUE, FALSE),
  ...
)
```

* by default, all arguments shared  
* rest of arguments must be shared  
* smoothers and random intercepts must be shared

---

# An aside on mixture models

Positive components may be modeled as a mixture of 2 distributions

* Finite mixture model (2 components)

* Also referred to as "ECE" (extreme catch event) model, Thorson et al. (2012)

* Mechanisms: shoaling, etc.

* See `gamma_mix()` and `lognormal_mix()`

* Can be delta model as `delta_gamma_mix()` and `delta_lognormal_mix()`

---

# SDMs with presence-only data

Infinitely Weighted Logistic Regression (IWLR)  
* [Fithian & Hastie (2013)](https://doi.org/10.1214/13-AOAS667)

Downweighted Poisson Regression (DWPR)  
* [Renner et al. 2015](https://doi.org/10.1111/2041-210X.12352)

Code examples with sdmTMB [here](https://github.com/pbs-assess/sdmTMB/blob/main/scratch/julia-vignettes/presence_absence.Rmd)