clv-bq-2.ipynb

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This document walks through how to do Customer Lifetime Value (CLV) analysis\n",
      "using [BigQuery Export for Google Analytics](https://support.google.com/analytics/answer/3437618?hl=en). "
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Intro"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to follow this guide and execute all of the code using your own data, you need the following:\n",
      "\n",
      "  1. Access to [BigQuery Export for Google Analytics](https://support.google.com/analytics/answer/3437618) \n",
      "  2. Ecommerce or another conversion activity being tracked\n",
      "  3. Data for at least a few months\n",
      "\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Outline"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This article will use BigQuery Export to calculate Customer Lifetime Value and\n",
      "some related metrics by completing the following steps:\n",
      "\n",
      "  1. Query BigQuery to extract the data needed\n",
      "  2. Import this data into R \n",
      "  3. Use the data to build a model that forecasts CLV and related metrics for each customer:\n",
      "     * Customer Lifetime Value\n",
      "     * Expected transactions\n",
      "     * Expected spend per transaction\n",
      "     * The probability that a given customer is still active\n",
      "  4. Import the CLV calculations back into BigQuery\n",
      "  5. Analyze the CLV calculations using BigQuery\n",
      "\n",
      "This article will outline each of these steps."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "CLV"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Customer Lifetime Value is is the dollar amount of money that an individual\n",
      "customer will spend with a given business in the future. It is often used to:\n",
      "\n",
      "  * Value segments or all of your customer base \n",
      "  * Decide how much to spend acquiring new customers in a given segment\n",
      "  * Decide how much to spend retaining certain customers \n",
      "  * Rank customers\n",
      "  * Measure success of marketing action based upon baseline CLV forecast\n",
      "\n",
      "Additionally, the probability that a customer is active is used to:\n",
      "\n",
      "  * Determine size of active customer base\n",
      "  * Identify customers who are on the brink of becoming inactive and take action\n",
      "\n",
      "Taken together, a strong model of user behavior serves as the foundation for\n",
      "many marketing activities and measurement.\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Talk about the model\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Big Query"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, you need to extract the data from BigQuery. The following `gcp.bigquery` import makes the BigQuery functionality available to this notebook. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import gcp\n",
      "import gcp.bigquery as bq"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 778
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As long as you are using Ecommerce tracking or Goals, all of the data needed to\n",
      "calculate CLV is available via BigQuery Export. \n",
      "\n",
      "This query extracts the date, number of transactions, and transaction revenue\n",
      "for all transactions among first time visitors in a given date range (i.e. a cohort).\n",
      "\n",
      "The query below is customized as follows. Modify to suit your business. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class Column(object):\n",
      "    def __init__(self, name):\n",
      "        self._name = name\n",
      "    def _repr_sql_(self):\n",
      "        return self._name\n",
      "\n",
      "\n",
      "ga_view_id = 33324909\n",
      "#ga_view_id = 44956929\n",
      "#ga_view_id = 62092124\n",
      "# starting November 12, 2014\n",
      "#ga_view_id = 89571105 \n",
      "visitor_id = Column('fullVisitorId')\n",
      "conversion = Column('totals.transactions')\n",
      "conversion_revenue = Column('totals.transactionRevenue')\n",
      "start_date = '2014-01-01'\n",
      "end_date = '2014-08-01'\n",
      "cohort_end_date = '2014-03-31'\n",
      "end_of_cal_period = '2014-05-01'\n",
      "sampling_rate = Column('1/50')\n",
      "join_each_used = Column('') # if needed set this to 'EACH' rename to use_join_each"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 779
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that all of the input values needed have been specified, run the query below to view the raw data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%bq_sql event_log_query\n",
      "SELECT\n",
      "  *\n",
      "FROM\n",
      "  (\n",
      "  SELECT\n",
      "    date,\n",
      "    $visitor_id,\n",
      "    $conversion_revenue,\n",
      "    $conversion,\n",
      "  FROM\n",
      "    TABLE_DATE_RANGE([941929509095:$ga_view_id.ga_sessions_],\n",
      "      TIMESTAMP($start_date),\n",
      "      TIMESTAMP($end_date))\n",
      "  WHERE\n",
      "    $conversion IS NOT NULL\n",
      "    ) a\n",
      "JOIN\n",
      "  EACH\n",
      "  (\n",
      "  SELECT\n",
      "    $visitor_id\n",
      "  FROM\n",
      "    TABLE_DATE_RANGE([941929509095:$ga_view_id.ga_sessions_],\n",
      "      TIMESTAMP($start_date),\n",
      "      TIMESTAMP($cohort_end_date))\n",
      "  WHERE\n",
      "    totals.newVisits IS NOT NULL\n",
      "    AND RAND() < $sampling_rate\n",
      "  GROUP BY\n",
      "    1\n",
      "    ) b\n",
      "ON\n",
      "  a.$visitor_id=b.$visitor_id\n",
      "ORDER BY\n",
      "  date"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 780
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print event_log_query.sql"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "SELECT\n",
        "  *\n",
        "FROM\n",
        "  (\n",
        "  SELECT\n",
        "    date,\n",
        "    fullVisitorId,\n",
        "    totals.transactionRevenue,\n",
        "    totals.transactions,\n",
        "  FROM\n",
        "    TABLE_DATE_RANGE([941929509095:33324909.ga_sessions_],\n",
        "      TIMESTAMP(\"2014-01-01\"),\n",
        "      TIMESTAMP(\"2014-08-01\"))\n",
        "  WHERE\n",
        "    totals.transactions IS NOT NULL\n",
        "    ) a\n",
        "JOIN\n",
        "  EACH\n",
        "  (\n",
        "  SELECT\n",
        "    fullVisitorId\n",
        "  FROM\n",
        "    TABLE_DATE_RANGE([941929509095:33324909.ga_sessions_],\n",
        "      TIMESTAMP(\"2014-01-01\"),\n",
        "      TIMESTAMP(\"2014-03-31\"))\n",
        "  WHERE\n",
        "    totals.newVisits IS NOT NULL\n",
        "    AND RAND() < 1/50\n",
        "  GROUP BY\n",
        "    1\n",
        "    ) b\n",
        "ON\n",
        "  a.fullVisitorId=b.fullVisitorId\n",
        "ORDER BY\n",
        "  date\n"
       ]
      }
     ],
     "prompt_number": 781
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "event_log_data = event_log_query.results()\n",
      "event_log_data.to_dataframe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>a_date</th>\n",
        "      <th>a_fullVisitorId</th>\n",
        "      <th>a_totals_transactionRevenue</th>\n",
        "      <th>a_totals_transactions</th>\n",
        "      <th>b_fullVisitorId</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 4390204632354546178</td>\n",
        "      <td>  209000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 4390204632354546178</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 1925554275363355376</td>\n",
        "      <td>   29000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 1925554275363355376</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 1661204767780881402</td>\n",
        "      <td>   49000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 1661204767780881402</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 3314683506482981451</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 3314683506482981451</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 6246694908791653438</td>\n",
        "      <td>   10000000</td>\n",
        "      <td>  3</td>\n",
        "      <td> 6246694908791653438</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 4528809343029884946</td>\n",
        "      <td>    2000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 4528809343029884946</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 5788301282741864766</td>\n",
        "      <td>    9000000</td>\n",
        "      <td> 12</td>\n",
        "      <td> 5788301282741864766</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 4981226745425029372</td>\n",
        "      <td>  150000000</td>\n",
        "      <td>  2</td>\n",
        "      <td> 4981226745425029372</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7053120811556958333</td>\n",
        "      <td>   50000000</td>\n",
        "      <td>  3</td>\n",
        "      <td> 7053120811556958333</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9    </th>\n",
        "      <td> 20140101</td>\n",
        "      <td>  712193355312038720</td>\n",
        "      <td>  120000000</td>\n",
        "      <td>  1</td>\n",
        "      <td>  712193355312038720</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2600032258725151578</td>\n",
        "      <td>  100000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 2600032258725151578</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>11   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2600032258725151578</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  2</td>\n",
        "      <td> 2600032258725151578</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>12   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2894583065807656887</td>\n",
        "      <td>   11000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 2894583065807656887</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2240912931971950543</td>\n",
        "      <td>   10000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 2240912931971950543</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>14   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2383435765215606382</td>\n",
        "      <td>   42000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 2383435765215606382</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>15   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 5513514386154886922</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 5513514386154886922</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>16   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 5904823728302470158</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 5904823728302470158</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>17   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 8210607896464213692</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  3</td>\n",
        "      <td> 8210607896464213692</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>18   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2918635651471797859</td>\n",
        "      <td>   50000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 2918635651471797859</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>19   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7198838795528318052</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  3</td>\n",
        "      <td> 7198838795528318052</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>20   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 7124770074464060753</td>\n",
        "      <td>  274000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 7124770074464060753</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>21   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 6235990673468969254</td>\n",
        "      <td>  300000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 6235990673468969254</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>22   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2430023451571139127</td>\n",
        "      <td>   49000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 2430023451571139127</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>23   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 2430023451571139127</td>\n",
        "      <td>   49000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 2430023451571139127</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>24   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 4278554797126442565</td>\n",
        "      <td>   95000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 4278554797126442565</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>25   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 1356238463146260984</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 1356238463146260984</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>26   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 1356238463146260984</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 1356238463146260984</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>27   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 1356238463146260984</td>\n",
        "      <td>    9000000</td>\n",
        "      <td>  2</td>\n",
        "      <td> 1356238463146260984</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>28   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 1089480363657252762</td>\n",
        "      <td>  150000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 1089480363657252762</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>29   </th>\n",
        "      <td> 20140101</td>\n",
        "      <td> 3500550647146289639</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>  5</td>\n",
        "      <td> 3500550647146289639</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>...</th>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "      <td>...</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36746</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 7974921102243799580</td>\n",
        "      <td>   29000000</td>\n",
        "      <td>  4</td>\n",
        "      <td> 7974921102243799580</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36747</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 7223049079504258820</td>\n",
        "      <td>    5000000</td>\n",
        "      <td> 26</td>\n",
        "      <td> 7223049079504258820</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36748</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 2414677627914487037</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  3</td>\n",
        "      <td> 2414677627914487037</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36749</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 2414677627914487037</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  4</td>\n",
        "      <td> 2414677627914487037</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36750</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 2275133556355591567</td>\n",
        "      <td>   23000000</td>\n",
        "      <td>  2</td>\n",
        "      <td> 2275133556355591567</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36751</th>\n",
        "      <td> 20140801</td>\n",
        "      <td>  956757688014107651</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  1</td>\n",
        "      <td>  956757688014107651</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36752</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 7924160185129858602</td>\n",
        "      <td>   85000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 7924160185129858602</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36753</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 4159965531704345167</td>\n",
        "      <td>   30000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 4159965531704345167</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36754</th>\n",
        "      <td> 20140801</td>\n",
        "      <td>  936956127853095065</td>\n",
        "      <td>   50000000</td>\n",
        "      <td> 13</td>\n",
        "      <td>  936956127853095065</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36755</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 8007633402827607377</td>\n",
        "      <td>  149000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 8007633402827607377</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36756</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 3035404327511294471</td>\n",
        "      <td>   25000000</td>\n",
        "      <td>  2</td>\n",
        "      <td> 3035404327511294471</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36757</th>\n",
        "      <td> 20140801</td>\n",
        "      <td>  539489962973275401</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  1</td>\n",
        "      <td>  539489962973275401</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36758</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 8815280961792256419</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 8815280961792256419</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36759</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 4959531091796375576</td>\n",
        "      <td>   15000000</td>\n",
        "      <td>  6</td>\n",
        "      <td> 4959531091796375576</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36760</th>\n",
        "      <td> 20140801</td>\n",
        "      <td>  450919499585616536</td>\n",
        "      <td>  295000000</td>\n",
        "      <td>  2</td>\n",
        "      <td>  450919499585616536</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36761</th>\n",
        "      <td> 20140801</td>\n",
        "      <td>  450919499585616536</td>\n",
        "      <td> 1195000000</td>\n",
        "      <td>  5</td>\n",
        "      <td>  450919499585616536</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36762</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 6966590341660554091</td>\n",
        "      <td>    5000000</td>\n",
        "      <td> 19</td>\n",
        "      <td> 6966590341660554091</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36763</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 2383435765215606382</td>\n",
        "      <td>   19000000</td>\n",
        "      <td>  3</td>\n",
        "      <td> 2383435765215606382</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36764</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 2541633721563166375</td>\n",
        "      <td>   20000000</td>\n",
        "      <td>  2</td>\n",
        "      <td> 2541633721563166375</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36765</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 8396930690236546384</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>  2</td>\n",
        "      <td> 8396930690236546384</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36766</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 6783144342759410206</td>\n",
        "      <td>    2000000</td>\n",
        "      <td>  2</td>\n",
        "      <td> 6783144342759410206</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36767</th>\n",
        "      <td> 20140801</td>\n",
        "      <td>  333967449900570709</td>\n",
        "      <td>  800000000</td>\n",
        "      <td>  1</td>\n",
        "      <td>  333967449900570709</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36768</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 6626843426231554433</td>\n",
        "      <td>   10000000</td>\n",
        "      <td>  3</td>\n",
        "      <td> 6626843426231554433</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36769</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 7067929321916772755</td>\n",
        "      <td>   45000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 7067929321916772755</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36770</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 9195959014345857667</td>\n",
        "      <td>   17000000</td>\n",
        "      <td>  3</td>\n",
        "      <td> 9195959014345857667</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36771</th>\n",
        "      <td> 20140801</td>\n",
        "      <td>  333695226298598368</td>\n",
        "      <td>    5000000</td>\n",
        "      <td>  1</td>\n",
        "      <td>  333695226298598368</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36772</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 2122663303946501958</td>\n",
        "      <td>   50000000</td>\n",
        "      <td>  1</td>\n",
        "      <td> 2122663303946501958</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36773</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 7418347238222743936</td>\n",
        "      <td>    2000000</td>\n",
        "      <td>  2</td>\n",
        "      <td> 7418347238222743936</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36774</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 7418347238222743936</td>\n",
        "      <td>    2000000</td>\n",
        "      <td>  4</td>\n",
        "      <td> 7418347238222743936</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>36775</th>\n",
        "      <td> 20140801</td>\n",
        "      <td> 7418347238222743936</td>\n",
        "      <td>    1000000</td>\n",
        "      <td>  4</td>\n",
        "      <td> 7418347238222743936</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>36776 rows \u00d7 5 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 782,
       "text": [
        "         a_date      a_fullVisitorId  a_totals_transactionRevenue  \\\n",
        "0      20140101  4390204632354546178                    209000000   \n",
        "1      20140101  1925554275363355376                     29000000   \n",
        "2      20140101  1661204767780881402                     49000000   \n",
        "3      20140101  3314683506482981451                      5000000   \n",
        "4      20140101  6246694908791653438                     10000000   \n",
        "5      20140101  4528809343029884946                      2000000   \n",
        "6      20140101  5788301282741864766                      9000000   \n",
        "7      20140101  4981226745425029372                    150000000   \n",
        "8      20140101  7053120811556958333                     50000000   \n",
        "9      20140101   712193355312038720                    120000000   \n",
        "10     20140101  2600032258725151578                    100000000   \n",
        "11     20140101  2600032258725151578                      1000000   \n",
        "12     20140101  2894583065807656887                     11000000   \n",
        "13     20140101  2240912931971950543                     10000000   \n",
        "14     20140101  2383435765215606382                     42000000   \n",
        "15     20140101  5513514386154886922                      5000000   \n",
        "16     20140101  5904823728302470158                      5000000   \n",
        "17     20140101  8210607896464213692                      1000000   \n",
        "18     20140101  2918635651471797859                     50000000   \n",
        "19     20140101  7198838795528318052                      1000000   \n",
        "20     20140101  7124770074464060753                    274000000   \n",
        "21     20140101  6235990673468969254                    300000000   \n",
        "22     20140101  2430023451571139127                     49000000   \n",
        "23     20140101  2430023451571139127                     49000000   \n",
        "24     20140101  4278554797126442565                     95000000   \n",
        "25     20140101  1356238463146260984                      1000000   \n",
        "26     20140101  1356238463146260984                      1000000   \n",
        "27     20140101  1356238463146260984                      9000000   \n",
        "28     20140101  1089480363657252762                    150000000   \n",
        "29     20140101  3500550647146289639                      5000000   \n",
        "...         ...                  ...                          ...   \n",
        "36746  20140801  7974921102243799580                     29000000   \n",
        "36747  20140801  7223049079504258820                      5000000   \n",
        "36748  20140801  2414677627914487037                      1000000   \n",
        "36749  20140801  2414677627914487037                      1000000   \n",
        "36750  20140801  2275133556355591567                     23000000   \n",
        "36751  20140801   956757688014107651                      1000000   \n",
        "36752  20140801  7924160185129858602                     85000000   \n",
        "36753  20140801  4159965531704345167                     30000000   \n",
        "36754  20140801   936956127853095065                     50000000   \n",
        "36755  20140801  8007633402827607377                    149000000   \n",
        "36756  20140801  3035404327511294471                     25000000   \n",
        "36757  20140801   539489962973275401                      1000000   \n",
        "36758  20140801  8815280961792256419                      1000000   \n",
        "36759  20140801  4959531091796375576                     15000000   \n",
        "36760  20140801   450919499585616536                    295000000   \n",
        "36761  20140801   450919499585616536                   1195000000   \n",
        "36762  20140801  6966590341660554091                      5000000   \n",
        "36763  20140801  2383435765215606382                     19000000   \n",
        "36764  20140801  2541633721563166375                     20000000   \n",
        "36765  20140801  8396930690236546384                      5000000   \n",
        "36766  20140801  6783144342759410206                      2000000   \n",
        "36767  20140801   333967449900570709                    800000000   \n",
        "36768  20140801  6626843426231554433                     10000000   \n",
        "36769  20140801  7067929321916772755                     45000000   \n",
        "36770  20140801  9195959014345857667                     17000000   \n",
        "36771  20140801   333695226298598368                      5000000   \n",
        "36772  20140801  2122663303946501958                     50000000   \n",
        "36773  20140801  7418347238222743936                      2000000   \n",
        "36774  20140801  7418347238222743936                      2000000   \n",
        "36775  20140801  7418347238222743936                      1000000   \n",
        "\n",
        "       a_totals_transactions      b_fullVisitorId  \n",
        "0                          1  4390204632354546178  \n",
        "1                          1  1925554275363355376  \n",
        "2                          1  1661204767780881402  \n",
        "3                          1  3314683506482981451  \n",
        "4                          3  6246694908791653438  \n",
        "5                          1  4528809343029884946  \n",
        "6                         12  5788301282741864766  \n",
        "7                          2  4981226745425029372  \n",
        "8                          3  7053120811556958333  \n",
        "9                          1   712193355312038720  \n",
        "10                         1  2600032258725151578  \n",
        "11                         2  2600032258725151578  \n",
        "12                         1  2894583065807656887  \n",
        "13                         1  2240912931971950543  \n",
        "14                         1  2383435765215606382  \n",
        "15                         1  5513514386154886922  \n",
        "16                         1  5904823728302470158  \n",
        "17                         3  8210607896464213692  \n",
        "18                         1  2918635651471797859  \n",
        "19                         3  7198838795528318052  \n",
        "20                         1  7124770074464060753  \n",
        "21                         1  6235990673468969254  \n",
        "22                         1  2430023451571139127  \n",
        "23                         1  2430023451571139127  \n",
        "24                         1  4278554797126442565  \n",
        "25                         1  1356238463146260984  \n",
        "26                         1  1356238463146260984  \n",
        "27                         2  1356238463146260984  \n",
        "28                         1  1089480363657252762  \n",
        "29                         5  3500550647146289639  \n",
        "...                      ...                  ...  \n",
        "36746                      4  7974921102243799580  \n",
        "36747                     26  7223049079504258820  \n",
        "36748                      3  2414677627914487037  \n",
        "36749                      4  2414677627914487037  \n",
        "36750                      2  2275133556355591567  \n",
        "36751                      1   956757688014107651  \n",
        "36752                      1  7924160185129858602  \n",
        "36753                      1  4159965531704345167  \n",
        "36754                     13   936956127853095065  \n",
        "36755                      1  8007633402827607377  \n",
        "36756                      2  3035404327511294471  \n",
        "36757                      1   539489962973275401  \n",
        "36758                      1  8815280961792256419  \n",
        "36759                      6  4959531091796375576  \n",
        "36760                      2   450919499585616536  \n",
        "36761                      5   450919499585616536  \n",
        "36762                     19  6966590341660554091  \n",
        "36763                      3  2383435765215606382  \n",
        "36764                      2  2541633721563166375  \n",
        "36765                      2  8396930690236546384  \n",
        "36766                      2  6783144342759410206  \n",
        "36767                      1   333967449900570709  \n",
        "36768                      3  6626843426231554433  \n",
        "36769                      1  7067929321916772755  \n",
        "36770                      3  9195959014345857667  \n",
        "36771                      1   333695226298598368  \n",
        "36772                      1  2122663303946501958  \n",
        "36773                      2  7418347238222743936  \n",
        "36774                      4  7418347238222743936  \n",
        "36775                      4  7418347238222743936  \n",
        "\n",
        "[36776 rows x 5 columns]"
       ]
      }
     ],
     "prompt_number": 782
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Building the Model in R"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that the data needed for the model is loaded into the notebook, R is used to build a model of customer behavior. This model will then be used to calculate CLV and related metrics. The [BTYD R package](http://cran.r-project.org/package=BTYD) will be used to run the Pareto/NBD Buy 'Til You Die (BTYD) model first\n",
      "introduced by [Schmittlein, Morrison, and Colombo](http://www.jstor.org/discover/10.2307/2631608?uid=3739584&uid=2129&uid=2&uid=70&uid=4&uid=3739256&sid=21105176808473) and later popularized by [Fader, Hardie, and Lee](http://brucehardie.com/papers/bgnbd_2004-04-20.pdf). TODO: add overview of Pareto/NBD"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "R Setup"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you do not already have R and rpy2 installed, do so now:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%bash\n",
      "apt-get update\n",
      "apt-get install r-base-dev -y\n",
      "apt-get install python-rpy2 -y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Hit http://security.debian.org jessie/updates InRelease\n",
        "Get:1 http://ftp.us.debian.org testing InRelease [191 kB]\n",
        "Hit http://security.debian.org jessie/updates/main amd64 Packages\n",
        "Get:2 http://http.debian.net jessie InRelease [191 kB]\n",
        "Get:3 http://ftp.us.debian.org testing/main Sources [9270 kB]\n",
        "Get:4 http://http.debian.net jessie-updates InRelease [117 kB]\n",
        "Get:5 http://http.debian.net jessie/main amd64 Packages [9088 kB]\n",
        "Get:6 http://http.debian.net jessie-updates/main amd64 Packages [20 B]\n",
        "Fetched 18.9 MB in 4s (4194 kB/s)\n",
        "Reading package lists...\n",
        "Reading package lists...\n",
        "Building dependency tree...\n",
        "Reading state information...\n",
        "r-base-dev is already the newest version.\n",
        "0 upgraded, 0 newly installed, 0 to remove and 174 not upgraded.\n",
        "Reading package lists...\n",
        "Building dependency tree...\n",
        "Reading state information...\n",
        "python-rpy2 is already the newest version.\n",
        "0 upgraded, 0 newly installed, 0 to remove and 174 not upgraded.\n"
       ]
      }
     ],
     "prompt_number": 184
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now load rpy2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rpy2.ipython"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The rpy2.ipython extension is already loaded. To reload it, use:\n",
        "  %reload_ext rpy2.ipython\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Install the [BTYD R Package](http://cran.r-project.org/web/packages/BTYD/index.html)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "install.packages('BTYD', repos='http://cran.us.r-project.org', dependencies=TRUE)\n",
      "library(BTYD)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Installing package into '/usr/local/lib/R/site-library'\n",
        "(as 'lib' is unspecified)\n",
        "trying URL 'http://cran.us.r-project.org/src/contrib/BTYD_2.4.tar.gz'\n",
        "Content type 'application/x-gzip' length 692236 bytes (676 Kb)\n",
        "opened URL\n",
        "==================================================\n",
        "downloaded 676 Kb\n",
        "\n",
        "\n",
        "The downloaded source packages are in\n",
        "\t'/tmp/RtmpB5Zkxy/downloaded_packages'\n",
        "Loading required package: hypergeo\n"
       ]
      }
     ],
     "prompt_number": 146
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Run the Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to run the BTYD models, import the data from BigQuery into R."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas\n",
      "df = pandas.DataFrame(event_log_data)\n",
      "#dataframe = com.convert_to_r_dataframe(df)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 783
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%Rpush df"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 784
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The code below prepares the data for the Pareto/NBD, runs the model, and then prints out the parameter estimates."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i start_date,end_date,cohort_end_date,end_of_cal_period\n",
      "\n",
      "numCusts <- length(df)\n",
      "date <- rep(NA, numCusts)\n",
      "cust <- rep(NA, numCusts)\n",
      "sales <- rep(NA, numCusts)\n",
      "for(i in 1:numCusts) {\n",
      "    date[i] <- df[[i]][1][[1]]\n",
      "    cust[i] <- df[[i]][2][[1]]\n",
      "    sales[i] <- df[[i]][3][[1]]\n",
      "}\n",
      "elog <- data.frame(cust = cust, date = date, sales = sales)\n",
      "elog$sales <- elog$sales / 10^6\n",
      "\n",
      "# format dates\n",
      "elog$date <- as.Date(elog$date, \"%Y%m%d\")\n",
      "\n",
      "# set key dates\n",
      "end.of.cal.period <- as.Date(end_of_cal_period)\n",
      "T.end <- max(elog$date)\n",
      "T.star <- as.numeric(T.end - end.of.cal.period)\n",
      "T.tot <- as.numeric(max(elog$date) - min(elog$date))\n",
      "\n",
      "dataset <- dc.ElogToCbsCbt(elog, per=\"day\", \n",
      "  T.cal=end.of.cal.period)\n",
      "\n",
      "# estimate model\n",
      "cal.cbs <- dataset[[\"cal\"]][[\"cbs\"]]\n",
      "params <- pnbd.EstimateParameters(cal.cbs)\n",
      "\n",
      "print(params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Started making CBS and CBT from the ELOG...\n",
        "...Completed Freq CBT\n",
        "Finished filtering out customers not in the birth period.\n",
        "No dissipation requested.\n",
        "Started merging same-date transactions...\n",
        "... Finished merging same-date transactions.\n",
        "Started Creating Repeat Purchases\n",
        "Finished Creating Repeat Purchases\n",
        "Started Building CBS and CBT for calibration period...\n",
        "Started Building CBT...\n",
        "...Completed Freq CBT\n",
        "Started Building CBT...\n",
        "...Completed Freq CBT\n",
        "Started making calibration period CBS...\n",
        "Finished building CBS.\n",
        "Finished building CBS and CBT for calibration period.\n",
        "Started building CBS and CBT for holdout period...\n",
        "Started Building CBT...\n",
        "...Completed Freq CBT\n",
        "Started making holdout period CBS...\n",
        "Finished building CBS.\n",
        "Finished building CBS and CBT for holdout.\n",
        "...Finished Making All CBS and CBT\n",
        "[1] 0.4503136 5.3909625 0.8433057 4.8640010\n"
       ]
      }
     ],
     "prompt_number": 785
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Analyze the Model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we have estimated the parameters of the Pareto/NBD, we can use it to make projections. For example, the code below prints the expected number of transactions for a new customer in one year."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R print(pnbd.Expectation(params, t=365))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "[1] 2.518467\n"
       ]
      }
     ],
     "prompt_number": 786
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Model fit can also be assessed. The graph below is a histogram of repeat transactions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# histogram\n",
      "pnbd.PlotFrequencyInCalibration(params, cal.cbs, 7)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "         [,1]     [,2]     [,3]     [,4]     [,5]     [,6]    [,7]     [,8]\n",
        "[1,] 6601.000 1287.000 535.0000 330.0000 188.0000 123.0000 109.000 542.0000\n",
        "[2,] 6588.455 1269.274 554.2791 314.3905 203.5084 142.6448 105.422 537.0263\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mJqY5EQ8AN6Dr3G700qVLK1asuO2225SpBgBgZv2G/Wa+vr7btm1bvXp1c8Yw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\ni7G8zBEOTSIhxLRp0w4cOFB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      }
     ],
     "prompt_number": 787
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following two graphs show incremental and cumulative transactions, respectively, for both the data and as fit by the model. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# inc tracking\n",
      "T.cal <- cal.cbs[,3]\n",
      "actual.inc.tracking.data <- cbind(dataset[['cal']][['cbt']], \n",
      "  dataset[['holdout']][['cbt']])\n",
      "actual.inc.tracking.data <- apply(actual.inc.tracking.data, 2, sum)\n",
      "inc.tracking <- pnbd.PlotTrackingInc(params, T.cal, T.tot, \n",
      "  actual.inc.tracking.data, xlab=\"Day\", title=\"Tracking Daily Transactions\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Q8G/LGRsbW1lZ6XqcsQ0VB2Kx2GAwqFQqsVg8YsSIU6dO0V91raCTkpJKSkpY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      }
     ],
     "prompt_number": 788
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# cum tracking\n",
      "cum.tracking <- pnbd.PlotTrackingCum(params, T.cal, T.tot,\n",
      "  cumsum(actual.inc.tracking.data), xlab=\"Day\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9e6lxY8aiAxCUoDdu3NivXz9zc3M9PT1zc3NTU1NPT0/2IwNgVHJy8siRI8eN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\nRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 789
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In addition to forecasting how many times a new customer will purchase in the next year, you can use the model to forecast how many times each existing customer will purchase in the next year, conditional on their past behavior. You can also compute the probability that they are still alive or active (p_Alive). Both the expected transactions and probability of being alive for each customer are computed below, conditional on their observed behavior."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "x <- cal.cbs[, \"x\"]\n",
      "t.x <- cal.cbs[, \"t.x\"]\n",
      "T.cal <- cal.cbs[, \"T.cal\"]\n",
      "conditional_expected_transactions <- pnbd.ConditionalExpectedTransactions(params, T.star = 365,\n",
      "x, t.x, T.cal)\n",
      "p_Alive <- pnbd.PAlive(params, x, t.x, T.cal)\n",
      "output <- data.frame(visitorId=dataset$cust.data$cust, conditional_expected_transactions=conditional_expected_transactions, p_Alive=p_Alive)\n",
      "head(output)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "            visitorId conditional_expected_transactions    p_Alive\n",
        "1 4390204632354546178                         0.0160109 0.02342353\n",
        "2 1925554275363355376                         0.0160109 0.02342353\n",
        "3 1661204767780881402                         0.0160109 0.02342353\n",
        "4 3314683506482981451                         0.0160109 0.02342353\n",
        "5 6246694908791653438                         0.0160109 0.02342353\n",
        "6 4528809343029884946                         0.0160109 0.02342353\n"
       ]
      }
     ],
     "prompt_number": 790
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is one final step before importing this table back into BigQuery - forecasting how much each customer will spend per transaction. The Gamma / Gamma model to forecast average spend per customer is run below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "#cal.cbt <- dc.CreateSpendCBT(elog, is.avg.spend = FALSE)\n",
      "cal.cbt <- dc.ElogToCbsCbt(elog, per=\"day\", T.cal=end.of.cal.period, cohort.birth.per=as.Date(cohort_end_date), statistic=\"total.spend\")\n",
      "cal.cbs <- cal.cbt$cal$cbs\n",
      "cal.cbt <- cal.cbt$cal$cbt\n",
      "calculateAvgSpend <- function(cbt.row) {\n",
      "    purchaseCols = which(cbt.row != 0)\n",
      "    sum(cbt.row[purchaseCols]) / length(purchaseCols)\n",
      "}\n",
      "\n",
      "m.x <- apply(cal.cbt, 1, calculateAvgSpend)\n",
      "m.x[which(is.na(m.x))] <- 0\n",
      "spendParams <- spend.EstimateParameters(m.x, cal.cbs[,1])\n",
      "print(spendParams)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Started making CBS and CBT from the ELOG...\n",
        "...Completed Freq CBT\n",
        "Finished filtering out customers not in the birth period.\n",
        "No dissipation requested.\n",
        "Started merging same-date transactions...\n",
        "... Finished merging same-date transactions.\n",
        "Started Creating Repeat Purchases\n",
        "Finished Creating Repeat Purchases\n",
        "Started Building CBS and CBT for calibration period...\n",
        "Started Building CBT...\n",
        "...Completed Spend CBT\n",
        "Started Building CBT...\n",
        "...Completed Spend CBT\n",
        "Started making calibration period CBS...\n",
        "Finished building CBS.\n",
        "Finished building CBS and CBT for calibration period.\n",
        "Started building CBS and CBT for holdout period...\n",
        "Started Building CBT...\n",
        "...Completed Spend CBT\n",
        "Started making holdout period CBS...\n",
        "Finished building CBS.\n",
        "Finished building CBS and CBT for holdout.\n",
        "...Finished Making All CBS and CBT\n",
        "[1]   0.1808343   1.2010350 144.6492924\n"
       ]
      }
     ],
     "prompt_number": 795
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "spend.plot.average.transaction.value <- function(params, m.x.vector, x.vector, \n",
      "    xlab = \"Average Transaction Value\", ylab = \"Marginal Distribution of Average Transaction Value\", \n",
      "    title = \"Actual vs. Expected Average Transaction Value Across Customers\") {\n",
      "    \n",
      "    if (any(m.x.vector < 0) || !is.numeric(m.x.vector)) \n",
      "        stop(\"m.x must be numeric and may not contain negative numbers.\")\n",
      "    if (any(x.vector < 0) || !is.numeric(x.vector)) \n",
      "        stop(\"x must be numeric and may not contain negative numbers.\")\n",
      "    \n",
      "    if (any(x.vector == 0) || any(m.x.vector == 0)) {\n",
      "        warning(\"Customers with 0 transactions or 0 average spend in spend.plot.average.transaction.value have been removed before plotting.\")\n",
      "    }\n",
      "    \n",
      "    if (length(m.x.vector) != length(x.vector)) {\n",
      "        stop(\"m.x.vector and x.vector must be the same length.\")\n",
      "    }\n",
      "    \n",
      "    # remove any customers with zero repeat transactions\n",
      "    ave.spending <- m.x.vector[which(x.vector > 0)]\n",
      "    tot.transactions <- x.vector[which(x.vector > 0)]\n",
      "    \n",
      "    f.m.x <- spend.marginal.likelihood(params, ave.spending, tot.transactions)\n",
      "    plot(ave.spending, y = f.m.x, pch = 16, type = \"n\", xlab = xlab, ylab = ylab, \n",
      "        main = title)\n",
      "    lines(density(ave.spending, bw = \"nrd\", adjust = 0.6), col = 1, lty = 1)\n",
      "    lines(smooth.spline(ave.spending, y = f.m.x, w = tot.transactions, df = 15), \n",
      "        col = 2, lty = 2)\n",
      "    legend(\"topright\", legend = c(\"Actual\", \"Model\"), col = 1:2, lty = 1:2, lwd = 1)\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 743
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R \n",
      "spend.plot.average.transaction.value(spendParams, m.x, cal.cbs[,1], title = \"Actual vs. Expected Avg Transaction Value Across Customers\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VbRRzOnjwYJ8+fdzd3Ymod+/eP//8c0BAABFFRUUdOHDAy8uLiD777DOt6k1MTGRfiMXi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\nAABMQYMGAABMQYMGAABMQYMGAABM/QWZuh/FtNQy7QAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 744
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "expected_spend <- spend.expected.value(spendParams, m.x, cal.cbs[,1])\n",
      "output$expected_spend <- expected_spend\n",
      "output$clv <- output$expected_spend * output$conditional_expected_transactions\n",
      "output[1:20,]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "             visitorId conditional_expected_transactions    p_Alive\n",
        "1  7934380424896492592                       0.003081246 0.01664270\n",
        "2  1769320725392701794                       0.003081246 0.01664270\n",
        "3  7327239071930204483                       0.003081246 0.01664270\n",
        "4  3398029245237463311                       0.003081246 0.01664270\n",
        "5  6349538733918012999                       0.003081246 0.01664270\n",
        "6  4886333055087975382                       0.003081246 0.01664270\n",
        "7  2420925095930549397                       0.003081246 0.01664270\n",
        "8  8927557617430365996                       0.003081246 0.01664270\n",
        "9   196731236079953884                       0.003081246 0.01664270\n",
        "10 6561983321210142159                       0.003081246 0.01664270\n",
        "11 3376114239034121942                       0.003081246 0.01664270\n",
        "12 6409715628076482922                       0.003081246 0.01664270\n",
        "13 1322306984560844336                       0.003081246 0.01664270\n",
        "14 5099824613672933700                       0.003081246 0.01664270\n",
        "15 4811619942900484801                       0.007738696 0.01022868\n",
        "16 8981923468081902280                       0.003081246 0.01664270\n",
        "17 6958273373722122964                       0.003081246 0.01664270\n",
        "18 5863295912855780719                       0.003081246 0.01664270\n",
        "19 6777826812476305673                       0.003081246 0.01664270\n",
        "20 3899134534339540045                       0.003081246 0.01664270\n",
        "   expected_spend       clv\n",
        "1        260.5943 0.8029553\n",
        "2        260.5943 0.8029553\n",
        "3        260.5943 0.8029553\n",
        "4        260.5943 0.8029553\n",
        "5        260.5943 0.8029553\n",
        "6        260.5943 0.8029553\n",
        "7        260.5943 0.8029553\n",
        "8        260.5943 0.8029553\n",
        "9        260.5943 0.8029553\n",
        "10       260.5943 0.8029553\n",
        "11       260.5943 0.8029553\n",
        "12       260.5943 0.8029553\n",
        "13       260.5943 0.8029553\n",
        "14       260.5943 0.8029553\n",
        "15       454.6239 3.5181959\n",
        "16       260.5943 0.8029553\n",
        "17       260.5943 0.8029553\n",
        "18       260.5943 0.8029553\n",
        "19       260.5943 0.8029553\n",
        "20       260.5943 0.8029553\n"
       ]
      }
     ],
     "prompt_number": 745
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "which.max(output[,5])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ogn2N0bvGCvsABeuAe8E++wAF64Cz4MX+UGu4NeRfYh+gYB1wcZG1IVBeXB7YyIssLWGb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\nrkJggg==\n"
      }
     ],
     "prompt_number": 755
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Analyzing the data in BigQuery"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Import CLV table into BigQuery and run some queries and do analysis"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 467
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}