# sar: Spatial simultaneous autoregressive (SAR) structures In brms: Bayesian Regression Models using 'Stan'

## Description

Set up an spatial simultaneous autoregressive (SAR) term in brms. The function does not evaluate its arguments – it exists purely to help set up a model with SAR terms.

## Usage

 `1` ```sar(M, type = "lag") ```

## Arguments

 `M` An object specifying the spatial weighting matrix. Can be either the spatial weight matrix itself or an object of class `listw` or `nb`, from which the spatial weighting matrix can be computed. `type` Type of the SAR structure. Either `"lag"` (for SAR of the response values) or `"error"` (for SAR of the residuals). More information is provided in the 'Details' section.

## Details

The `lagsar` structure implements SAR of the response values:

y = ρ W y + η + e

The `errorsar` structure implements SAR of the residuals:

y = η + u, u = ρ W u + e

In the above equations, η is the predictor term and e are independent normally or t-distributed residuals. Currently, only families `gaussian` and `student` support SAR structures.

## Value

An object of class `'sar_term'`, which is a list of arguments to be interpreted by the formula parsing functions of brms.

`autocor-terms`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```## Not run: data(oldcol, package = "spdep") fit1 <- brm(CRIME ~ INC + HOVAL + sar(COL.nb, type = "lag"), data = COL.OLD, data2 = list(COL.nb = COL.nb), chains = 2, cores = 2) summary(fit1) plot(fit1) fit2 <- brm(CRIME ~ INC + HOVAL + sar(COL.nb, type = "error"), data = COL.OLD, data2 = list(COL.nb = COL.nb), chains = 2, cores = 2) summary(fit2) plot(fit2) ## End(Not run) ```