I am building a quantile regression model + LASSO penalization for the boston housing data in R. I found 2 packages that can build this kind of models: rqPen and quantreg. rqPen implements a cross validation process to tune the LASSO parameter lambda, so I decided to use this one. I considered 100 different lambda values automatically chosen by the algorithm and 10 folds:
library(rqPen)
library(mlbench)
data("BostonHousing")
help(BostonHousing)
x_boston <- data.matrix(BostonHousing[,-14])
y_boston <- BostonHousing[,14]
cv_m1_boston <- cv.rq.pen(x_boston,y_boston, penalty="LASSO", nlambda=100, nfolds=10, tau=.5, cvFunc="AE")
The results from the CV are that the smallest absolute error is 4.2 achieved with a lambda value of 0.46. This model considers only the predictors "zn, "tax", "b" and "lstat" and sends to zero the coefficients associated to the rest of the predictors.
m1_boston <- rq.lasso.fit(x_boston[i_train,], y_boston[i_train], tau=0.5, lambda=0.46)
Coefficients:
intercept crim zn indus chas nox rm age dis rad
27.175724364 0.000000000 0.025560221 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
tax ptratio b lstat
-0.008151729 0.000000000 0.007577458 -0.495927958
I decided to build the same model using the other package, the quantreg package, but maintaining the lambda value. I expected the models form the two packages to be not exactly equal but similar in terms of the predictors included in the models.
library(quantreg)
m2_boston <- rq(medv~., data=BostonHousing[i_train,], tau=0.5,method = "lasso", lambda=0.46)
And I found that in this model all the predictors were being used, so it was completly different to the first one.
Coefficients:
(Intercept) crim zn indus chas1 nox rm age dis rad
15.528274036 -0.128622834 0.038896192 0.007109711 1.385725245 -7.221209356 5.144134214 -0.035033485 -1.075032872 0.165388801
tax ptratio b lstat
-0.010579964 -0.765578313 0.012533729 -0.283032080
Am I doing something wrong? is the rqPen package failing on the computations?
