ModifiedBetaGeoFitter doens't converge about lifetimes

[mszep]

For posterity: I have experienced the exact same problem, with a and b converging to values of 1e-6 and smaller. Fortunately I was able to stabilize the algorithm by setting initial values of 0.5 for each. My intuition is that very small initial values can trigger this problem, and maybe it would be sensible to set the random initialization to be 1.0 + uniform(0.05) rather than normal(mu=1.0, std=0.05) as I believe it is now.

[rhydomako]

Hi Marco,

I wasn't able to reproduce your findings. I ran a modified script to generate/fit a bunch of times:

import matplotlib.pylab as plt
import pandas as pd

import lifetimes.generate_data as gen
from lifetimes import estimation

T = 40
r = 0.24
alpha = 4.41
a = 0.8
b = 2.43

fitter = estimation.ModifiedBetaGeoFitter()

params = []
for _ in range(500):
    data = gen.modified_beta_geometric_nbd_model(T, r, alpha, a, b, size=1000)
    fitter.fit(data['frequency'],data['recency'],data['T'])

    params.append(fitter._unload_params('r','alpha','a','b'))

df = pd.DataFrame(params, columns=['r','alpha','a','b'])

fig, axes = plt.subplots(nrows=2, ncols=2)
df.hist('r', bins=100, range=(0,1), ax=axes[0,0])
df.hist('alpha', bins=100, range=(2,7), ax=axes[0,1])
df.hist('a', bins=100, range=(0.2,4), ax=axes[1,0])
df.hist('b', bins=100, range=(0,10), ax=axes[1,1])

which produced the following distributions:

I should note that I've clipped some outliers where sometimes the fitting failed and produced a and b params in the 10^6 range, but that happened something like 2 times in 500 trials.

I'm not sure why you're seeing so many fitted parameters close to zero...

[CamDavidsonPilon]

Great script @rhydomako. I tried this too on my system (using 0.2.2.1). Output below:

I also get sometimes wild values for (a,b) (not shown here), but by adding a small penalizer_coef=0.01, the results are more sensible (below)

The max value of a in this simulation was 34.50