def test_conditional_probability_alive_returns_1_if_no_repeat_purchases(
self, cdnow_customers):
bfg = estimation.BetaGeoFitter()
bfg.fit(cdnow_customers['frequency'], cdnow_customers['recency'],
cdnow_customers['T'])
assert bfg.conditional_probability_alive(0, 1, 1) == 1.0
def test_customer_lifetime_value_with_bgf(self):
ggf = estimation.GammaGammaFitter()
ggf.params_ = OrderedDict({'p': 6.25, 'q': 3.74, 'v': 15.44})
bgf = estimation.BetaGeoFitter()
bgf.fit(cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['recency'],
cdnow_customers_with_monetary_value['T'],
iterative_fitting=3)
ggf_clv = ggf.customer_lifetime_value(
bgf, cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['recency'],
cdnow_customers_with_monetary_value['T'],
cdnow_customers_with_monetary_value['monetary_value'])
utils_clv = utils.customer_lifetime_value(
bgf, cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['recency'],
cdnow_customers_with_monetary_value['T'],
ggf.conditional_expected_average_profit(
cdnow_customers_with_monetary_value['frequency'],
cdnow_customers_with_monetary_value['monetary_value']))
npt.assert_equal(ggf_clv.values, utils_clv.values)
def test_probability_of_n_purchases_up_to_time_same_as_R_BTYD(self):
""" See https://cran.r-project.org/web/packages/BTYD/BTYD.pdf """
from collections import OrderedDict
bgf = estimation.BetaGeoFitter()
bgf.params_ = OrderedDict({
'r': 0.243,
'alpha': 4.414,
'a': 0.793,
'b': 2.426
})
# probability that a customer will make 10 repeat transactions in the
# time interval (0,2]
expected = 1.07869e-07
actual = bgf.probability_of_n_purchases_up_to_time(2, 10)
assert abs(expected - actual) < 10e-5
# probability that a customer will make no repeat transactions in the
# time interval (0,39]
expected = 0.5737864
actual = bgf.probability_of_n_purchases_up_to_time(39, 0)
assert abs(expected - actual) < 10e-5
# PMF
expected = np.array([
0.0019995214, 0.0015170236, 0.0011633150, 0.0009003148,
0.0007023638, 0.0005517902, 0.0004361913, 0.0003467171,
0.0002769613, 0.0002222260
])
actual = np.array([
bgf.probability_of_n_purchases_up_to_time(30, n)
for n in range(11, 21)
])
npt.assert_array_almost_equal(expected, actual, decimal=5)
def test_save_load_bgnbd_no_data(self, cdnow_customers):
bgf = estimation.BetaGeoFitter(penalizer_coef=0.0)
bgf.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
bgf.save_model(PATH_SAVE_BGNBD_MODEL, save_data=False)
bgf_new = estimation.BetaGeoFitter()
bgf_new.load_model(PATH_SAVE_BGNBD_MODEL)
assert bgf_new.__dict__['penalizer_coef'] == bgf.__dict__['penalizer_coef']
assert bgf_new.__dict__['_scale'] == bgf.__dict__['_scale']
assert bgf_new.__dict__['params_'] == bgf.__dict__['params_']
assert bgf_new.__dict__['_negative_log_likelihood_'] == bgf.__dict__['_negative_log_likelihood_']
assert bgf_new.__dict__['predict'](1, 1, 2, 5) == bgf.__dict__['predict'](1, 1, 2, 5)
assert bgf_new.expected_number_of_purchases_up_to_time(1) == bgf.expected_number_of_purchases_up_to_time(1)
assert isinstance(bgf_new.__dict__['data'], list)
# remove saved model
os.remove(PATH_SAVE_BGNBD_MODEL)
def test_conditional_probability_alive_is_between_0_and_1(self, cdnow_customers):
bfg = estimation.BetaGeoFitter()
bfg.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
for i in range(0, 100, 10):
for j in range(0, 100, 10):
for k in range(j, 100, 10):
assert 0 <= bfg.conditional_probability_alive(i, j, k) <= 1.0
def test_expectation_returns_same_value_Hardie_excel_sheet(self, cdnow_customers):
bfg = estimation.BetaGeoFitter()
bfg.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'], tol=1e-6)
times = np.array([0.1429, 1.0, 3.00, 31.8571, 32.00, 78.00])
expected = np.array([0.0078 ,0.0532 ,0.1506 ,1.0405,1.0437, 1.8576])
actual = bfg.expected_number_of_purchases_up_to_time(times)
npt.assert_array_almost_equal(actual, expected, decimal=3)
def test_save_load_bgnbd(self, cdnow_customers):
"""Test saving and loading model for BG/NBD."""
bgf = estimation.BetaGeoFitter(penalizer_coef=0.0)
bgf.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
bgf.save_model(PATH_SAVE_BGNBD_MODEL)
bgf_new = estimation.BetaGeoFitter()
bgf_new.load_model(PATH_SAVE_BGNBD_MODEL)
assert bgf_new.__dict__['penalizer_coef'] == bgf.__dict__['penalizer_coef']
assert bgf_new.__dict__['_scale'] == bgf.__dict__['_scale']
assert bgf_new.__dict__['params_'] == bgf.__dict__['params_']
assert bgf_new.__dict__['_negative_log_likelihood_'] == bgf.__dict__['_negative_log_likelihood_']
assert (bgf_new.__dict__['data'] == bgf.__dict__['data']).all().all()
assert bgf_new.__dict__['predict'](1, 1, 2, 5) == bgf.__dict__['predict'](1, 1, 2, 5)
assert bgf_new.expected_number_of_purchases_up_to_time(1) == bgf.expected_number_of_purchases_up_to_time(1)
# remove saved model
os.remove(PATH_SAVE_BGNBD_MODEL)
def test_save_load_bgnbd_no_data_replace_with_empty_str(self, cdnow_customers):
"""Test saving and loading model for BG/NBD without data with replaced value empty str."""
bgf = estimation.BetaGeoFitter(penalizer_coef=0.0)
bgf.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
bgf.save_model(PATH_SAVE_BGNBD_MODEL, save_data=False, values_to_save=[''])
bgf_new = estimation.BetaGeoFitter()
bgf_new.load_model(PATH_SAVE_BGNBD_MODEL)
assert bgf_new.__dict__['penalizer_coef'] == bgf.__dict__['penalizer_coef']
assert bgf_new.__dict__['_scale'] == bgf.__dict__['_scale']
assert bgf_new.__dict__['params_'] == bgf.__dict__['params_']
assert bgf_new.__dict__['_negative_log_likelihood_'] == bgf.__dict__['_negative_log_likelihood_']
assert bgf_new.__dict__['predict'](1, 1, 2, 5) == bgf.__dict__['predict'](1, 1, 2, 5)
assert bgf_new.expected_number_of_purchases_up_to_time(1) == bgf.expected_number_of_purchases_up_to_time(1)
assert bgf_new.__dict__['data'] is ''
# remove saved model
os.remove(PATH_SAVE_BGNBD_MODEL)
def test_params_out_is_close_to_Hardie_paper(self, cdnow_customers):
bfg = estimation.BetaGeoFitter()
bfg.fit(cdnow_customers['x'], cdnow_customers['t_x'],
cdnow_customers['T'])
expected = np.array([0.243, 4.414, 0.793, 2.426])
npt.assert_array_almost_equal(
expected,
np.array(bfg._unload_params('r', 'alpha', 'a', 'b')),
decimal=3)
def test_penalizer_term_will_shrink_coefs_to_0(self, cdnow_customers):
bfg_no_penalizer = estimation.BetaGeoFitter()
bfg_no_penalizer.fit(cdnow_customers['x'], cdnow_customers['t_x'],
cdnow_customers['T'])
params_1 = np.array(list(bfg_no_penalizer.params_.values()))
bfg_with_penalizer = estimation.BetaGeoFitter(penalizer_coef=0.1)
bfg_with_penalizer.fit(cdnow_customers['x'], cdnow_customers['t_x'],
cdnow_customers['T'])
params_2 = np.array(list(bfg_with_penalizer.params_.values()))
assert np.all(params_2 < params_1)
bfg_with_more_penalizer = estimation.BetaGeoFitter(penalizer_coef=10)
bfg_with_more_penalizer.fit(cdnow_customers['x'],
cdnow_customers['t_x'],
cdnow_customers['T'])
params_3 = np.array(list(bfg_with_more_penalizer.params_.values()))
assert np.all(params_3 < params_2)
def test_fit_with_index(self, cdnow_customers):
bgf = estimation.BetaGeoFitter(penalizer_coef=0.0)
index = range(len(cdnow_customers), 0, -1)
bgf.fit(
cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
index=index
)
assert (bgf.data.index == index).all() == True
bgf = estimation.BetaGeoFitter(penalizer_coef=0.0)
bgf.fit(
cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
index=None
)
assert (bgf.data.index == index).all() == False
def test_conditional_probability_alive_matrix(self, cdnow_customers):
bfg = estimation.BetaGeoFitter()
bfg.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
Z = bfg.conditional_probability_alive_matrix()
max_t = int(bfg.data['T'].max())
assert Z[0][0] == 1
for t_x in range(Z.shape[0]):
for x in range(Z.shape[1]):
assert Z[t_x][x] == bfg.conditional_probability_alive(x, t_x, max_t)
def test_conditional_expectation_returns_same_value_as_Hardie_excel_sheet(self, cdnow_customers):
bfg = estimation.BetaGeoFitter()
bfg.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
x = 2
t_x = 30.43
T = 38.86
t = 39
expected = 1.226
actual = bfg.conditional_expected_number_of_purchases_up_to_time(t, x, t_x, T)
assert abs(expected - actual) < 0.001
def test_scaling_inputs_gives_same_or_similar_results(self):
bgf = estimation.BetaGeoFitter()
bgf.fit(cdnow_customers['frequency'], cdnow_customers['recency'],
cdnow_customers['T'])
scale = 10
bgf_with_large_inputs = estimation.BetaGeoFitter()
bgf_with_large_inputs.fit(cdnow_customers['frequency'],
scale * cdnow_customers['recency'],
scale * cdnow_customers['T'],
iterative_fitting=2)
assert bgf_with_large_inputs._scale < 1.
assert abs(
bgf_with_large_inputs.conditional_probability_alive(
1, scale * 1, scale * 2) -
bgf.conditional_probability_alive(1, 1, 2)) < 10e-5
assert abs(
bgf_with_large_inputs.conditional_probability_alive(
1, scale * 2, scale * 10) -
bgf.conditional_probability_alive(1, 2, 10)) < 10e-5
def test_using_weights_col_gives_correct_results(self, cdnow_customers):
cdnow_customers_weights = cdnow_customers.copy()
cdnow_customers_weights['weights'] = 1.0
cdnow_customers_weights = cdnow_customers_weights.groupby(
['frequency', 'recency', 'T'])['weights'].sum()
cdnow_customers_weights = cdnow_customers_weights.reset_index()
assert (cdnow_customers_weights['weights'] > 1).any()
bgf_weights = estimation.BetaGeoFitter(penalizer_coef=0.0)
bgf_weights.fit(cdnow_customers_weights['frequency'],
cdnow_customers_weights['recency'],
cdnow_customers_weights['T'],
weights=cdnow_customers_weights['weights'])
bgf_no_weights = estimation.BetaGeoFitter(penalizer_coef=0.0)
bgf_no_weights.fit(cdnow_customers['frequency'],
cdnow_customers['recency'], cdnow_customers['T'])
npt.assert_almost_equal(
np.array(bgf_no_weights._unload_params('r', 'alpha', 'a', 'b')),
np.array(bgf_weights._unload_params('r', 'alpha', 'a', 'b')),
decimal=4)
def test_no_runtime_warnings_high_frequency(self, cdnow_customers):
old_settings = np.seterr(all='raise')
bgf = estimation.BetaGeoFitter(penalizer_coef=0.0)
bgf.fit(cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
index=None)
p_alive = bgf.conditional_probability_alive(frequency=1000,
recency=10,
T=100)
np.seterr(**old_settings)
assert p_alive == 0.