I frequently predict proportions (e.g., proportion of year during which a customer is active). This is a regression task because the dependent variables is a float, but the dependent variable is bound between the 0 and 1. Googling around, I had a hard time finding the a good way to model this situation, so I’ve written here what I think is the most straight forward solution.
I am guessing there’s a better way to do this with MCMC, so please comment below if you know a better way.
Let’s get started by importing some libraries for making random data.
1 2 

Create random regression data.
1 2 3 4 5 6 7 8 9 

Shrink down the dependent variable so it’s bound between 0 and 1.
1 2 3 4 

Make a quick plot to confirm that the data is bound between 0 and 1.
1 2 3 4 5 6 7 

All the data here is fake which worries me, but beggars can’t be choosers and this is just a quick example.
Below, I apply a plain GLM to the data. This is what you would expect if you treated this as a plain regression problem
1 2 3 4 5 

Here’s the actual values plotted (xaxis) against the predicted values (yaxis). The model does a decent job, but check out the values on the yaxis  the linear model predicts negative values!
1


Obviously the linear model above isn’t correctly modeling this data since it’s guessing values that are impossible.
I followed this tutorial which recommends using a GLM with a logit link and the binomial family. Checking out the statsmodels module reference, we can see the default link for the binomial family is logit.
Below I apply a GLM with a logit link and the binomial family to the data.
1 2 3 

Here’s the actual data (xaxis) plotted against teh predicted data. You can see the fit is much better!
1


1 2 

CPython 3.6.3
IPython 6.1.0
numpy 1.13.3
matplotlib 2.0.2
sklearn 0.19.1
seaborn 0.8.0
statsmodels 0.8.0
compiler : GCC 7.2.0
system : Linux
release : 4.13.038generic
machine : x86_64
processor : x86_64
CPU cores : 4
interpreter: 64bit