Lasso – How to Perform LASSO Regression with a Dependent Variable Between 0 and 1

generalized linear modellassoregressionsigmoid-curve

I am trying to do a LASSO regression on some data. However, my dependent variable is between 0 and 1. How do I go about this? Do I just apply a sigmoid function to the regression output?

This will surely force the outcome to the 0-1 range, but I am not sure of the technical implications.

Best Answer

Since the response variable is between 0 to 1, i.e., you should perform a beta regression. The package 'gamlss' allows you to do that in addition to fit your model using Lasso.

library(betareg)
data(GasolineYield)
library(gamlss)

X <- with(GasolineYield, cbind(gravity,pressure,temp10,temp,batch))
# standarise data 1-------------------------------------------------------------
sX <- scale(X)
# ridge
m1 <- gamlss(yield~ri(sX), data = GasolineYield)
# lasso
m2 <- gamlss(yield~ri(sX, Lp=1), data = GasolineYield)
# best subset
m3 <- gamlss(yield~ri(sX, Lp=0), data = GasolineYield)

# summary
summary(m1)
summary(m2)
summary(m3)

# plotting the coefficients
plot(getSmo(m1))
plot(getSmo(m2))
plot(getSmo(m3))

There are some variations for beta regression. Take a look at the GAMLSS Manual.

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