diff --git a/R/convenience-functions.R b/R/convenience-functions.R
index 3fb3ddd..24f8707 100644
--- a/R/convenience-functions.R
+++ b/R/convenience-functions.R
@@ -171,7 +171,7 @@ sim_sar <- function(m = 1,
                     w,                    
                     type = c("SEM", "SLM"),
                     approx = FALSE,
-                    K = 15,
+                    K = 20,
                     ...) {
     check_sa_data(mu, w)
     type <- match.arg(type)
@@ -625,7 +625,7 @@ me_diag <- function(fit,
     }
 }
 
-#' Extract eigenfunctions of a connectivity matrix for spatial filtering
+#' Prepare data for spatial filtering
 #'
 #' @export
 #' @param C A binary spatial weights matrix. See \code{\link[geostan]{shape2mat}}.
diff --git a/vignettes/raster-regression.Rmd b/vignettes/raster-regression.Rmd
index d869ab5..31f4afd 100644
--- a/vignettes/raster-regression.Rmd
+++ b/vignettes/raster-regression.Rmd
@@ -122,8 +122,10 @@ sar_list <- prep_sar_data2(row = row, col = col)
 W <- sar_list$W
 
 z <- sim_sar(rho = .8, w = W, quick = TRUE)
-y <- sim_sar(mu = -.5 * z, rho = .9, w = W, quick = TRUE)
+y <- sim_sar(mu = -.5 * z, rho = .7, w = W, quick = TRUE)
 dat <- cbind(y, z)
 ```
 
+The approximate method uses matrix powers, and for high values of SA (especially values of rho greater than 0.9) the approximation is sensitive to the number of powers taken. In `sim_sar` this is controlled by the argument `K`. For `rho = 0.9`, you may need to raise the default value of K for the approximation to hold. Notice that $0.9^{45} = 0.009$, which is near zero and should provide sound results, whereas $0.9^25 = 0.07$ which is not quite there, and $0.9^{15} = 0.2$ will be completely inadequate. In geostan 0.8.0, the default is $K = 20$.
+
 ## References