def test_fit_with_index(self, cdnow_customers):
mbgf = lt.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 = lt.ModifiedBetaGeoFitter()
mbgf.fit(cdnow_customers["frequency"],
cdnow_customers["recency"],
cdnow_customers["T"],
index=None)
assert (mbgf.data.index == index).all() == False
def test_conditional_probability_alive_returns_lessthan_1_if_no_repeat_purchases(
self, cdnow_customers):
mbfg = lt.ModifiedBetaGeoFitter()
mbfg.fit(cdnow_customers["frequency"], cdnow_customers["recency"],
cdnow_customers["T"])
assert mbfg.conditional_probability_alive(0, 1, 1) < 1.0
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 = lt.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 """
mbgf = lt.ModifiedBetaGeoFitter()
mbgf.params_ = pd.Series({
"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_penalizer_term_will_shrink_coefs_to_0(self, cdnow_customers):
mbfg_no_penalizer = lt.ModifiedBetaGeoFitter()
mbfg_no_penalizer.fit(cdnow_customers["frequency"],
cdnow_customers["recency"], cdnow_customers["T"])
params_1 = mbfg_no_penalizer.params_
mbfg_with_penalizer = lt.ModifiedBetaGeoFitter(penalizer_coef=0.1)
mbfg_with_penalizer.fit(cdnow_customers["frequency"],
cdnow_customers["recency"],
cdnow_customers["T"])
params_2 = mbfg_with_penalizer.params_
assert params_2.sum() < params_1.sum()
mbfg_with_more_penalizer = lt.ModifiedBetaGeoFitter(penalizer_coef=1.0)
mbfg_with_more_penalizer.fit(cdnow_customers["frequency"],
cdnow_customers["recency"],
cdnow_customers["T"])
params_3 = mbfg_with_more_penalizer.params_
assert params_3.sum() < params_2.sum()
def test_params_out_is_close_to_BTYDplus(self, cdnow_customers):
""" See https://github.com/mplatzer/BTYDplus """
mbfg = lt.ModifiedBetaGeoFitter()
mbfg.fit(cdnow_customers["frequency"], cdnow_customers["recency"],
cdnow_customers["T"])
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)
def test_conditional_probability_alive_is_between_0_and_1(
self, cdnow_customers):
mbfg = lt.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_scaling_inputs_gives_same_or_similar_results(
self, cdnow_customers):
mbgf = lt.ModifiedBetaGeoFitter()
mbgf.fit(cdnow_customers["frequency"], cdnow_customers["recency"],
cdnow_customers["T"])
scale = 10.0
mbgf_with_large_inputs = lt.ModifiedBetaGeoFitter()
mbgf_with_large_inputs.fit(cdnow_customers["frequency"],
scale * cdnow_customers["recency"],
scale * cdnow_customers["T"])
assert mbgf_with_large_inputs._scale < 1.0
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_conditional_probability_alive_matrix(self, cdnow_customers):
mbfg = lt.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_expectation_returns_same_value_Hardie_excel_sheet(
self, cdnow_customers):
mbfg = lt.ModifiedBetaGeoFitter()
mbfg.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 = mbfg.expected_number_of_purchases_up_to_time(times)
npt.assert_allclose(actual, expected, rtol=0.05)
def test_conditional_expectation_returns_same_value_as_Hardie_excel_sheet(
self, cdnow_customers):
mbfg = lt.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