I'm trying to understand why one would use a Conditional Autoregressive Model (CAR) vs a Spatial Autoregressive Model (SAR) to look at migratory decisions. I have been reading through some of the lit and need some help understanding this passage from:
Spatial Regression Models for Demographic Analysis, by Guangqing Chi & Jun Zhu (numbers and emphasis added to relate to how I'm understanding it so far)
"Spatial error models and sometimes spatial lag models are referred to as the simultaneous autoregressive model (SAR). Another popular class of models is the conditional autoregressive (CAR) models. The key distinction between the SAR and the CAR models is in the model specification (Cressie 1993). (1) SAR models explain the relations among response variables at all locations on the lattice simultaneously and the spatial effect is considered to be endogenous. (2) In contrast, CAR models specify the distribution of a response variable at one location by conditioning on the values of its neighbors in the neighborhood and the spatial effect of the neighbors is considered to be exogenous (Anselin 2003). (3) While CAR models are popular in the statistics literature and many other disciplines, SAR models are favored in spatial econometrics and spatial demography, possibly because interpretation of the spatial autocorrelation coefficient resembles that of standard linear regression and thus may seem more natural. (4) The relation between the two types of models is close, however, as SAR models (from a spatial error model) may be represented by possibly higher order CAR models (Cressie 1993)."
Assuming the level is census blocks, am I understanding this correctly to mean that:
- SAR models consider the migration flows from all census blocks to matter, with closer census blocks being more important while
- CAR models just look at direct neighbors
- However, Demographers really just use SAR because habit and "it's easier to understand", and
- I'm not entirely sure what they really mean by higher order?
Did that make sense? Any advice would be appreciated!
P.S. I did see this answer here:Spatial statistics models: CAR vs SAR, and I still need a bit more help