Review GLMMs for index generation

[luke-a-rogers]

I think a great first three steps would be:

• Install the development version of R package sdmTMB and its dependencies including linking to the optimized BLAS library as described (all instructions at link)
• Read three key subsections from the sdmTMB paper including
  • 2.1. A spatial Gaussian random field GLMM
  • 2.5. Adding spatiotemporal random fields
  • 2.6. Additional model components
• Read the sdmTMB intro (and run code blocks) up to AIC(m1) for the first model fit

The model in the intro uses a binomial family for the error distribution with a logit link. We'll generally use a Poisson or similar with a log link, giving

$y_s \sim \mathrm{Poisson}(\mu_s)$

$\log (\mu_s) = \alpha + \beta x_s + \mathrm{...}$

In this case, the log link makes sure that $\mu_s$ is positive (Poisson needs a positive mean) and allows the linear expression on the RHS of ' $=$ ' to take on any value (positive or negative). The Poisson distribution allows the response variable $y_s$ to be count data (we'll use hook counts of dogfish from longline surveys). The $\mathrm{...}$ includes one spatial random field (a 'wiggly surface') and one spatiotemporal random field (a 'wiggly surface' that changes each year) as well as other terms. The subscript $s$ is an index giving geographic location.