Modeling for Monitoring




Goal

To consider modeling decisions and tradeoffs:

  • Modeling Objective

  • Choices among model types and fitting processes

  • Explanation/Inference vs Prediction

Case Study

Sampling Frame

Station Setup

Project Goals

  • Primary: To map winter wolverine distributions across the western U.S. to track changes in occurence over time (i.e., contraction or expansion)
  • Secondary: To understand the factors that govern wolverine occurence in the western United States.

Modeling Option 1

Naive Occupancy:

\(\hat{\psi} = \frac{\sum y_i}{n}\), \(y \in \{0,1\}\)

Modeling Option 2

Fit occupancy model with covariates:

\[ \begin{align*} \textbf{y}_{i} \sim& \text{Binomial}(z_i\times p_{i}, J)\\ z_i \sim& \text{Bernoulli}(\psi_i)\\ \text{logit}(\psi_{i}) =& \alpha_0 + \alpha_1 \times \text{human.mod}_{i} + \\ &\alpha_2 \times \text{elev}_{i} + \alpha_3 \times \text{snow.depth}_{i} \\ \text{logit}(p_{i}) =& \beta_0 \\ \end{align*} \]

Modeling Option 2a

Predict occupancy for the whole sampling frame . I.e., prediction with covariates.

Modeling Option 2b

Predict occupancy only at sampled sites

Modeling Option 3

Multi-model comparison; predict occupancy at the whole sampling frame or only sampled sites

model AIC DeltaAIC AIC.Weights
psi ~ 1
psi ~ human.mod
psi ~ elev
psi ~ snow.depth
psi ~ human.mod + elev + snow.depth

Modeling Option 4a

Predictions from a spatial occupancy model at the whole sampling frame. For example, intrinsic conditional autoregressive model (ICAR).

  • covariates are not needed
  • leverages ‘closeness’ of the detection data to estimate occupancy

Modeling Option 4b

Predictions from a spatial occupancy model WITH COVARIATES at the whole sampling frame.

  • can add covariates on detection or occupancy
  • the spatial process and spatial covariates are not necessarily uniquely identifiable (inference may be unclear)

Modeling Option 5

Prediction from a non-linear supervised machine learning algorithm at the whole sampling frame. For example, ‘random forests’, ‘gradient boosting’, ‘maximum entropy’.

  • covariates required
  • non-linear relationships are handled
  • correlation among variables is fine
  • trains model based on cross validation

To do

  • Group up and discuss
  • List out the benefits/costs of each option, in terms of objectives 1 and 2.
  • What option would you pick? Why?
    • If you make your own chimera option (mix match model type and model fitting), you need to say why it’s better and how practical it is to accomplish.
  • Can ask me questions

Options Summary

  1. Naive occupancy
  2. Single occupancy model, predict –> sampling frame OR sampled sites
  3. Multi-model occupancy approach, predict –> sampling frame OR sampled sites
  4. Single spatial occupancy model. No covariates or with covariates. Predict –> sampling frame
  5. Non-linear supervised machine learning algorithm. Predict –> sampling frame