I spent some time writing my own "partial.function-plotter" before I realized it was already bundled in the R randomForest library.
[EDIT ...but then I spent a year making the CRAN package forestFloor, which is by my opinion significantly better than classical partial dependence plots]
Partial.function plot are great in instances as this simulation example you show here, where the explaining variable do not interact with other variables. If each explaining variable contribute additively to the target-Y by some unknown function, this method is great to show that estimated hidden function. I often see such flattening in the borders of partial functions.
Some reasons:
randomForsest has an argument called 'nodesize=5' which means no tree will subdivide a group of 5 members or less. Therefore each tree cannot distinguish with further precision.
Bagging/bootstrapping layer of ensemple smooths by voting the many step functions of the individual trees - but only in the middle of the data region. Nearing the borders of data represented space, the 'amplitude' of the partial.function will fall.
Setting nodesize=3 and/or get more observations compared to noise can reduce this border flatting effect...
When signal to noise ratio falls in general in random forest the predictions scale condenses. Thus the predictions are not absolutely terms accurate, but only linearly correlated with target. You can see the a and b values as examples of and extremely low signal to noise ratio, and therefore these partial functions are very flat. It's a nice feature of random forest that you already from the range of predictions of training set can guess how well the model is performing. OOB.predictions is great also..
flattening of partial plot in regions with no data is reasonable:
As random forest and CART are data driven modeling, I personally like the concept that these models do not extrapolate. Thus prediction of c=500 or c=1100 is the exactly same as c=100 or in most instances also c=98.
Here is a code example with the border flattening is reduced:
I have not tried the gbm package...
here is some illustrative code based on your eaxample...
#more observations are created...
a <- runif(5000, 1, 100)
b <- runif(5000, 1, 100)
c <- (1:5000)/50 + rnorm(100, mean = 0, sd = 0.1)
y <- (1:5000)/50 + rnorm(100, mean = 0, sd = 0.1)
par(mfrow = c(1,3))
plot(y ~ a); plot(y ~ b); plot(y ~ c)
Data <- data.frame(matrix(c(y, a, b, c), ncol = 4))
names(Data) <- c("y", "a", "b", "c")
library(randomForest)
#smaller nodesize "not as important" when there number of observartion is increased
#more tress can smooth flattening so boundery regions have best possible signal to noise, data specific how many needed
plot.partial = function() {
partialPlot(rf.model, Data[,2:4], x.var = "a",xlim=c(1,100),ylim=c(1,100))
partialPlot(rf.model, Data[,2:4], x.var = "b",xlim=c(1,100),ylim=c(1,100))
partialPlot(rf.model, Data[,2:4], x.var = "c",xlim=c(1,100),ylim=c(1,100))
}
#worst case! : with 100 samples from Data and nodesize=30
rf.model <- randomForest(y ~ a + b + c, data = Data[sample(5000,100),],nodesize=30)
plot.partial()
#reasonble settings for least partial flattening by few observations: 100 samples and nodesize=3 and ntrees=2000
#more tress can smooth flattening so boundery regions have best possiblefidelity
rf.model <- randomForest(y ~ a + b + c, data = Data[sample(5000,100),],nodesize=5,ntress=2000)
plot.partial()
#more observations is great!
rf.model <- randomForest(y ~ a + b + c,
data = Data[sample(5000,5000),],
nodesize=5,ntress=2000)
plot.partial()
First of all, I think you're using the gbm.step function from the dismo package.
Even though your y ranges from 0.02 to 0.38, the model can still decide that certain variables (or certain ranges of a variable) have a negative contribution to y's value. If this is the case, the marginal effects plot will include negative values.
Finally, use the plot.gbm function from the gbm package to get the values used for the marginal dependency plots:
library(gbm)
model <- gbm(Sepal.Width ~ ., distribution = "gaussian", data=iris)
plot(model, 'Species', return.grid=TRUE)
Species y
1 setosa 3.067434
2 versicolor 3.052529
3 virginica 3.052915
I think this plot uses a slightly different approach than dismo::gbm.plot, but the results should be similar.
Best Answer
Yes, it's really easy. Check out
?plot.gbm. The usage goes like this:and looks like
i.varcontrols the index of the variable to plot. You can also do two (or more) way plots using