Model performance in quantile modelling

I am using quantile regression (for example via gbm or quantreg in R) - not focusing on the median but instead an upper quantile (e.g. 75th). Coming from a predictive modeling background, I want to measure how well the model fits on a test set and be able to describe this to a business user. My question is how? In a typical setting with a continuous target I could do the following:

• Calculate the overall RMSE
• Decile the data set by the predicted value and compare the average actual to the average predicted in each decile.
• Etc.

What can be done in this case, where there really is no actual value (i don't think at least) to compare the prediction to?

Here is an example code:

install.packages("quantreg")
library(quantreg)

install.packages("gbm")
library(gbm)

data("barro")

trainIndx<-sample(1:nrow(barro),size=round(nrow(barro)*0.7),replace=FALSE)
train<-barro[trainIndx,]
valid<-barro[-trainIndx,]

modGBM<-gbm(y.net~., # formula
data=train, # dataset
distribution=list(name="quantile",alpha=0.75), # see the help for other choices
n.trees=5000, # number of trees
shrinkage=0.005, # shrinkage or learning rate,
# 0.001 to 0.1 usually work
interaction.depth=5, # 1: additive model, 2: two-way interactions, etc.
bag.fraction = 0.5, # subsampling fraction, 0.5 is probably best
train.fraction = 0.5, # fraction of data for training,
# first train.fraction*N used for training
n.minobsinnode = 10, # minimum total weight needed in each node
cv.folds = 5, # do 3-fold cross-validation
keep.data=TRUE, # keep a copy of the dataset with the object
verbose=TRUE) # don’t print out progress

best.iter<-gbm.perf(modGBM,method="cv")

pred<-predict(modGBM,valid,best.iter)


Now what - since we don't observe the percentile of the conditional distribution?

I hypothesized several methods and I would like to know if they are correct and if there are better ones - also how to interpret the first:

1. Calculate the average value from the loss functions:

qregLoss<-function(actual, estimate,quantile)
{
(sum((actual-estimate)*(quantile-((actual-estimate)<0))))/length(actual)

}


This is the loss function for quantile regression - but how do we interpret the value?

2. Should we expect that if for example we are calculating the 75th percentile that on a test set, the predicted value should be greater than the actual value around 75% of the time?

Are there other methods formal or heuristic to describe how well the model predicts new cases?

• Section 3 in this paper might be useful. Mar 23, 2013 at 19:01
• @tchakravarty I think that link has gone dead May 9, 2018 at 1:54