Predictive Analytics#

Goal :-

What is likelihood that a customer will purchase?
If they do, How much they will spend?

Imports#

import pandas as pd
import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
import seaborn as sns
import datetime as dt
from sklearn.cluster import AgglomerativeClustering
from scipy.cluster.hierarchy import dendrogram, linkage
from sklearn.pipeline import Pipeline, make_pipeline
from sklearn.preprocessing import StandardScaler, RobustScaler, FunctionTransformer
from sklearn.linear_model import LogisticRegression, LinearRegression
import statsmodels.api as sm
import statsmodels.formula.api as smf

Data Collection and Feature Engineering#

Read Dataset#

df = pd.read_csv("W106_purchases.txt", sep='\t', names=['consumer_id','purchase_amount', 'date_of_purchase'], parse_dates=['date_of_purchase'] )
df['year_of_purchase'] = df['date_of_purchase'].dt.year
max_date = df['date_of_purchase'].max() + dt.timedelta(days=1)
df['days_since'] = (max_date - df['date_of_purchase']).dt.days
df.head()

	consumer_id	purchase_amount	date_of_purchase	year_of_purchase	days_since
0	760	25.0	2009-11-06	2009	2247
1	860	50.0	2012-09-28	2012	1190
2	1200	100.0	2005-10-25	2005	3720
3	1420	50.0	2009-07-09	2009	2367
4	1940	70.0	2013-01-25	2013	1071

Generate Consumer_df Input and Target (Revenue_2015)#

def get_consumer_df(df, offset=0):
    df = df.copy()
    df = df[df['days_since']>offset]
    consumer_df = df.groupby('consumer_id').agg(recency=('days_since', 'min'),
                                            frequency=('date_of_purchase', 'count'),
                                            # monetary=('purchase_amount', 'mean'),
                                            avg_purchase_amount=('purchase_amount', 'mean'),
                                            max_purchase_amount=('purchase_amount', 'max'),
                                            first_purchase=('days_since', 'max'), 
                                            # revenue_till_date=('purchase_amount', 'sum'),
                                            
                                            # first_purchase_date=('date_of_purchase', 'min'),
                                            # first_purchase_year=('year_of_purchase', 'min'),
                                            # last_purchase_date=('date_of_purchase', 'max'),
                                            # last_purchase_year=('year_of_purchase', 'max'),
                                           ); consumer_df.head()
    consumer_df['recency'] = consumer_df['recency']  - offset
    consumer_df['first_purchase'] = consumer_df['first_purchase'] - offset
    # consumer_df['segment'] = np.nan
    # rec_filter  = consumer_df['recency'] 
    # first_purchase_filter = consumer_df['first_purchase']
    # consumer_df.loc[(rec_filter <=365)  & (consumer_df['monetary'] >= 100), 'segment'] = 'active high'
    # consumer_df.loc[(rec_filter <=365)  & (consumer_df['monetary'] < 100), 'segment'] = 'active low'""
    # consumer_df.loc[(rec_filter <=365) & (first_purchase_filter <=365) & (consumer_df['monetary'] >= 100) , 'segment'] = 'new active high'
    # consumer_df.loc[(rec_filter <=365) & (first_purchase_filter <=365) & (consumer_df['monetary'] < 100) , 'segment'] = 'new active low'
    # consumer_df.loc[(rec_filter>365) & (rec_filter<=2*365) & (consumer_df['monetary'] >= 100), 'segment'] = 'warm high'
    # consumer_df.loc[(rec_filter>365) & (rec_filter<=2*365) & (consumer_df['monetary'] < 100), 'segment'] = 'warm low'
    # consumer_df.loc[(rec_filter>365) & (rec_filter<=2*365) & (first_purchase_filter <=2*365) & (consumer_df['monetary'] >= 100) , 'segment'] = 'new warm high'
    # consumer_df.loc[(rec_filter>365) & (rec_filter<=2*365) & (first_purchase_filter <=2*365) & (consumer_df['monetary'] < 100) , 'segment'] = 'new warm low'
    # consumer_df.loc[(rec_filter>2*365) & (rec_filter<=3*365), 'segment'] = 'cold'
    # consumer_df.loc[(rec_filter>3*365), 'segment'] = 'inactive'
    return consumer_df

revenue_df = df[df['year_of_purchase']==2015].groupby('consumer_id').agg(revenue_2015=('purchase_amount', 'sum')); revenue_df.head()

	revenue_2015
consumer_id
80	80.0
480	45.0
830	50.0
850	60.0
860	60.0

cons_df_2014 = get_consumer_df(df, offset=365); cons_df_2014.head()

	recency	frequency	avg_purchase_amount	max_purchase_amount	first_purchase
consumer_id
10	3464	1	30.0	30.0	3464
80	302	6	70.0	80.0	3386
90	393	10	115.8	153.0	3418
120	1036	1	20.0	20.0	1036
130	2605	2	50.0	60.0	3345

Prepare Training dataset#

df_insample = pd.merge(cons_df_2014, revenue_df, left_index=True,right_index=True, how='left')
df_insample['active_2015'] = 1
df_insample.loc[df_insample.revenue_2015.isnull(), 'active_2015']=0
df_insample = df_insample.fillna(0)
df_insample.head()

	recency	frequency	avg_purchase_amount	max_purchase_amount	first_purchase	revenue_2015	active_2015
consumer_id
10	3464	1	30.0	30.0	3464	0.0	0
80	302	6	70.0	80.0	3386	80.0	1
90	393	10	115.8	153.0	3418	0.0	0
120	1036	1	20.0	20.0	1036	0.0	0
130	2605	2	50.0	60.0	3345	0.0	0

Prepare Out of Sample Dataset#

df_outsample = get_consumer_df(df, offset=0);df_outsample.shape

(18417, 5)

df_outsample.head()

	recency	frequency	avg_purchase_amount	max_purchase_amount	first_purchase
consumer_id
10	3829	1	30.000000	30.0	3829
80	343	7	71.428571	80.0	3751
90	758	10	115.800000	153.0	3783
120	1401	1	20.000000	20.0	1401
130	2970	2	50.000000	60.0	3710

Predictive Models#

def process_df(df):
    df_cp = df.copy()
    df_cp['frequency'] = np.log1p(df_cp['frequency'])
    df_cp['avg_purchase_amount'] = np.log1p(df_cp['avg_purchase_amount'])
    return df_cp

Likelihood of Purchase#

df_insample.columns

Index(['recency', 'frequency', 'avg_purchase_amount', 'max_purchase_amount',
       'first_purchase', 'revenue_2015', 'active_2015'],
      dtype='object')

input_ds = df_insample[['recency', 'frequency', 'avg_purchase_amount', 'max_purchase_amount',
       'first_purchase']]
y = df_insample['active_2015']
X = sm.add_constant(input_ds); X.head()

	const	recency	frequency	avg_purchase_amount	max_purchase_amount	first_purchase
consumer_id
10	1.0	3464	1	30.0	30.0	3464
80	1.0	302	6	70.0	80.0	3386
90	1.0	393	10	115.8	153.0	3418
120	1.0	1036	1	20.0	20.0	1036
130	1.0	2605	2	50.0	60.0	3345

model_purchase_incidence = sm.Logit(y, X).fit()

Optimization terminated successfully.
         Current function value: 0.365836
         Iterations 8

model_purchase_incidence.summary()

Logit Regression Results
Dep. Variable:	active_2015	No. Observations:	16905
Model:	Logit	Df Residuals:	16899
Method:	MLE	Df Model:	5
Date:	Sat, 28 May 2022	Pseudo R-squ.:	0.3214
Time:	19:48:41	Log-Likelihood:	-6184.5
converged:	True	LL-Null:	-9113.9
Covariance Type:	nonrobust	LLR p-value:	0.000

	coef	std err	z	P>\|z\|	[0.025	0.975]
const	-0.5331	0.044	-12.087	0.000	-0.620	-0.447
recency	-0.0020	6e-05	-32.748	0.000	-0.002	-0.002
frequency	0.2195	0.015	14.840	0.000	0.191	0.249
avg_purchase_amount	0.0004	0.000	1.144	0.253	-0.000	0.001
max_purchase_amount	-0.0002	0.000	-0.574	0.566	-0.001	0.000
first_purchase	-1.167e-05	3.93e-05	-0.297	0.766	-8.86e-05	6.53e-05

Amount of Purchase#

df_insample[df_insample['active_2015']==1]

	recency	frequency	avg_purchase_amount	max_purchase_amount	first_purchase	revenue_2015	active_2015
consumer_id
80	302	6	70.000000	80.0	3386	80.0	1
480	16	11	62.272727	235.0	3313	45.0	1
830	267	6	48.333333	60.0	3374	50.0	1
850	62	8	28.125000	30.0	3051	60.0	1
860	267	9	53.333333	60.0	3643	60.0	1
...	...	...	...	...	...	...	...
234590	1	1	20.000000	20.0	1	25.0	1
234640	1	1	30.000000	30.0	1	45.0	1
234660	1	1	35.000000	35.0	1	40.0	1
234760	1	1	20.000000	20.0	1	15.0	1
236660	390	2	75.000000	100.0	684	100.0	1

3886 rows × 7 columns

model_monetary_prediction = smf.ols(formula='revenue_2015 ~ avg_purchase_amount + max_purchase_amount', data=df_insample[df_insample['active_2015']==1])

res = model_monetary_prediction.fit()

res.summary()

OLS Regression Results
Dep. Variable:	revenue_2015	R-squared:	0.605
Model:	OLS	Adj. R-squared:	0.605
Method:	Least Squares	F-statistic:	2979.
Date:	Sat, 28 May 2022	Prob (F-statistic):	0.00
Time:	20:01:40	Log-Likelihood:	-24621.
No. Observations:	3886	AIC:	4.925e+04
Df Residuals:	3883	BIC:	4.927e+04
Df Model:	2
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	20.7471	2.381	8.713	0.000	16.079	25.415
avg_purchase_amount	0.6749	0.033	20.575	0.000	0.611	0.739
max_purchase_amount	0.2923	0.024	12.367	0.000	0.246	0.339

Omnibus:	5580.836	Durbin-Watson:	2.007
Prob(Omnibus):	0.000	Jarque-Bera (JB):	8162692.709
Skew:	7.843	Prob(JB):	0.00
Kurtosis:	226.980	Cond. No.	315.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

y = res.predict(df_insample[df_insample['active_2015']==1]).values
x = df_insample[df_insample['active_2015']==1]['revenue_2015'].values
sns.scatterplot(x,y)

/opt/anaconda/envs/aiking/lib/python3.9/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

<AxesSubplot:>

../../_images/03_predictive_analytics_28_2.png

model_monetary_prediction2 = smf.ols(formula='np.log(revenue_2015) ~ np.log(avg_purchase_amount) + np.log(max_purchase_amount)', data=df_insample[df_insample['active_2015']==1])
res2 = model_monetary_prediction2.fit()
res2.summary()

OLS Regression Results
Dep. Variable:	np.log(revenue_2015)	R-squared:	0.693
Model:	OLS	Adj. R-squared:	0.693
Method:	Least Squares	F-statistic:	4377.
Date:	Sat, 28 May 2022	Prob (F-statistic):	0.00
Time:	20:12:35	Log-Likelihood:	-2644.6
No. Observations:	3886	AIC:	5295.
Df Residuals:	3883	BIC:	5314.
Df Model:	2
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	0.3700	0.040	9.242	0.000	0.292	0.448
np.log(avg_purchase_amount)	0.5488	0.042	13.171	0.000	0.467	0.631
np.log(max_purchase_amount)	0.3881	0.038	10.224	0.000	0.314	0.463

Omnibus:	501.505	Durbin-Watson:	1.961
Prob(Omnibus):	0.000	Jarque-Bera (JB):	3328.833
Skew:	0.421	Prob(JB):	0.00
Kurtosis:	7.455	Cond. No.	42.2

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

y = res2.predict(df_insample[df_insample['active_2015']==1]).values
x = np.log(df_insample[df_insample['active_2015']==1]['revenue_2015'].values)
sns.scatterplot(x,y)

/opt/anaconda/envs/aiking/lib/python3.9/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

<AxesSubplot:>

../../_images/03_predictive_analytics_30_2.png

Scoring and Out of Sample Prediction#

out = df_outsample.copy()
out['Prob']= model_purchase_incidence.predict(sm.add_constant(df_outsample.copy())) 
out['Monetary'] = np.exp( res2.predict(df_outsample.copy()))
out['Score'] = out['Prob']*out['Monetary']
out.head()

	recency	frequency	avg_purchase_amount	max_purchase_amount	first_purchase	Prob	Monetary	Score
consumer_id
10	3829	1	30.000000	30.0	3829	0.000380	35.048014	0.013326
80	343	7	71.428571	80.0	3751	0.575159	82.558085	47.484052
90	758	10	115.800000	153.0	3783	0.538104	138.426136	74.487670
120	1401	1	20.000000	20.0	1401	0.044037	23.970452	1.055597
130	2970	2	50.000000	60.0	3710	0.002568	60.709281	0.155924

out.describe().T 

	count	mean	std	min	25%	50%	75%	max
recency	18417.0	1253.037900	1081.437868	1.000000	244.000000	1070.000000	2130.000000	4014.000000
frequency	18417.0	2.782375	2.936888	1.000000	1.000000	2.000000	3.000000	45.000000
avg_purchase_amount	18417.0	57.792985	154.360109	5.000000	21.666667	30.000000	50.000000	4500.000000
max_purchase_amount	18417.0	68.756314	194.317960	5.000000	25.000000	30.000000	60.000000	4500.000000
first_purchase	18417.0	1984.009882	1133.405441	1.000000	988.000000	2087.000000	2992.000000	4016.000000
Prob	18417.0	0.224987	0.251136	0.000263	0.012637	0.106187	0.397817	0.999904
Monetary	18417.0	65.632173	147.887338	6.540053	28.999793	35.048014	57.298430	3832.952670
Score	18417.0	18.833654	70.211180	0.003298	0.455815	4.556268	17.957241	2854.156430

Note

Expected revenue for each customer based on score = 18.83

AIBook

Predictive Analytics

Contents

Predictive Analytics#

Imports#

Data Collection and Feature Engineering#

Read Dataset#

Generate Consumer_df Input and Target (Revenue_2015)#

Prepare Training dataset#

Prepare Out of Sample Dataset#

Predictive Models#

Likelihood of Purchase#

Amount of Purchase#

Scoring and Out of Sample Prediction#