Prediction variance (map) for predictions derived using RandomForest package

You can do this to get the mean and SD for each observation (note the
mean should match the value in predictions$aggregate:

y_data$rf_mean <- apply(predictions$individual, MARGIN=1, mean)
y_data$rf_sd <- apply(predictions$individual, MARGIN=1, sd)
y_data$rf_cv <- apply(predictions$individual, MARGIN=1, sd)

On Sun, Jun 23, 2013 at 5:51 AM, Tomislav Hengl
<hengl at spatial-analyst.net> wrote:

Dear list,

I have a question about the randomForest models. I'm trying to figure out a
way to estimate the prediction variance (spatially) for the randomForest
function (http://cran.r-project.org/web/packages/randomForest/).

If I run a GLM I can also derive the prediction variance using:

demo(meuse, echo=FALSE)
meuse.ov <- over(meuse, meuse.grid)
meuse.ov <- cbind(meuse.ov, meuse at data)
omm0 <- glm(log1p(om)~dist+ffreq, meuse.ov, family=gaussian())
om.glm <- predict.glm(omm0, meuse.grid, se.fit=TRUE)
str(om.glm)

List of 3
 $ fit           : Named num [1:3103] 2.34 2.34 2.32 2.29 2.34 ...
  ..- attr(*, "names")= chr [1:3103] "1" "2" "3" "4" ...
 $ se.fit        : Named num [1:3103] 0.0491 0.0491 0.0481 0.046 0.0491 ...
  ..- attr(*, "names")= chr [1:3103] "1" "2" "3" "4" ...
 $ residual.scale: num 0.357

when I fit a randomForest model, I do not get any estimate of the model
uncertainty (for each pixel) but just the predictions:

meuse.ov <- meuse.ov[-omm0$na.action,]
x <- randomForest(log1p(om)~dist+ffreq, meuse.ov)
om.rf <- predict(x, meuse.grid)
str(om.rf)

 Named num [1:3103] 2.49 2.49 2.51 2.44 2.49 ...
 - attr(*, "names")= chr [1:3103] "1" "2" "3" "4" ...

Does anyone has an idea how to map the prediction variance (i.e. estimated
or propagated error) for the randomForest models spatially?

I've tried deriving a propagated error for the randomForest models (every
fit gives another model due to random component):

l.rfk <- data.frame(om_1 = rep(NA, nrow(meuse.grid)))
for(i in 1:50){

+   suppressWarnings(suppressMessages(x <-
randomForest(log1p(om)~dist+ffreq, meuse.ov)))
+   l.rfk[,paste("om",i,sep="_")] <- predict(x, meuse.grid)
+ } ## takes ca 1 minute

meuse.grid$om.rfkvar <- om.rfk at predicted$var1.var + apply(l.rfk, 1, var)

but the prediction variance I get is rather small (much smaller than e.g.
the GLM variance). Here is the complete code with some plots:

R code:
https://code.google.com/p/gsif/source/browse/trunk/meuse/RK_vs_RandomForestK.R

Predictions UK vs randomForest-kriging:
https://gsif.googlecode.com/svn/trunk/meuse/Fig_meuse_RK_vs_RFK.png

thanx,

T. (Tom) Hengl
Url: http://www.wageningenur.nl/en/Persons/dr.-T-Tom-Hengl.htm
Network: http://profiles.google.com/tom.hengl
Publications: http://scholar.google.com/citations?user=2oYU7S8AAAAJ