def test_scaling_inputs_gives_same_or_similar_results(self, cdnow_customers):
mbgf = estimation.ModifiedBetaGeoFitter()
mbgf.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
scale = 10.
mbgf_with_large_inputs = estimation.ModifiedBetaGeoFitter()
mbgf_with_large_inputs.fit(cdnow_customers['frequency'], scale * cdnow_customers['recency'], scale * cdnow_customers['T'], iterative_fitting=2)
assert mbgf_with_large_inputs._scale < 1.
assert abs(mbgf_with_large_inputs.conditional_probability_alive(1, scale * 1, scale * 2) - mbgf.conditional_probability_alive(1, 1, 2)) < 10e-2
assert abs(mbgf_with_large_inputs.conditional_probability_alive(1, scale * 2, scale * 10) - mbgf.conditional_probability_alive(1, 2, 10)) < 10e-2
def test_fit_method_allows_for_better_accuracy_by_using_iterative_fitting(self, cdnow_customers):
mbfg1 = estimation.ModifiedBetaGeoFitter()
mbfg2 = estimation.ModifiedBetaGeoFitter()
np.random.seed(0)
mbfg1.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
np.random.seed(0)
mbfg2.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'], iterative_fitting=5)
assert mbfg1._negative_log_likelihood_ >= mbfg2._negative_log_likelihood_
def test_mgbf_does_not_hang_for_small_datasets_but_can_be_improved_with_iterative_fitting(self, cdnow_customers):
reduced_dataset = cdnow_customers.ix[:2]
mbfg1 = estimation.ModifiedBetaGeoFitter()
mbfg2 = estimation.ModifiedBetaGeoFitter()
np.random.seed(0)
mbfg1.fit(reduced_dataset['frequency'], reduced_dataset['recency'], reduced_dataset['T'])
np.random.seed(0)
mbfg2.fit(reduced_dataset['frequency'], reduced_dataset['recency'], reduced_dataset['T'], iterative_fitting=10)
assert mbfg1._negative_log_likelihood_ >= mbfg2._negative_log_likelihood_
def test_penalizer_term_will_shrink_coefs_to_0(self, cdnow_customers):
mbfg_no_penalizer = estimation.ModifiedBetaGeoFitter()
mbfg_no_penalizer.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
params_1 = np.array(list(mbfg_no_penalizer.params_.values()))
mbfg_with_penalizer = estimation.ModifiedBetaGeoFitter(penalizer_coef=0.1)
mbfg_with_penalizer.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'], iterative_fitting=3)
params_2 = np.array(list(mbfg_with_penalizer.params_.values()))
assert params_2.sum() < params_1.sum()
mbfg_with_more_penalizer = estimation.ModifiedBetaGeoFitter(penalizer_coef=1.)
mbfg_with_more_penalizer.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'], iterative_fitting=5)
params_3 = np.array(list(mbfg_with_more_penalizer.params_.values()))
assert params_3.sum() < params_2.sum()
def test_fit_with_index(self, cdnow_customers):
mbgf = estimation.ModifiedBetaGeoFitter()
index = range(len(cdnow_customers), 0, -1)
mbgf.fit(cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
index=index)
assert (mbgf.data.index == index).all() == True
mbgf = estimation.ModifiedBetaGeoFitter()
mbgf.fit(cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
index=None)
assert (mbgf.data.index == index).all() == False
def test_purchase_predictions_do_not_differ_much_if_looking_at_hourly_or_daily_frequencies(
self):
transaction_data = load_transaction_data(parse_dates=['date'])
daily_summary = utils.summary_data_from_transaction_data(
transaction_data,
'id',
'date',
observation_period_end=max(transaction_data.date),
freq='D')
hourly_summary = utils.summary_data_from_transaction_data(
transaction_data,
'id',
'date',
observation_period_end=max(transaction_data.date),
freq='h')
thirty_days = 30
hours_in_day = 24
mbfg = estimation.ModifiedBetaGeoFitter()
np.random.seed(0)
mbfg.fit(daily_summary['frequency'], daily_summary['recency'],
daily_summary['T'])
thirty_day_prediction_from_daily_data = mbfg.expected_number_of_purchases_up_to_time(
thirty_days)
np.random.seed(0)
mbfg.fit(hourly_summary['frequency'], hourly_summary['recency'],
hourly_summary['T'])
thirty_day_prediction_from_hourly_data = mbfg.expected_number_of_purchases_up_to_time(
thirty_days * hours_in_day)
npt.assert_almost_equal(thirty_day_prediction_from_daily_data,
thirty_day_prediction_from_hourly_data)
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
mbgf = estimation.ModifiedBetaGeoFitter()
mbgf.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 = mbgf.probability_of_n_purchases_up_to_time(2, 10)
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([
mbgf.probability_of_n_purchases_up_to_time(30, n)
for n in range(11, 21)
])
npt.assert_allclose(expected, actual, rtol=0.5)
def test_conditional_probability_alive_returns_lessthan_1_if_no_repeat_purchases(
self, cdnow_customers):
mbfg = estimation.ModifiedBetaGeoFitter()
mbfg.fit(cdnow_customers['frequency'], cdnow_customers['recency'],
cdnow_customers['T'])
assert mbfg.conditional_probability_alive(0, 1, 1) < 1.0
def test_conditional_probability_alive_is_between_0_and_1(self, cdnow_customers):
mbfg = estimation.ModifiedBetaGeoFitter()
mbfg.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 <= mbfg.conditional_probability_alive(i, j, k) <= 1.0
def test_expectation_returns_same_value_Hardie_excel_sheet(self, cdnow_customers):
mbfg = estimation.ModifiedBetaGeoFitter()
mbfg.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'], tol=1e-6, iterative_fitting=3)
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 = mbfg.expected_number_of_purchases_up_to_time(times)
npt.assert_allclose(actual, expected, rtol=0.05)
def test_conditional_probability_alive_matrix(self, cdnow_customers):
mbfg = estimation.ModifiedBetaGeoFitter()
mbfg.fit(cdnow_customers['frequency'], cdnow_customers['recency'], cdnow_customers['T'])
Z = mbfg.conditional_probability_alive_matrix()
max_t = int(mbfg.data['T'].max())
for t_x in range(Z.shape[0]):
for x in range(Z.shape[1]):
assert Z[t_x][x] == mbfg.conditional_probability_alive(x, t_x, max_t)
def test_conditional_expectation_returns_same_value_as_Hardie_excel_sheet(self, cdnow_customers):
mbfg = estimation.ModifiedBetaGeoFitter()
mbfg.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 = mbfg.conditional_expected_number_of_purchases_up_to_time(t, x, t_x, T)
assert abs(expected - actual) < 0.05
def test_params_out_is_close_to_BTYDplus(self, cdnow_customers):
""" See https://github.com/mplatzer/BTYDplus """
mbfg = estimation.ModifiedBetaGeoFitter()
mbfg.fit(cdnow_customers['frequency'],
cdnow_customers['recency'],
cdnow_customers['T'],
iterative_fitting=3)
expected = np.array([0.525, 6.183, 0.891, 1.614])
npt.assert_array_almost_equal(
expected,
np.array(mbfg._unload_params('r', 'alpha', 'a', 'b')),
decimal=3)