08_行销（Marketing）预测生命周期价值 （CLV）

在营销中，对营销活动的预算始终是挑战。我们不想花太多钱而导致ROI下降。但是，我们也不想花费太多，也没有明显的影响或结果。在确定营销策略的预算时，至关重要的是要知道运行给定的营销活动会带来多少预期回报。了解单个客户的客户生命周期价值（CLV）可以帮助营销人员证明其营销预算的合理性，并定位潜在的高价值客户。通常，获取新客户要比保留现有客户更为昂贵，因此，为了建立具有正ROI的营销策略，了解生命周期价值和与获取新客户相关的成本至关重要。例如，如果客户的平均CLV为100元，而获得新客户仅需花费10元，那么在获得新客户时，我们的业务就会产生更多的收入。

有多种方法可以计算CLV。一种方法是找到客户的平均购买金额，购买频率和寿命，并进行简单的计算以获得CLV。例如，考虑一个假设的案例，客户的平均购买金额为100，并且他/她平均每月进行五次购买。则该客户每月的平均价值为500美元，这就是平均购买金额乘以平均购买频率。现在，我们需要知道该客户的生命周期。估算客户生命周期的一种方法是查看平均每月客户流失率，即客户离开并终止与公司的业务关系的客户所占的百分比。您可以用客户流失率除以客户的生命周期。假设在我们假设的情况下，客户流失率为5％，则估计客户的生命周期为20年 （1/5%)。给定该客户每月的平均价值为500元，寿命为20年，则该客户的CLV为120,000。最终的CLV金额是通过将500（每月的平均值）乘以12个月以及20年的寿命来计算的。

在本文中，我会建立一个回归模型来预测连续的变量CLV。我会使用一个在线零售的数据集，仍然是来自Kaggle，数据集是OnlineRetail.csv 。

# This Python 3 environment comes with many helpful analytics libraries installed
# It is defined by the kaggle/python Docker image: https://github.com/kaggle/docker-python
# For example, here's several helpful packages to load

import numpy as np # linear algebra
import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)

# Input data files are available in the read-only "../input/" directory
# For example, running this (by clicking run or pressing Shift+Enter) will list all files under the input directory

import os
for dirname, _, filenames in os.walk('/kaggle/input'):
    for filename in filenames:
        print(os.path.join(dirname, filename))

# You can write up to 5GB to the current directory (/kaggle/working/) that gets preserved as output when you create a version using "Save & Run All" 
# You can also write temporary files to /kaggle/temp/, but they won't be saved outside of the current session

/kaggle/input/onlineretail/OnlineRetail.csv

Load Packages

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score, median_absolute_error

%matplotlib inline

Load the data

df=pd.read_csv(r"../input/onlineretail/OnlineRetail.csv", encoding="cp1252")

df.head(3)

	InvoiceNo	StockCode	Description	Quantity	InvoiceDate	UnitPrice	CustomerID	Country
0	536365	85123A	WHITE HANGING HEART T-LIGHT HOLDER	6	12/1/2010 8:26	2.55	17850.0	United Kingdom
1	536365	71053	WHITE METAL LANTERN	6	12/1/2010 8:26	3.39	17850.0	United Kingdom
2	536365	84406B	CREAM CUPID HEARTS COAT HANGER	8	12/1/2010 8:26	2.75	17850.0	United Kingdom

df.shape

(541909, 8)

Data Clean-Up

Negative Quantity

df.loc[df['Quantity'] <= 0].shape

(10624, 8)

df = df.loc[df['Quantity'] > 0]

Missing CustomerID

df = df[pd.notnull(df['CustomerID'])]

Excluding Incomplete Month

print('Date Range: %s ~ %s' % (df['InvoiceDate'].min(), df['InvoiceDate'].max()))

Date Range: 1/10/2011 10:32 ~ 9/9/2011 9:52

df = df.loc[df['InvoiceDate'] < '2011-12-01']

Total Sales

df['Sales'] = df['Quantity'] * df['UnitPrice']

Per Order Data

orders_df = df.groupby(['CustomerID', 'InvoiceNo']).agg({
    'Sales': sum,
    'InvoiceDate': max
})

orders_df

		Sales	InvoiceDate
CustomerID	InvoiceNo
12346.0	541431	77183.60	1/18/2011 10:01
12347.0	537626	711.79	12/7/2010 14:57
	542237	475.39	1/26/2011 14:30
	573511	1294.32	10/31/2011 12:25
	581180	224.82	12/7/2011 15:52
...	...	...	...
18283.0	578262	313.65	11/23/2011 13:27
	579673	223.61	11/30/2011 12:59
	580872	208.00	12/6/2011 12:02
18287.0	570715	1001.32	10/12/2011 10:23
	573167	70.68	10/28/2011 9:29

8750 rows ?? 2 columns

Data Analysis

def groupby_mean(x):
    return x.mean()

def groupby_count(x):
    return x.count()

def purchase_duration(x):
    return (x.max() - x.min()).days

def avg_frequency(x):
    return (x.max() - x.min()).days/x.count()

groupby_mean.__name__ = 'avg'
groupby_count.__name__ = 'count'
purchase_duration.__name__ = 'purchase_duration'
avg_frequency.__name__ = 'purchase_frequency'

orders_df['InvoiceDate']=pd.to_datetime(orders_df['InvoiceDate'])

summary_df = orders_df.reset_index().groupby('CustomerID').agg({
    'Sales': [min, max, sum, groupby_mean, groupby_count],
    'InvoiceDate': [min, max, purchase_duration, avg_frequency]
})

summary_df

	Sales					InvoiceDate
	min	max	sum	avg	count	min	max	purchase_duration	purchase_frequency
CustomerID
12346.0	77183.60	77183.60	77183.60	77183.600000	1.0	2011-01-18 10:01:00	2011-01-18 10:01:00	0	0.00
12347.0	224.82	1294.32	2706.32	676.580000	4.0	2010-12-07 14:57:00	2011-12-07 15:52:00	365	91.25
12348.0	227.44	892.80	1120.24	560.120000	2.0	2010-12-16 19:09:00	2011-01-25 10:42:00	39	19.50
12349.0	1757.55	1757.55	1757.55	1757.550000	1.0	2011-11-21 09:51:00	2011-11-21 09:51:00	0	0.00
12350.0	334.40	334.40	334.40	334.400000	1.0	2011-02-02 16:01:00	2011-02-02 16:01:00	0	0.00
...	...	...	...	...	...	...	...	...	...
18276.0	335.86	335.86	335.86	335.860000	1.0	2011-10-27 10:54:00	2011-10-27 10:54:00	0	0.00
18277.0	110.38	110.38	110.38	110.380000	1.0	2011-10-12 15:22:00	2011-10-12 15:22:00	0	0.00
18282.0	77.84	77.84	77.84	77.840000	1.0	2011-12-02 11:43:00	2011-12-02 11:43:00	0	0.00
18283.0	1.95	313.65	1292.11	143.567778	9.0	2011-01-06 14:14:00	2011-12-06 12:02:00	333	37.00
18287.0	70.68	1001.32	1072.00	536.000000	2.0	2011-10-12 10:23:00	2011-10-28 09:29:00	15	7.50

3251 rows ?? 9 columns

summary_df.columns = ['_'.join(col).lower() for col in summary_df.columns]

summary_df = summary_df.loc[summary_df['invoicedate_purchase_duration'] > 0]

ax = summary_df.groupby('sales_count').count()['sales_avg'][:20].plot(
    kind='bar', 
    color='skyblue',
    figsize=(12,7), 
    grid=True
)

ax.set_ylabel('count')

plt.show()

ax = summary_df['invoicedate_purchase_frequency'].hist(
    bins=20,
    color='skyblue',
    rwidth=0.7,
    figsize=(12,7)
)

ax.set_xlabel('avg. number of days between purchases')
ax.set_ylabel('count')

plt.show()

Predicting 3-Month CLV

Data Preparation

clv_freq = '3M'
data_df = orders_df.reset_index().groupby([
    'CustomerID',
    pd.Grouper(key='InvoiceDate', freq=clv_freq)
]).agg({
    'Sales': [sum, groupby_mean, groupby_count],
})

data_df.columns = ['_'.join(col).lower() for col in data_df.columns]

data_df = data_df.reset_index()

date_month_map = {
    str(x)[:10]: 'M_%s' % (i+1) for i, x in enumerate(
        sorted(data_df.reset_index()['InvoiceDate'].unique(), reverse=True)
    )
}

data_df['M'] = data_df['InvoiceDate'].apply(lambda x: date_month_map[str(x)[:10]])
date_month_map

{'2011-12-31': 'M_1', '2011-03-31': 'M_2', '2010-12-31': 'M_3'}

data_df.head(10)

	CustomerID	InvoiceDate	sales_sum	sales_avg	sales_count	M
0	12346.0	2011-03-31	77183.60	77183.60	1.0	M_2
1	12347.0	2010-12-31	711.79	711.79	1.0	M_3
2	12347.0	2011-03-31	475.39	475.39	1.0	M_2
3	12347.0	2011-12-31	1519.14	759.57	2.0	M_1
4	12348.0	2010-12-31	892.80	892.80	1.0	M_3
5	12348.0	2011-03-31	227.44	227.44	1.0	M_2
6	12349.0	2011-12-31	1757.55	1757.55	1.0	M_1
7	12350.0	2011-03-31	334.40	334.40	1.0	M_2
8	12352.0	2011-03-31	296.50	296.50	1.0	M_2
9	12352.0	2011-12-31	311.73	311.73	1.0	M_1

Building Sample Set

features_df = pd.pivot_table(
    data_df.loc[data_df['M'] != 'M_1'], 
    values=['sales_sum', 'sales_avg', 'sales_count'], 
    columns='M', 
    index='CustomerID'
)

features_df.columns = ['_'.join(col) for col in features_df.columns]
features_df.head(3)

	sales_avg_M_2	sales_avg_M_3	sales_count_M_2	sales_count_M_3	sales_sum_M_2	sales_sum_M_3
CustomerID
12346.0	77183.60	NaN	1.0	NaN	77183.60	NaN
12347.0	475.39	711.79	1.0	1.0	475.39	711.79
12348.0	227.44	892.80	1.0	1.0	227.44	892.80

features_df = features_df.fillna(0)
response_df = data_df.loc[
    data_df['M'] == 'M_1',
    ['CustomerID', 'sales_sum']
]

response_df.columns = ['CustomerID', 'CLV_'+clv_freq]

response_df.head(10)

	CustomerID	CLV_3M
3	12347.0	1519.14
6	12349.0	1757.55
9	12352.0	311.73
11	12356.0	58.35
12	12357.0	6207.67
13	12358.0	683.20
15	12359.0	2876.85
16	12360.0	1043.78
19	12362.0	2648.89
20	12364.0	609.38

sample_set_df = features_df.merge(
    response_df, 
    left_index=True, 
    right_on='CustomerID',
    how='left'
)

sample_set_df = sample_set_df.fillna(0)
sample_set_df['CLV_'+clv_freq].describe()

count     1682.000000
mean       920.706231
std       3712.676313
min          0.000000
25%          0.000000
50%        218.835000
75%        745.132500
max      79497.890000
Name: CLV_3M, dtype: float64

Regression Models

target_var = 'CLV_'+clv_freq
all_features = [x for x in sample_set_df.columns if x not in ['CustomerID', target_var]]

x_train, x_test, y_train, y_test = train_test_split(
    sample_set_df[all_features], 
    sample_set_df[target_var], 
    test_size=0.3
)

Linear regression

reg_fit = LinearRegression()
reg_fit.fit(x_train, y_train)

LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)

reg_fit.intercept_

227.53656034899996

coef = pd.DataFrame(list(zip(all_features, reg_fit.coef_)))
coef.columns = ['feature', 'coef']

coef

	feature	coef
0	sales_avg_M_2	-0.802312
1	sales_avg_M_3	-0.570974
2	sales_count_M_2	-130.463301
3	sales_count_M_3	-259.197597
4	sales_sum_M_2	1.215923
5	sales_sum_M_3	2.099159

Evaluation

train_preds =  reg_fit.predict(x_train)
test_preds = reg_fit.predict(x_test)

R^2

print('In-Sample R-Squared: %0.4f' % r2_score(y_true=y_train, y_pred=train_preds))
print('Out-of-Sample R-Squared: %0.4f' % r2_score(y_true=y_test, y_pred=test_preds))

In-Sample R-Squared: 0.7456
Out-of-Sample R-Squared: 0.1633

Median Absolute Error

print('In-Sample MSE: %0.4f' % median_absolute_error(y_true=y_train, y_pred=train_preds))
print('Out-of-Sample MSE: %0.4f' % median_absolute_error(y_true=y_test, y_pred=test_preds))

In-Sample MSE: 277.4823
Out-of-Sample MSE: 276.4211

plt.scatter(y_train, train_preds)
plt.plot([0, max(y_train)], [0, max(train_preds)], color='gray', lw=1, linestyle='--')

plt.xlabel('actual')
plt.ylabel('predicted')
plt.title('In-Sample Actual vs. Predicted')
plt.grid()

plt.show()

plt.scatter(y_test, test_preds)
plt.plot([0, max(y_test)], [0, max(test_preds)], color='gray', lw=1, linestyle='--')

plt.xlabel('actual')
plt.ylabel('predicted')
plt.title('Out-of-Sample Actual vs. Predicted')
plt.grid()

plt.show()

EOD