notebooks/survey_calibration_simulated.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "XhdK9tifRPYR"
      },
      "source": [
        "This is a toy example of using empirical calibration for survey calibration."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "cellView": "form",
        "colab": {},
        "colab_type": "code",
        "id": "NBeKkRlhq1-Q"
      },
      "outputs": [],
      "source": [
        "#@title Copyright 2019 The Empirical Calibration Authors.\n",
        "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "#     https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License.\n",
        "# ============================================================================"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "rLVCPSCxCJez"
      },
      "source": [
        "\u003ctable align=\"left\"\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/google/empirical_calibration/blob/master/notebooks/survey_calibration_simulated.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" /\u003eRun in Google Colab\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://github.com/google/empirical_calibration/blob/master/notebooks/survey_calibration_simulated.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" /\u003eView source on GitHub\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "\u003c/table\u003e"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "VGDMBD7TRIf4"
      },
      "source": [
        "## Imports"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "hzy_rdy7WXyS"
      },
      "outputs": [],
      "source": [
        "from matplotlib import pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "sns.set_style('whitegrid')\n",
        "%config InlineBackend.figure_format='retina'\n",
        "\n",
        "# install and import ec\n",
        "!pip install -q git+https://github.com/google/empirical_calibration\n",
        "import empirical_calibration as ec"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "D8orhXBdZq9l"
      },
      "source": [
        "## Selection Bias"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "N2BGbpoHcLOc"
      },
      "source": [
        "Generate a population of size 1000."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 34
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 266,
          "status": "ok",
          "timestamp": 1562597634220,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "aJ9oaJ4VeD2b",
        "outputId": "ce9e65f4-4d69-40af-9d12-65914e3ed73f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "true population mean is 25.0114142022.\n"
          ]
        }
      ],
      "source": [
        "np.random.seed(123)\n",
        "N = 1000  # population size.\n",
        "df_population = pd.DataFrame({\n",
        "    'x1': np.repeat(['F', 'F', 'M', 'M'], repeats=N),\n",
        "    'x2': np.repeat(['H', 'L', 'H', 'L'], repeats=N),\n",
        "    'y': (np.repeat([1e1, 2e1, 3e1, 4e1], repeats=N) +\n",
        "          np.random.normal(size=4*N)),\n",
        "    'response_rate': np.repeat([1.0e-2, 1.1e-2, 1.2e-2, 1.3e-2],\n",
        "                               repeats=N)\n",
        "})\n",
        "true_mean = df_population['y'].mean()\n",
        "print('true population mean is {}.'.format(true_mean))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "utqFsTLJEUjP"
      },
      "source": [
        "Define a function that draws a sample and calculates the estimates of mean."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "CkmBwMobdm2A"
      },
      "outputs": [],
      "source": [
        "def simulate(seed):\n",
        "  \"\"\"Draws sample and calculates (un)weighted estimates.\"\"\"\n",
        "  np.random.seed(seed)\n",
        "  responded = (np.random.uniform(size=4*N) \u003c=\n",
        "               df_population['response_rate'])\n",
        "  df_sample = df_population.loc[responded]\n",
        "  weights, _ = ec.from_formula(\n",
        "      formula='~x1+x2',\n",
        "      df=df_sample,\n",
        "      target_df=df_population,\n",
        "      objective=ec.Objective.QUADRATIC)\n",
        "  return pd.Series({\n",
        "      'n': df_sample.shape[0],\n",
        "      'unweighted': df_sample['y'].mean(),\n",
        "      'weighted': df_sample['y'].mul(weights).sum()})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 86
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 374,
          "status": "ok",
          "timestamp": 1562597635027,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "CRB-gGkpWcNu",
        "outputId": "1f0b4f6d-54d1-4785-e9d9-c61b68fde9da"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "n             58.000000\n",
              "unweighted    27.434867\n",
              "weighted      25.135381\n",
              "dtype: float64"
            ]
          },
          "execution_count": 14,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Try it out.\n",
        "simulate(123)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "BlwdzFnfetYi"
      },
      "outputs": [],
      "source": [
        "# Do it 1000 times and collect results.\n",
        "result = pd.DataFrame(simulate(seed) for seed in range(1000))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 51
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 243,
          "status": "ok",
          "timestamp": 1562597719097,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "aaZYjzvn_w7s",
        "outputId": "5a9c8837-d4e5-4612-e773-bbf10458da0e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "unweighted rmse is 1.99259828407\n",
            "weighted rmse is 0.150640397789\n"
          ]
        }
      ],
      "source": [
        "# Calculate rmse.\n",
        "print('unweighted rmse is {}'.format(\n",
        "    np.sqrt(np.mean((result['unweighted']-true_mean)**2))))\n",
        "\n",
        "print('weighted rmse is {}'.format(\n",
        "    np.sqrt(np.mean((result['weighted']-true_mean)**2))))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 502
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 829,
          "status": "ok",
          "timestamp": 1562597720682,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "qyTeGKSF6dMT",
        "outputId": "a2d055ca-aa5e-4f61-c29e-9533afb51124"
      },
      "outputs": [
        {
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Wrl2bgQMHNgqjk+Tkk0/O8ccf7/xqAAAAgK84gTRfap/e6dygQ4cO2WOPPbJu3bq88847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\ndy71H3300SkWi3n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            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f782f2dab10\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 485,
              "width": 722
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# visually compare unweighted vs weighted estimates.\n",
        "def compare_estimates(unweighted, weighted, truth,\n",
        "                      figsize=(12, 8),\n",
        "                      fontsize=22,\n",
        "                      output_path=None):\n",
        "  f = plt.figure(figsize=figsize)\n",
        "  plt.rcParams.update({'font.size': fontsize})\n",
        "  plt.hist(unweighted,\n",
        "           alpha=0.4,\n",
        "           color='orange',\n",
        "           edgecolor='none',\n",
        "           label='unweighted')\n",
        "  plt.hist(weighted,\n",
        "           alpha=0.4,\n",
        "           color='blue',\n",
        "           edgecolor='none',\n",
        "           label='weighted')\n",
        "  plt.axvline(truth, linestyle='dashed', color='red')\n",
        "  plt.legend(loc='upper left')\n",
        "  plt.show()\n",
        "  if output_path is not None:\n",
        "     f.savefig(output_path, bbox_inches='tight')\n",
        "\n",
        "compare_estimates(unweighted=result['unweighted'],\n",
        "                  weighted=result['weighted'],\n",
        "                  truth=true_mean)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "last_runtime": {
        "build_target": "//research/colab/notebook:notebook_backend",
        "kind": "private"
      },
      "name": "survey_calibration_simulated.ipynb",
      "provenance": [],
      "version": "0.3.2"
    },
    "kernelspec": {
      "display_name": "Python 2",
      "name": "python2"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}