priors: Priors for 'rsstap' models

In apeterson91/rsstap: Spline Spatial Temporal Aggregated Predictors

Description

Priors for 'rsstap' models

GLMs

Using one spatial aggregated predictor as an example, stap_(g)lm models have the following form.

g(μ_i) = Z_i^T δ + ∑_d ∑_l β_lφ_l(d)

Currently the priors in rsstap are fixed and are always of the following form:

p(δ) \propto 1

σ \sim C^+(0,5)

β \sim MVN_L(0,∑_k S_k τ_k)

τ_k \sim Exp(1)

Where S_k are generated from the jagam function and sum to form a complete precision matrix with different τ penalties along the diagonal.

GLMERs

Using only one spatial aggregated predictor as an example, stap_(g)lmer models have the following form:

g(μ_{ij}) = Z_{ij}^T δ + ∑_d ∑_l β_lφ_l(d) + W_{ij}^Tb_i

Where

b_i \sim N(0,Σ)

priors for δ,β,σ,τ_k are the same as before, but now Σ is decomposed as described here.

apeterson91/rsstap documentation built on April 7, 2021, 4:36 p.m.