When would one prefer to use a Conditional Autoregressive model over a Simultaneous Autoregressive model when modelling autocorrelated geo-referenced aerial data?
My House Value is a function of my home Gardening Investment.
My House Value is a function of the House Values of my neighbours.
My House Value is a function of the Gardening Investment of my neighbours.
As the Encyclopedia of GIS states, the conditional autoregressive model (CAR) is appropriate for situations with first order dependency or relatively local spatial autocorrelation, and simultaneous autoregressive model (SAR) is more suitable where there are second order dependency or a more global spatial autocorrelation.
This is made clear by the fact that CAR obeys the spatial version of the Markov property, namely it assumes that the state of a particular area is influenced its neighbors and not neighbors of neighbors, etc. (i.e. it is spatially “memoryless”, instead of temporally), whereas SAR does not assume such. This is due to the different ways in which they specify their variance-covariance matrixes. So, when the spatial Markov property obtains, CAR provides a simpler way to model autocorrelated geo-referenced areal data.
See Gis And Spatial Data Analysis: Converging Perspectives for more details.