Zakka_Canada_CLV.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Your Customers' Lifetime Value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Customer LifeTime Value\n",
    "\n",
    "Lifetimes can be used to analyze our customers based on a few assumption:\n",
    "\n",
    "Customers interact with us when they are “alive”.\n",
    "\n",
    "Customers under study may “die” after some period of time.\n",
    "\n",
    "I’ve quoted “alive” and “die” as these are the most abstract terms (they are used similarly to “birth” and “death” in survival analysis). Whenever we have individuals repeating occurrences, we can use Lifetimes to help understand users behaviour."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specific Application: Customer Lifetime Value\n",
    "As emphasized by P. Fader and B. Hardie, understanding and acting on customer lifetime value (CLV) is the most important part of our business’s sales efforts.\n",
    "\n",
    "Lifetimes is a Python library to calculate CLV. This is what we are doing today: Calculating CLV with Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Susan\\Anaconda3\\lib\\site-packages\\statsmodels\\compat\\pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Susan\n"
     ]
    }
   ],
   "source": [
    "from lifetimes.plotting import *\n",
    "from lifetimes.utils import *\n",
    "from lifetimes.estimation import *\n",
    "import pandas as pd\n",
    "from scipy.stats import beta, gamma, invgamma, norm\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import datetime as dt\n",
    "import warnings\n",
    "from random import uniform \n",
    "from statsmodels.api import OLS\n",
    "import numpy as np\n",
    "warnings.filterwarnings('ignore')\n",
    "%cd\n",
    "sns.set_palette(\"husl\")\n",
    "sns.set(rc={'image.cmap': 'coolwarm'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "trans_data = pd.read_csv('orders.csv')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Customer ID</th>\n",
       "      <th>Date</th>\n",
       "      <th>Subtotal</th>\n",
       "      <th>State</th>\n",
       "      <th>Country</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34</td>\n",
       "      <td>6/21/2007</td>\n",
       "      <td>86.0</td>\n",
       "      <td>ON</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>38</td>\n",
       "      <td>6/27/2007</td>\n",
       "      <td>38.4</td>\n",
       "      <td>ON</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>47</td>\n",
       "      <td>7/2/2007</td>\n",
       "      <td>53.5</td>\n",
       "      <td>MO</td>\n",
       "      <td>United States</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>61</td>\n",
       "      <td>7/14/2007</td>\n",
       "      <td>7.0</td>\n",
       "      <td>ON</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>78</td>\n",
       "      <td>7/21/2007</td>\n",
       "      <td>55.5</td>\n",
       "      <td>ON</td>\n",
       "      <td>Canada</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Customer ID       Date  Subtotal State        Country\n",
       "0           34  6/21/2007      86.0    ON         Canada\n",
       "1           38  6/27/2007      38.4    ON         Canada\n",
       "2           47   7/2/2007      53.5    MO  United States\n",
       "3           61  7/14/2007       7.0    ON         Canada\n",
       "4           78  7/21/2007      55.5    ON         Canada"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Customer ID      int64\n",
       "Date            object\n",
       "Subtotal       float64\n",
       "State           object\n",
       "Country         object\n",
       "dtype: object"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Entries: 22408\n"
     ]
    }
   ],
   "source": [
    "trans_data['Date'] = pd.to_datetime(trans_data['Date'])\n",
    "print('Number of Entries: %s' % len(trans_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Customer ID             int64\n",
       "Date           datetime64[ns]\n",
       "Subtotal              float64\n",
       "State                  object\n",
       "Country                object\n",
       "dtype: object"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2007-06-21 00:00:00')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data['Date'].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2015-12-19 00:00:00')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data['Date'].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>frequency</th>\n",
       "      <th>recency</th>\n",
       "      <th>T</th>\n",
       "      <th>monetary_value</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Customer ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2.0</td>\n",
       "      <td>794.0</td>\n",
       "      <td>1117.0</td>\n",
       "      <td>7.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3062.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3037.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3115.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3109.0</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             frequency  recency       T  monetary_value\n",
       "Customer ID                                            \n",
       "7                  2.0    794.0  1117.0            7.57\n",
       "9                  0.0      0.0  3062.0            0.00\n",
       "30                 0.0      0.0  3037.0            0.00\n",
       "34                 0.0      0.0  3115.0            0.00\n",
       "38                 0.0      0.0  3109.0            0.00"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = summary_data_from_transaction_data(trans_data, 'Customer ID', 'Date', monetary_value_col='Subtotal', observation_period_end='2015-12-31')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Frequency represents the number of repeat purchases the customer has made. This means that it's one less than the total number of purchases. \n",
    "\n",
    "* T represents the age of the customer in whatever time units chosen (daily, in the above dataset). This is equal to the duration between a customer's first purchase and the end of the period under study.\n",
    "\n",
    "* Recency represents the age of the customer when they made their most recent purchases. This is equal to the duration between a customer's first purchase and their latest purchase. (Thus if they have made only 1 purchase, the recency is 0.)\n",
    "\n",
    "The unit of time is in days in our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    3498.000000\n",
      "mean        2.605489\n",
      "std         2.996117\n",
      "min         1.000000\n",
      "25%         1.000000\n",
      "50%         1.000000\n",
      "75%         3.000000\n",
      "max        43.000000\n",
      "Name: frequency, dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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+FhH/CbwxIr4CjAAX9rlOSVr0+hoQmfkk8HuFXWdOG3cE+MO+FCVJKvJGOUlSkQEhSSoy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\nkor+H/Y+yPRKtiFoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166bcfa5390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[data['frequency'] > 0]['frequency'].plot(kind='hist', bins=20)\n",
    "print(data[data['frequency'] > 0]['frequency'].describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.727336503235\n"
     ]
    }
   ],
   "source": [
    "print(sum(data['frequency'] == 0)/float(len(data)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most customers are one time buyers, that is 72.7% of customers only make one purchase. Below we look at their recency distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.727336503235\n",
      "count    3498.000000\n",
      "mean      441.194969\n",
      "std       511.513487\n",
      "min         1.000000\n",
      "25%        55.000000\n",
      "50%       245.500000\n",
      "75%       661.000000\n",
      "max      2923.000000\n",
      "Name: recency, dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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mm4t+en1J6gxgIiJOAo4CPgM8uu3zEeA+YHu9vPd4R9u27ZjbSgfA2Nh4x89arZFpPx80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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166bd4ec3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data[data['recency'] != 0]['recency'].plot(kind='hist', bins=20)\n",
    "print(sum(data['recency'] == 0)/float(len(data)))\n",
    "print(data[data['recency'] != 0]['recency'].describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Customers that have a frequency of zero (customers that have not made repeat purchases) also have a recency of zero so we isolate for repeat customer only. Considering the analysis ranges within a span of eight years, having 50% of your customer churn before a year (245) is even up and 75% of your customers churn before two years (661) should be a concern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<lifetimes.BetaGeoFitter: fitted with 12829 subjects, a: 1.31, alpha: 25.33, b: 1.96, r: 0.09>\n"
     ]
    }
   ],
   "source": [
    "bgf = BetaGeoFitter(penalizer_coef=0.0)\n",
    "bgf.fit(data['frequency'], data['recency'], data['T'], )\n",
    "print(bgf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting the BG/NBD Model\n",
    "In quick summary, the BG/NBD model assumes that each customer makes repeat purchases at different intervals. This interval between purchases is modeled by an exponential distribution with a transaction rate $\\lambda$. Furthermore, after each transaction, the customer has a $p%$ chance of going inactive (or dying) which is modelled by a shifted Geometric distribution. These two major parameters are further refined for heterogenity across customers through a Gamma distribution for $\\lambda$ and a Beta distribution for $p$. Thus we have four total parameters $r$, $\\alpha$ (gamma distro) and $a$, $b$ (Beta distro) estimated below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.02)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yherlbL69V7Wcq5ZvL/Tj7xw9CNSOzisaDjiSJPWf45QkCehPcXQL8DyAci33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\nSZIAiyNJkiRJAiyOJEmSJAmA/w9eVtA/kxbfcQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166bd1a3a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gbd = beta.rvs(bgf.params_['a'], bgf.params_['b'], size = 50000)\n",
    "ggd = gamma.rvs(bgf.params_['r'], scale=1./bgf.params_['alpha'], size = 50000)\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.subplot(121)\n",
    "plt.title('Heterogenity of $p$')\n",
    "temp = plt.hist(gbd, 20, facecolor='pink', alpha=0.75)\n",
    "plt.subplot(122)\n",
    "plt.title('Heterogenity of $\\lambda$')\n",
    "temp = plt.hist(ggd, 500, facecolor='pink', alpha=0.75)\n",
    "plt.xlim(0.0,0.02)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since everything goes back to the two major parameters, we can use our heterogenity parameters to model the uncertainty in the two. As shown above, the probability of a customer dropping out has a large range but mostly centered between 15% to 60% after a certain transaction. On the other hand, our customer transaction rate falls mostly within 0 and 0.01."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fact Checking\n",
    "Peter Fader in his Youtube talk on CLV provides four simple plots to illustrate the accuracy of the model and its associated behavioral story when applied to real data sets. I will replicate two of them below on our data to ensure that the model is indeed a good fit for our customers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x166beee5cf8>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hBkhHHPmMIZ8J4hxgorsPMbO2wBSgSdb75cCnwNL4d9Xy1Qll1Vq8+Iu6iLlGhRp3pb6M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\nIomUIEREJNH/A3aLmzpEmFPQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166bee65a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_period_transactions(bgf, max_frequency=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After fitting the BG/NBD model, we can fact check through looking at the fitted repeat purchase for the entire customer database. Above plots the Actual repeat purchase frequency versus the Model repeat purchase frequency. As shown, the model performs relatively well in fitting the repeat purchase pattern. It overestimates one and six repeat purchases while underestimating three repeat purchases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2007-06-21 00:00:00')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data['Date'].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2015-12-19 00:00:00')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data['Date'].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x166bf0652b0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zBfMOLMLF5MKTox7AzxzkaEnEyxPIQwUMiA4xdH5DhiBGCLGuvm0p5Zgz1KhQ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\nfwD8SWdTegvTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166bf1379b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary_cal_holdout = calibration_and_holdout_data(trans_data, 'Customer ID', 'Date', \n",
    "                                        calibration_period_end='2015-01-01',\n",
    "                                        observation_period_end='2015-12-19' )   \n",
    "bgf.fit(summary_cal_holdout['frequency_cal'], summary_cal_holdout['recency_cal'], summary_cal_holdout['T_cal'])\n",
    "plot_calibration_purchases_vs_holdout_purchases(bgf, summary_cal_holdout, n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can further validate our model by checking for presence of overfitting. Separating our dataset into two sets: training (2007- 2014 end) and test (2015), we can fit our model with training and see how well it forecasts our customer's out of sample purchasing habit. The plot above shows our fitted model prediction (green) versus our out of sample repeat purchase frequency (blue). Each tick on the x-axis is composed of customers that have been grouped such that they have had $x$ repeat purchases. the Y axis shows the mean of that group's subsequent repeat purchase. For example, for all customers within our training period that have had 4 repeat purchases, the same group had on average about 0.42 purchases and the model predicted the same as well. From this plot, we can see that the model performs relatively well in identifying repeat purchases within the lower ranges (less than 6) but is unable to properly forecast buying behaviors of customers with more frequent purchasing habits."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R/F Matrix Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x166bef71780>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WAt6vqtcXuH/HcSYZ9crknZRKm1KPuZg6jtMpk/mZUjNEZAtCssCy8fWSb0NV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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166befb03c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_frequency_recency_matrix(bgf, T=365)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that if a customer has bought 30 times from us, and their latest purchase was when they were 2500 days old (given the individual is 2500 days old), then they are your best customer (bottom-right). Our coldest customers are those that are in the top-right corner: they bought a lot quickly, and we haven't seen them in ages.\n",
    "\n",
    "There's also that beautiful \"tail\" around (10,2000). That represents the customer who buys infrequently, but we've seen him or her recently, so they might buy again - we're not sure if they are dead or just between purchases.\n",
    "\n",
    "Another interesting matrix to look at is the probability of still being alive:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a given random customer with his/her observed $(x,t_x)$, we can calculate the probability as of today that they are still alive. In other words, are they still interested in maintaining a purchasing relationship with our company in the future? According to the model, it's very likely as long as they bought recently. Even if they only bought once, they have about a 60-70% chance that they will buy again in the future. Customers that are considered dead are usually ones that haven't made an order in a while."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x166befedb38>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pepbrnAQukYhm4MYMW4jIDri1Bk7CFWx4MXCwqv6sz33rC+HcZGvmuHO7buMM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\nSCSAJIaJRCIBwP8HeddpVr58SJQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166bee8e128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_probability_alive_matrix(bgf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is interesting to note that for a given recency, customer's with more frequency are more likely to be considered dead. This is a property of the model that illustrates a clear behavioral story: If we observe customers making more frequent purchases, then having a prolonged period of inactivity makes it very likely that they've died off. For example, Two customers $A$ and $B$ that both last purchased 1.5 years ago ($t_x\\approx 2700$) but purchased 10 and 30 times respectively. We believe that it is more likely that customer B has died ($p=0.0$) while customer A still has a fair chance of being alive and making purchases in the future ($p\\approx 0.4$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analyzing Customer's Historical Path\n",
    "One last plot that was developed in lifetimes allows us to fully appreciate the model at a granular customer-base level. Indeed, we can observe each of our customer's historical purchasing path and measure our confidence that they have not dropped out in between purchases. To get a small and relevant subsample, I will let the bgf model create projections for the next month purchasing pattern of my entire current customer-base and pick out 6 of my best customers. As shown, our best customers that are projected to make more future repeat purchases are often our newest ones. This makes sense since the model has revealed to us before that our customer base has a tendency to drop off after a short period of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             frequency  recency      T  monetary_value  predicted_purchases\n",
      "Customer ID                                                                \n",
      "10920             19.0    757.0  801.0       61.354211             0.593734\n",
      "13527             11.0    318.0  348.0      103.427273             0.693523\n",
      "14008              9.0    242.0  261.0      124.136667             0.749611\n",
      "12780             14.0    445.0  461.0      110.073571             0.761943\n",
      "13577             12.0    247.0  275.0       55.782500             0.893935\n",
      "14263             17.0    198.0  219.0      323.521176             1.521947\n"
     ]
    }
   ],
   "source": [
    "t = 31\n",
    "data['predicted_purchases'] = bgf.conditional_expected_number_of_purchases_up_to_time(t, data['frequency'], data['recency'], data['T'])\n",
    "best_projected_cust = data.sort_values('predicted_purchases').tail(6)\n",
    "print(data.sort_values('predicted_purchases').tail(6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we can plot these six individuals over the course of their lifetime to observe their purchasing behavior. Among these top 6 customers, they are sorted by expected future purchases ascendingly. Adding a one month cushion, we can infer the probability that these customers are alive or dead if we have not seen them purchase by the end of the month. For example, for customer $\\tt{14263}$ with a short life-time but very recent purchases, we expect him/her to return and buy at-leasts once during the month of January. If however, we don't see this person make an order by the middle of Jan 2016, there is a good chance that they're dead.\n",
    "\n",
    "Looking at the overall picture, there's not much pattern that can be generalized across all 6 individuals but we can identify certain seasonal behaviors for certain people, for example:\n",
    "\n",
    "Customer $\\tt{13577}$ tends to buy at an equal interval with the exception between September 2015 and Nov 2015.\n",
    "Customers $\\tt{12780}$,  $\\tt{13527}$ and $\\tt{10920}$ tends to buy during the early stage of their life-cycle and then repeat at a much slower interval\n",
    "Customer $\\tt{14008}$ first bought at a slower interval but increased his/her frequency over time. We can reasonably assume that they started bying more as their business expanded and became more successful."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Customer Probability Histories\n",
    "Given a customer transaction history, we can calculate their historical probability of being alive, according to our trained model. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x166bf44c198>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JqeS/qJkOW6/ZO84A5SUB3vySNiamwtz/2FkP70QIIYRY+grm5MCxD36IdM9v2icHjr/5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\nxs1qBZNTYY6dG3B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1l/tGGbgx6WzwoWH0/tTj1VYW09RQxsmuQSajZensHefgyWOOhsl0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\niIjEQQNnEREREZE4aOAsIiIiIhKH/w/EJ3+YBS4/8gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166bf4662b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,6))\n",
    "id = 13577\n",
    "days_since_birth = 801\n",
    "sp_trans = trans_data.loc[trans_data['Customer ID'] == id]\n",
    "plot_history_alive(bgf, days_since_birth, sp_trans, 'Date')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x166bf4e0048>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qXPXMthLIY9Q0f0E4vkAzcuzeao5O4AVlEaXnrlI6OtV9Q/Mt0CpnTVfcM0UM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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166bf4e00b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,6))\n",
    "id = 14008\n",
    "days_since_birth = 261\n",
    "sp_trans = trans_data.loc[trans_data['Customer ID'] == id]\n",
    "plot_history_alive(bgf, days_since_birth, sp_trans, 'Date')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x166bf34fe80>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RIhxcVdVYghxVHNK9FU/eNpSCNuks2niIZ99YxeEy+cpaeOgj4bZ9u8NetqJY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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x166bf5dc470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,6))\n",
    "id = 13527\n",
    "days_since_birth = 275\n",
    "sp_trans = trans_data.loc[trans_data['Customer ID'] == id]\n",
    "plot_history_alive(bgf, days_since_birth, sp_trans, 'Date')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Customer Value in Dollars: The Gamma-Gamma Model\n",
    "In a traditional RFM matrix, each customer can be assigned a monetary value with his or her customer profile. This value is usually calculated as the mean transaction value of his or her purchasing history. Transaction value is a loosely based word around any metric that the business might be interested in. Zakka Canada reports an average profit margin of 55%, I will multiply that by the revenue. Note that we are only interested in customers that have repeat purchases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             frequency  recency       T  monetary_value  predicted_purchases\n",
      "Customer ID                                                                 \n",
      "7                  2.0    794.0  1117.0           7.570             0.030012\n",
      "64                 1.0    772.0  3037.0         131.190             0.002833\n",
      "101                1.0     38.0  2348.0          34.860             0.000410\n",
      "115                6.0   2593.0  3016.0         144.915             0.042516\n",
      "129                1.0    736.0  3041.0          14.520             0.002722\n"
     ]
    }
   ],
   "source": [
    "returning_customers_summary = data[data['frequency']>0]\n",
    "print(returning_customers_summary.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Gamma-Gamma model and the independence assumption\n",
    "The model we are going to use to estimate the CLV for our userbase is called the Gamma-Gamma submodel, which relies upon an important assumption. The Gamma-Gamma submodel, in fact, assumes that there is no relationship between the monetary value and the purchase frequency. In practice we need to check whether the Pearson correlation between the two vectors is close to 0 in order to use this model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>monetary_value</th>\n",
       "      <th>frequency</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>monetary_value</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.065976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>frequency</th>\n",
       "      <td>0.065976</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                monetary_value  frequency\n",
       "monetary_value        1.000000   0.065976\n",
       "frequency             0.065976   1.000000"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returning_customers_summary[['monetary_value', 'frequency']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point we can train our Gamma-Gamma submodel and predict the conditional, expected average lifetime value of our customers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<lifetimes.GammaGammaFitter: fitted with 3498 subjects, p: 2.66, q: 3.06, v: 72.63>\n"
     ]
    }
   ],
   "source": [
    "ggf = GammaGammaFitter(penalizer_coef = 0)\n",
    "ggf.fit(returning_customers_summary['frequency'],\n",
    "        returning_customers_summary['monetary_value'])\n",
    "print(ggf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now estimate the average transaction value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Customer ID\n",
      "7     31.633017\n",
      "9     93.759145\n",
      "30    93.759145\n",
      "34    93.759145\n",
      "38    93.759145\n",
      "41    93.759145\n",
      "47    93.759145\n",
      "48    93.759145\n",
      "53    93.759145\n",
      "61    93.759145\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(ggf.conditional_expected_average_profit(\n",
    "        data['frequency'],\n",
    "        data['monetary_value']\n",
    "    ).head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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