Spatio-temporal analysis of point patterns and lattice data

Spatial Models for Lattice Data
We will focus on the use of Generalized Linear Models
In particular, Poisson models
O i ∼ Po(µ i ) log(µ i ) = α+βx i +u i +v i
u i ∼ N(0,σ 2 u) is a random effect that accounts for non-spatial
variation
v i ∼ N(0,G) is a random effects that accounts for spatial variation,
encoded in variance-covariance matrix G:
Spatially Autoregressive Specification (SAR models)
G = σ 2 v[I −ρW] −1
Conditionally Autoregressive Specification (CAR models)
G = σ 2 v[(I −ρW) T (I −ρW)] −1
V. Gómez-Rubio (UCLM) Spatio-Temporal Analysis 14 / 22