notebooks/kang_schafer_population_mean.ipynb

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      "source": [
        "We illustrate empirical calibration on Kang-Schafer simulation under both correctly specified and misspecified models, and benchmark the execution time."
      ]
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      "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": "pSOpIN7fCN0V"
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      "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/kang_schafer_population_mean.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/kang_schafer_population_mean.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": "toc",
        "id": "FDLqKjdKKZMV"
      },
      "source": [
        "\u003e\u003e[Simulation](#scrollTo=UcGow9kNJsrl)\n",
        "\n",
        "\u003e\u003e[Imports](#scrollTo=VGDMBD7TRIf4)\n",
        "\n",
        "\u003e\u003e[Selection Bias](#scrollTo=D8orhXBdZq9l)\n",
        "\n",
        "\u003e\u003e[Correctly Specified Model](#scrollTo=X1D4OBiEZhnT)\n",
        "\n",
        "\u003e\u003e[Misspecified Model](#scrollTo=0zuCvTGVdMVj)\n",
        "\n",
        "\u003e\u003e[Adding transformations of covariates](#scrollTo=y4uYEPCnoUzG)\n",
        "\n",
        "\u003e\u003e[Adding extra covariates](#scrollTo=1Ji6iROgDYfv)\n",
        "\n",
        "\u003e\u003e[Benchmark Execution Time](#scrollTo=ITCnSqDiyjIx)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "UcGow9kNJsrl"
      },
      "source": [
        "## Simulation\n",
        "The true set of covariates is generated independently and identically\n",
        "distributed from the standard normal distribution\n",
        "$$\n",
        "(Z_1, Z_2, Z_3, Z_4) \\sim N(0, \\mathbf{I}_4).\n",
        "$$\n",
        "\n",
        "The outcome is generated as\n",
        "$$\n",
        "Y = 210 + 27.4 Z_1 + 13.7 Z_2 + 13.7 Z_3 + 13.7 Z_4 + \\epsilon,\n",
        "$$\n",
        "where $\\epsilon \\sim N(0, 1)$.\n",
        "\n",
        "\n",
        "The propensity score is defined as\n",
        "$$\n",
        "Pr(T = 1 | Z) = \\text{expit}(-Z_1 + 0.5 Z_2 - 0.25 Z_3 - 0.1 Z_4),\n",
        "$$\n",
        "where $\\text{expit}(x) = 1/(1+\\text{exp}(-x)).$\n",
        "\n",
        "This mechanism produces an equal-sized treated and control group\n",
        "on average. Given the covariates, the outcome is independent of the treatment\n",
        "assignment, thus the true ATT is zero. The overall outcome mean is 210. Due to\n",
        "the treatment selection bias, the outcome mean for the treated group (200) is\n",
        "lower than that of the control group (220).\n",
        "\n",
        "The typical exercise is to examine the performance of an observational method\n",
        "under both correctly specified and misspecified propensity score and/or outcome\n",
        "regression models. Misspecification occurs when the following nonlinear\n",
        "transformation $X_i$'s are observed in place of the true covariates\n",
        "\n",
        "\\begin{align*}\n",
        "X_{i1} \u0026 = \\exp(Z_{i1}/2), \\\\\n",
        "X_{i2} \u0026 = Z_{i2} / (1 + \\exp(Z_{i1})) + 10, \\\\\n",
        "X_{i3} \u0026 = (Z_{i1} Z_{i3} / 25 + 0.6)^3, \\\\\n",
        "X_{i4} \u0026 = (Z_{i2} + Z_{i4} + 20)^2.\n",
        "\\end{align*}\n",
        "\n",
        "For more context, see [paper](www.stat.cmu.edu/~ryantibs/journalclub/kang_2007.pdf)."
      ]
    },
    {
      "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 patsy\n",
        "import seaborn as sns\n",
        "sns.set_style('whitegrid')\n",
        "%config InlineBackend.figure_format='retina'\n",
        "\n",
        "from google.colab import widgets\n",
        "\n",
        "# install and import ec\n",
        "!pip install -q git+https://github.com/google/empirical_calibration\n",
        "import empirical_calibration as ec\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "D8orhXBdZq9l"
      },
      "source": [
        "## Selection Bias"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "N2BGbpoHcLOc"
      },
      "source": [
        "We first simulate one dataset of size $2000$ to examine the selection bias."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "aJ9oaJ4VeD2b"
      },
      "outputs": [],
      "source": [
        "np.random.seed(123)\n",
        "simulation = ec.data.kang_schafer.Simulation(size=2000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "vzu2MXdaSg3l"
      },
      "outputs": [],
      "source": [
        "df = pd.DataFrame(\n",
        "    np.column_stack([\n",
        "        simulation.treatment, simulation.covariates,\n",
        "        simulation.transformed_covariates, simulation.outcome\n",
        "    ]))\n",
        "df.columns = [\n",
        "    \"treatment\", \"z1\", \"z2\", \"z3\", \"z4\", \"x1\", \"x2\", \"x3\", \"x4\", \"outcome\"\n",
        "]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "IO4Knf1Ta6hf"
      },
      "source": [
        "The treated group has a lower outcome mean than that of the control group, but the difference is not necessarily attributed to the causal effect of the treatment."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "height": 188
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 305,
          "status": "ok",
          "timestamp": 1562681934224,
          "user": {
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          "user_tz": 240
        },
        "id": "YgJ5P0WzS5Ed",
        "outputId": "bd2e7841-7399-429d-a01a-984cdc03b42f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "treatment         0.0         1.0\n",
            "z1           0.383066   -0.403063\n",
            "z2          -0.189319    0.244439\n",
            "z3           0.134996   -0.114127\n",
            "z4           0.017339   -0.018848\n",
            "x1           1.339729    0.907298\n",
            "x2           9.897616   10.123162\n",
            "x3           0.220736    0.220331\n",
            "x4         395.051555  410.947713\n",
            "outcome    219.997301  200.567004\n"
          ]
        }
      ],
      "source": [
        "print(df.groupby(\"treatment\").mean().T)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "1L9Hn3DxbD0I"
      },
      "source": [
        "The distributions of covariates or transformed covariates don't completely overlap between the treated and control groups."
      ]
    },
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      "cell_type": "code",
      "execution_count": 10,
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          "timestamp": 1562681979703,
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s2DA8//zzWLVqlfa1rVu3QhRFBAUFYcuWLXBzcwMA2NnZITY2FrGxsRBFEbt2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\nAQAAAAdB+QcAAAAcBOUfAAAAcBD/A3Oot+orhNLyAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75acc6e950\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 167,
              "width": 383
            },
            "tags": [
              "id4_content_0",
              "outputarea_id4",
              "user_output"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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XjmrsbW1tda5Tdal/JS/+t27div3798POzg4JCQnw8PDoNNbLywsAUF5ejtbWVq07/hQW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\n/wP9Iu6NoNkLtgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75ac5acc10\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 167,
              "width": 383
            },
            "tags": [
              "id4_content_0",
              "outputarea_id4",
              "user_output"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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79u36M+9OTk5ITExEa2srdu/ejb179yIuLg4uLi4GfYqiCAcHB+zbt0//NGcb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\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75acc83790\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 167,
              "width": 383
            },
            "tags": [
              "id4_content_0",
              "outputarea_id4",
              "user_output"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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SUnD16lU4OzsjKSlJ9+FGEASEhIRgw4YNEEUR3333HbKzsx8oFyIiIjIvbP6p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\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75adb2fa50\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 167,
              "width": 383
            },
            "tags": [
              "id4_content_0",
              "outputarea_id4",
              "user_output"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"9568cc76-a254-11e9-86b7-b3b4ddf7ea5c\"] = google.colab.output.setActiveOutputArea(window[\"947e0c9a-a254-11e9-86b7-b3b4ddf7ea5c\"]);\n",
              "//# sourceURL=js_2eb2005a25"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75b00ff450\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_0",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"95696c58-a254-11e9-86b7-b3b4ddf7ea5c\"] = google.colab.output.getActiveOutputArea();\n",
              "//# sourceURL=js_e3632a9de2"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75acc83150\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_1",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"95699764-a254-11e9-86b7-b3b4ddf7ea5c\"] = document.querySelector(\"#id4_content_1\");\n",
              "//# sourceURL=js_485389603d"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75b00ff250\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_1",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"9569c1c6-a254-11e9-86b7-b3b4ddf7ea5c\"] = google.colab.output.setActiveOutputArea(window[\"95699764-a254-11e9-86b7-b3b4ddf7ea5c\"]);\n",
              "//# sourceURL=js_b0cd4e9a6a"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75b00ff3d0\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_1",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"9569eed0-a254-11e9-86b7-b3b4ddf7ea5c\"] = window[\"id4\"].setSelectedTabIndex(1);\n",
              "//# sourceURL=js_808720a37c"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75b00ff410\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_1",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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6devk4+OjgoIClZaWyjAM/e53v9PYsWNrtc77779f06dP16FDhzR48GD5+vpa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\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75b0207e90\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 167,
              "width": 383
            },
            "tags": [
              "id4_content_1",
              "outputarea_id4",
              "user_output"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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vX+fYAQAAJMnF3gHgv5Z++JG9Q2hw7r//fp04cUJvvvmmNm/erE8//VSenp4q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\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75add48950\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 167,
              "width": 387
            },
            "tags": [
              "id4_content_1",
              "outputarea_id4",
              "user_output"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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TpsHf3x+mpqbIyMhAY2MjJk2ahLCwMJVy3t7eiIyMxIYNGzBjxgz4+fnB2toaWVlZqK2t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\nERFpYKFAREREREQa/h8ro6QqgT5vVgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75ada012d0\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 167,
              "width": 389
            },
            "tags": [
              "id4_content_1",
              "outputarea_id4",
              "user_output"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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z80NUVBQ2bdqEuXPnIigoCI6OjsjOzkZVVRUeffRR/PnPf5bisEhm3377LQDA\nx8cHrq6urbZXqVQQRREWFhYGn5Xg4OCAUaNGaR8AOHPmzBZtRo8erbdv80wAcP8SIlvb9t1pxdbW\nFgqFQu+2e/fu4bvvvgNgfDFTUFAQ8vLytA9KJCIiIjInSYoGtVqtXYPQTBAElJSUaGcR9H3ru2bN\nGgQEBCA5ORk5OTnQaDTw9vZGWFgY5s6da3B/S5YsgY+PD/bs2YPz58+jvr4eXl5eWLBgARYtWgRr\na2spDotkdvPmTQDGH+b3oOY1AY6Ojkaf5eHu7g4AqKqq0rvd0J23Hlx709jYaFJM+vTv39/gttu3\nb6OpqQmCIOgUKb/U2jEQERERSUmSoiEwMBAFBQXt6hscHIzg4OA293viiSfwxBNPtGuf1D2098nG\nDQ0NEkciLQsL064K7OrHQURERL2HbGsaiFrT/DwEY7fmfdCAAQMAAHfv3tXOOujTfDtfc9+utD36\n9eunLSpau7Uw0DWPgYiIiHoeFg3UZT366KMAgEuXLuHGjRuttvf19dVeBmforkJqtVp7i9a23Ja3\nNVI9pdza2hqPPPIIAMPHAADffPMNBEGQ9BiIiIiIDJHlOQ1Eppg4cSLc3Nxw48YNvPPOO9i0aZPR\n9v369cOECRPwzTffYOfOnZg+fXqLNnFxcaivr0ffvn3x1FNPSRarg4MDRFFETU3HH6A1bdo0FBYW\nIjU1FS+99BJcXFx0tn/11VfIy8vTPruCqKv4wsAD5Ko0GgCd84C5jvjuern258jB7jJGQkTU9XCm\ngbosKysrrFy5EqIo4t///jf+/Oc/44cfftBu//HHH/HRRx9h3bp12tdeffVVWFhYQKVS4c9//jMq\nKioA3L8l7/bt27Fz504IgoBly5YZXPDcHs2zA19++SV+/PHHDo01f/58DBo0CHfu3MGSJUtw/vx5\nAEBTUxPS0tLwl7/8BYIg4Ne//jUmTJjQ4diJiIiIWsOZhi5k58FP5A6hy5k5cyZu3LiBv//970hL\nS8PRo0dhb2+PpqYm7bMSHrw1qb+/P9566y28/fbbSEtLQ1paGpycnKBWq6HRaCAIAn73u99pn/ch\nlWeeeQabNm3ClStX8NRTT8HZ2Vl7t6WTJ0+2aSwnJyd88MEHWLp0KS5duoSwsDD07dsXjY2NqK+v\nhyAIUCgU+Pvf/y7pMRAREREZwqKhi7B4aLjcIXRZCxcuxK9//Wvs27cPmZmZ+PHHH2Fra4tf/epX\nCAoKwrNvr0pxAAAgAElEQVTPPqvT/o9//CPGjBmD+Ph4ZGVloaqqCo6Ojhg9ejT++Mc/YsqUKQb3\nZcraBH1tBgwYgMTERGzduhVnzpxBdXW1tkj5ZV9T9jFmzBh8+umn2LVrFz7//HOUlZXBysoKI0aM\nQHBwMMLDw3VuAduefRARERGZShDbe1/LXqqwsBBqtRoODg7w8fFptX1ubi4AICAgwNyhEUmG79u2\n50CTedqc4XSYofUGnaGqqhIA4Ow8ULYYTPGdn7/25668poF/n9JiPqXFfEqnOZemnnOaG9c0EBER\nERGRUSwaiIiIiIjIKBYNRERERERkFIsGIiIiIiIyindPIiIiAvBI/lntz5qrTmbfn+WEx82+DyIi\nqXCmgYiIiIiIjOJMAxERkQzirpe3q19xQyMAINeE/l351rFE1L1wpoGIiIiIiIySfaahoqICcXFx\nOH36NMrKyiCKIjw8PBAUFITnn38eXl5eevsdPnwYSqUSly5dgkajgbe3N0JDQxEeHs6n4RIRERER\nSUjWokGlUmHBggVQq9Vwd3fHpEmTAADnz5/Hhx9+iMOHDyM+Ph5jx47V6RcTEwOlUglbW1sEBQXB\n2toaGRkZWLt2LTIzMxEbG8vCgYiIiIhIIrIWDW+//TbUajX+8Ic/YM2aNbC0tAQAaDQarFmzBgcO\nHEB0dDQOHjyo7ZOWlgalUglXV1ckJydrZyKqqqoQERGB9PR0JCUlISIiQpZjIiIiIiLqaWQrGhoa\nGpCXlwdBEPDKK69oCwYAsLS0xKuvvooDBw6gsLAQ9fX16NOnDwBgx44dEAQBUVFROpcuOTs7Izo6\nGhEREYiLi2PRQEREXdqDt3hti4FVlQAA55qqVts+eOtY3uKViDpCtqLBwsICVlZW0Gg0EEWxxfbm\ny4vs7Oy0BUNFRQVUKhVsbGwwffr0Fn3Gjx8PNzc33LhxA3l5eS0ua5JTbm6u3CEQEREREbWLbHdP\nsrKyQlBQEADg/fffR2Njo3ZbY2Mj3n33XQiCgOeee077ukqlAgAMHz4cNjY2esf18/PTaUtERERE\nRB0j65qGt956C0uXLsXHH3+ML774AqNHjwYA5Ofno6amBgsWLMBrr72mbX/t2jUAwJAhQwyO6eHh\nodNWbgEBAXKH0GU1z74wR9JgPruvL6pr5A6BiIjIKFmLBi8vLyiVSqxcuRJffvklKioqtNtGjx6N\nxx57TGetQ11dHYD7lywZYm9vD1EUUVtba77AiYioR2MhR0SkS9ai4cyZM3j55Zfh6OiIf/7zn/D3\n94coijhz5gw2btyIFStW4JVXXsFLL70EANq1D1LfTjUlJQWpqakmtQ0LC4OnpyfUajXXKUiEeZQW\n8yktU/M5oLik3fuo0mja3bc7qfr/BbwkDVPyWXy7WvvzLStbc4bT7fGzU1rMp3QuXryIdevWmdQ2\nJCQEoaGhZolDtqLhp59+wvLly3H37l189NFHOpccPf300xg+fDh+97vfYdu2bZg1axaGDh2Kvn37\nAvh5xkGfuro6CIKgbWuK0tJSZGVlmdR26tSpJo9LRERERNQRNTU1Jp+nBgYGmi0O2YqGzz//HLdu\n3cLEiRP1rlEYOnQoxowZg+zsbGRmZmLo0KHadqWlpQbHLS8vB2B83cMvDRkyxOQkOzndv32dg4MD\nfHx8TN4HtcRr8KXFfEqrrfnUNN5t976Ke/ilMM3fiDs7D5Q5kp6hLfkc1v/nW65687NBL352Sov5\nlE5zLp2cnEw+T23L+W9byVY0lJWVAQAcHR0Ntmk+Qb99+zYAwNfXFwBQVFSEhoYGvXdQys/P12lr\nitDQUJOncgoLC6FWq00em4iIiIiovRQKBRITE+UOQ76iwdXVFQBw/vx5aDQanQXPwP3brl64cAEA\n4OnpCQBwd3eHr68vCgoKcOTIEcyZM0enT1ZWFsrLy+Hq6gp/f/9OOAoi6qo0mac71L95jUJHZhCI\niIh6Ctme0/Dkk0/Czs4OZWVlWL9+PRoaGrTbGhoasHbtWpSVlaFfv3544okntNuWLVsGURSxadMm\nlJT8vPCwsrISMTExEAQBkZGRnXosREREREQ9mWwzDc7Oznjrrbfw5ptvYv/+/UhPT8eoUaMgiiIu\nXLiAH3/8EX369MH69evh4OCg7Tdt2jSEh4dDqVRi9uzZmDhxIqytrZGRkYHa2lpMmTIF8+bNk+uw\niIiIiIh6HFlvufrss8/Cx8cH+/btQ05ODr7++msAgJubG/7whz9gwYIFePjhh1v0W7NmDQICApCc\nnIycnBxoNBp4e3sjLCwMc+fO7ezDICIiIiLq0WQtGgBg5MiR2LhxY5v7BQcHIzg42AwRERERERHR\ng2Rb00BERERERN0DiwYiIiIiIjKKRQMRERERERkl+5oGIiIiMo8vHnja+HfXy82yj8jB7mYZl4i6\nFs40EBERERGRUSwaiIiIiIjIKBYNRERERERkFIsGIiIiIiIyikUDEREREREZxaKBiIiIiIiMYtFA\nRERERERG8TkNRERGPHifeyIiot6KMw1ERERERGQUiwYiIiIiIjKKRQMRERERERnVJdY01NfXIyEh\nAWlpaSguLsa9e/cwcOBAjB49GgsXLoS/v79Oe1EUsX//fqSkpOCHH36ApaUlfHx8EB4ejuDgYJmO\ngoiIiIioZ5K9aLh69SqWLFmCkpISuLi4IDAwEDY2NigtLcXJkycxcuRInaKhqakJy5cvx2effQZH\nR0dMmjQJDQ0NyMjIwF/+8hfk5eXhjTfekPGIiIiIiIh6FlmLhjt37mDx4sW4du0aVqxYgRdffBGW\nlpba7bdv30Z1dbVOn7179+Kzzz7DI488gn379sHZ2RkAUFJSgvDwcCQlJWHixIl4+umnO/VYiIiI\niIh6KlnXNGzbtg1Xr17Fs88+ixUrVugUDADQr18/DBs2TPt7U1MTdu3aBUEQEB0drS0YAGDo0KGI\nioqCKIrYvn17px0DEREREVFPJ1vRcO/ePXz88ccQBAGRkZEm9Tl79iyqqqrg7u6OgICAFtunT58O\nKysr5Ofn48aNG1KHTERERETUK8l2edKFCxdQXV2NwYMH46GHHsKZM2dw6tQp3Lp1C4MGDcKkSZMw\nduxYnT4FBQUAAD8/P71j2tra4pFHHsHFixdRUFAAV1dXsx8HEREREVFPJ1vRcOnSJQDAsGHDsHr1\naqSmpkIQBO32Dz74AFOnTsWmTZtgY2MDALh27RoAYPDgwQbH9fDwwMWLF7VtiYiIiIioY2S7PKl5\ngXN2djY++eQTPP/88zh27Biys7Oxbds2uLu7Iz09HTExMdo+dXV1EAQBdnZ2Bse1t7cHANTW1pr3\nAIiIiIiIegnZZhpEUQQAaDQaPPfcc4iKitJu+81vfoNBgwbhueeew8GDB/Hiiy/C09NT2+fBGQkp\npKSkIDU11aS2YWFh8PT0hFqtRm5urqRx9FbMo7SYz/sGFJdIMk5VVaUk4xBzKbW25rO4uNgsceSW\nlZpl3M7Gz05pMZ/SuXjxItatW2dS25CQEISGhpolDtmKhr59+2p/fu6551psHz16NEaNGoULFy4g\nKysLnp6e6Nu3L0RRRF1dncFxm7c9OH5rSktLkZWVZVLbqVOnmjwuEf1swPeX5A6BiIio26mpqTH5\nPDUwMNBscchWNAwZMkT7s6enp942np6euHDhAm7evKnT5/r16wbHLS8vNzqmoVhMTbKTkxMAwMHB\nAT4+Pibvg1pq/hZC352wqO26ej41jXflDqFNiv9/psLZeaDMkXR/zd+IM5fSaG8+H7yFuZQCBrub\nZdzO0tU/O7sb5lM6zbl0cnIy+Tz1wfNrqclWNPj6+mp/rq6uxoABA1q0uXXrFoCf1yk098nPz9c7\n5t27d7ULrEeOHGlyLKGhoSZP5RQWFkKtVps8NhERERFReykUCiQmJsodhnwLod3c3PDoo48CADIy\nMlpsr6mpgUqlAnD/UiUA8Pf3x8CBA1FeXo6cnJwWfY4cOYLGxkaMGTOGt1slIiIiIpKIrE+EfuGF\nFyCKIrZt24aLFy9qX29oaMBbb72Fn376CaNHj9Y+r8HCwgJLliyBKIqIiYlBVVWVts+VK1ewefNm\nCIKAF154odOPhYiIiIiop5Lt8iTg/l2SlixZgvj4eDz33HN49NFH0b9/f5w7dw43btyAh4cHNm/e\nrNNn4cKFyMnJwWeffYapU6di4sSJuHfvHjIyMtDQ0ICIiAj85je/kemIiIiIiIh6HlmLBgB47bXX\n4O/vj6SkJBQUFODOnTvw8PDA4sWLsXTp0hZrHSwsLLBt2zYkJycjJSUFX331FSwtLeHn54fw8HDM\nnDlTpiMhIiIiIuqZZC8aAOCZZ57BM88806Y+8+bNw7x588wUERERERERNZN1TQMREREREXV9LBqI\niIiIiMgoFg1ERERERGQUiwYiIiIiIjKKRQMRERERERnFooGIiIiIiIxi0UBEREREREaxaCAiIiIi\nIqNYNBARERERkVFd4onQRNSzxF0vb/HaI9U1ku7jyf5Oko5HREREhnGmgYiIiIiIjGLRQERERERE\nRrFoICIiIiIio7imgaiX0mSeNtvYUq9fICIiInlxpoGIiIiIiIzqckXDli1boFAooFAosGfPHoPt\nDh8+jPDwcDz22GPw9/fH73//eyQnJ0MUxU6MloiIiIio5+tSlyedO3cOu3fvhoWFhdGT/5iYGCiV\nStja2iIoKAjW1tbIyMjA2rVrkZmZidjYWAiC0ImRExERERH1XF2maGhoaMDq1avh4uKCMWPG4Pjx\n43rbpaWlQalUwtXVFcnJyfDy8gIAVFVVISIiAunp6UhKSkJERERnhk9ERNSlPZJ/1izjfpZveNt3\nfv6S7CNysLsk4xBR+3WZy5NiY2Pxww8/ICYmBg4ODgbb7dixA4IgICoqSlswAICzszOio6MhiiLi\n4uI6I2QiIiIiol6hSxQN3377Lfbu3YvZs2dj8uTJBttVVFRApVLB2toa06dPb7F9/PjxcHNzw82b\nN5GXl2fGiImIiIiIeg/Zi4aGhgasXLkS/fv3xxtvvGG0rUqlAgAMHz4cNjY2etv4+fnptCUiIiIi\noo6RfU3Dli1bUFxcjHfffRf9+vUz2vbatWsAgCFDhhhs4+HhodOWiIiIiIg6RtaZhjNnziAhIQFT\npkzRe7nRL9XV1QEA7OzsDLaxt7eHKIqora2VLE4iIiIiot5MtpmG+vp6rF69Go6OjnjrrbdM6tN8\nG1apb6eakpKC1NRUk9qGhYXB09MTarUaubm5ksbRWzGP0jI1nwOKS8wWQ5VGY7axmxXfrjb7PgCg\nqqqyU/bTGzCX0uoO+SwuLpZknNyyUknGMboP/lskKeZTOhcvXsS6detMahsSEoLQ0FCzxCFb0bB5\n82aUlJRg/fr1GDhwoEl9+vbtC+DnGQd96urqIAiCtq0pSktLkZWVZVLbqVOnmjwuEZnP2U4oTIiI\niORWU1Nj8nlqYGCg2eKQrWg4fvw4LCwskJKSgpSUFJ1tly9fBgDs378fJ0+exLBhw7Bu3TrtWobS\nUsPfOJSXlwMwvu7hl4YMGWJykp2cnAAADg4O8PHxMXkf1FLztxABAQEyR9IztDWfmsa7ZouluLrG\nbGN3luZvcZ2dTftSgwxjLqXVnfI5bNgwScYJMONzGvhvkbSYT+k059LJycnk89S2nP+2lawLoZua\nmpCTk2Nw+7Vr13Dt2jXt+gRfX18AQFFRERoaGvTeQSk/P1+nrSlCQ0NNnsopLCyEWq02eWwiIiIi\novZSKBRITEyUOwz5ioaTJ08a3LZ69WocPHgQK1euxMKFC7Wvu7u7w9fXFwUFBThy5AjmzJmj0y8r\nKwvl5eVwdXWFv780T6EkIiIiecVdLzfb2MUNjQCA3OvlfPI0kRGyP6fBmOaFzw9atmwZRFHEpk2b\nUFLy80LOyspKxMTEQBAEREZGdmaYREREREQ9muzPaTBEX8EAANOmTUN4eDiUSiVmz56NiRMnwtra\nGhkZGaitrcWUKVMwb968To6WiIiIiKjn6rJFg7Hbqq5ZswYBAQFITk5GTk4ONBoNvL29ERYWhrlz\n53ZilERERGTII/lnO3V/3/nx0mQic+mSRcOGDRuwYcMGo22Cg4MRHBzcSREREREREfVeXXpNAxER\nERERyY9FAxERERERGcWigYiIiIiIjGLRQERERERERrFoICIiIiIio1g0EBERERGRUSwaiIiIiIjI\nKBYNRERERERkVJd8uBsRERFRZ4u7Xm72fUQOdjf7PojMgTMNRERERERkFIsGIiIiIiIyikUDERER\nEREZxaKBiIiIiIiMYtFARERERERG8e5JRF2AJvN0h8cYUFxyf6zGux0ei4iIiOhBshUNjY2NyM7O\nxqlTp3D27FmUlpaiuroazs7OGDt2LObPn4/AwECD/Q8fPgylUolLly5Bo9HA29sboaGhCA8PhyAI\nnXgkREREREQ9m2xFQ3Z2NhYtWgRBEODi4oLRo0fD3t4eRUVFSE9Px7Fjx7B8+XK8/PLLLfrGxMRA\nqVTC1tYWQUFBsLa2RkZGBtauXYvMzEzExsaycCAiIiIikohsRYMgCJg2bRoWLFiAcePG6Ww7cuQI\noqKisG3bNkyYMEFnxiEtLQ1KpRKurq5ITk6Gl5cXAKCqqgoRERFIT09HUlISIiIiOvV4iIiIiIh6\nKtkWQgcFBSE2NrZFwQAAM2bMQEhICADg0KFDOtt27NgBQRAQFRWlLRgAwNnZGdHR0RBFEXFxceYN\nnoiIiIioF+myd08aOXIkRFFEefnPj3SvqKiASqWCtbU1pk+f3qLP+PHj4ebmhps3byIvL68zwyUi\nIiIi6rG6bNFw5coVAMCgQYO0r6lUKgDA8OHDYWNjo7efn5+fTlsiIiIiIuqYLlk03Lx5EwcPHtSu\ne2h27do1AMCQIUMM9vXw8NBpS0REREREHdPligaNRoOoqCj89NNP+PWvf43Jkydrt9XV1QEA7Ozs\nDPa3t7eHKIqora01d6hERERERL1Cl3u425o1a/DNN99g8ODBeOedd3S2iaIIAJLfTjUlJQWpqakm\ntQ0LC4OnpyfUajVyc3MljaO3Yh5/fjCbFIolHKu9qjQauUOQTFVVpdwh9BjMpbSYz5aKi4tl6dsW\nuWWlnbIfufHfdulcvHgR69atM6ltSEgIQkNDzRJHlyoa1q1bhwMHDsDV1RX79u3DwIEDdbb37dsX\nwM8zDvrU1dVBEARtW1OUlpYiKyvLpLZTp041eVwiIiIioo6oqakx+TzV2IORO6rLFA0bN25EUlIS\nXFxcsHfvXp3bqTZrXstQWmq4Sm++25KxdQ/6xjU1yU5OTgAABwcH+Pj4mLwPaqn5W4iAgACZI5Gf\npvFuh8donmEYNmxoh8fqqOLqGrlD6LDmb3GdnQe20pJaw1xKi/k0bNiwYW3u0zzD0J6+7REw2L1T\n9iMX/tsuneZcOjk5mXye2pbz37bqEkXDO++8g71798LZ2Rnx8fHw9vbW287X1xcAUFRUhIaGBr13\nUMrPz9dpa4rQ0FCTp3IKCwuhVqtNHpuIiIiIqL0UCgUSExPlDkP+omHTpk2Ij49H//79ER8fjxEj\nRhhs6+7uDl9fXxQUFODIkSOYM2eOzvasrCyUl5fD1dUV/v7+5g6dqFv6ogfMAhAREVHnkvXuSe+9\n9x527dqFfv36IT4+HgqFotU+y5YtgyiK2LRpE0pKfl7wWVlZiZiYGAiCgMjISHOGTURERETUq8g2\n03Dy5Els374dgiBg6NChBqddHnroIZ0iYNq0aQgPD4dSqcTs2bMxceJEWFtbIyMjA7W1tZgyZQrm\nzZvXWYdBRERERNTjyVY03L59W3vr1PPnz+P8+fN6240fP77FzMGaNWsQEBCA5ORk5OTkQKPRwNvb\nG2FhYZg7d67ZY6eeT5N5Wu4QiIiojR7JP9vmPgObF5bXVLW573d+vBSaeg/ZioaQkBCEhIS0u39w\ncDCCg4MljIiIiIiIiPTpck+EJiIiIiKiroVFAxERERERGcWigYiIiIiIjJL9OQ1EREREvUXc9XKz\n7yOyhz91muTBooHIRF39oWhVGg0AoLiLx0lERETdDy9PIiIiIiIio1g0EBERERGRUSwaiIiIiIjI\nKBYNRERERERkFBdCU7egyTwtdwhEREQ6Hsk/26n7+87Pv1P3R/QgzjQQEREREZFRnGkgIiIi6gZM\nndnQXHWSZH+WEx6XZBzqGTjTQERERERERrFoICIiIiIio3h5EhEREVEP8kV1jSTjfHe9vM19ihsa\nAQC57ej7S5GD3Ts8BkmnWxcNhw8fhlKpxKVLl6DRaODt7Y3Q0FCEh4dDEAS5wyMiIiIi6hG6bdEQ\nExMDpVIJW1tbBAUFwdraGhkZGVi7di0yMzMRGxvLwoGIiIiISALdsmhIS0uDUqmEq6srkpOT4eXl\nBQCoqqpCREQE0tPTkZSUhIiICJkjJSIiIiJTPXiHKKnuAmUM7xBlum65EHrHjh0QBAFRUVHaggEA\nnJ2dER0dDVEUERcXJ2OEREREREQ9R7ebaaioqIBKpYKNjQ2mT5/eYvv48ePh5uaGGzduIC8vD2PH\njpUhSiIiIqLurT1PvB5YVQkAcK6pkjocklm3KxpUKhUAYPjw4bCxsdHbxs/PDydOnIBKpWLRYAbi\nnTsQy693eBz7HysAAE2Xvzfe0ML4hFhFwz381KjpcDzG9LOyNOv4RERERF1Ztysarl27BgAYMmSI\nwTYeHh46bUli9xog3uj4rdT61NwGgNbHaqVoqG5sREXDvQ7HY4wg6C9QiYiIiHqDbremoa6uDgBg\nZ2dnsI29vT1EUURtbW1nhUVERERE1GN1u5kGURQBQNLbqaakpCA1NdWktkuWLIGjoyPUajVyc3Ml\ni6FbaWqCRZME9abXrwAA55paaScCFo2GG92z7gN7qz4dj8eInwTAxtLarPvoKHf7vnKH0KMwn9Jh\nLqXFfEqL+ZSWlPk8f6+1E4SOa+wG53JlZWVYt26dSW1DQkIQGhpqlji6XdHQt+/9N2PzjIM+dXV1\nEARB27Y1paWlyMrKMqnt0qVLTWrXo1lYoMnAehJzabI2vD8BnfNGtu2EfRAREdF9jXIH0EVYWFiY\nfJ4aGBhotji6XdHQvJahtLTUYJvy8nKdtqaMaWqSKyvv3xWgqalJu3aC2ufixYuoqamBk5MTFAqF\n3OF0e8yntJhP6TCX0mI+pcV8Sov5lE5ZWRksLCxQWVlp8nmqqee+7SGIzdf7dBPl5eWYPHkybGxs\nkJOTo/cOSpMnT0ZFRQX2798Pf39/SfcfERGBrKwsBAYGIjExUdKxexvmUlrMp7SYT+kwl9JiPqXF\nfEqL+ZROV8tlt1sI7e7uDl9fX9y7dw9HjhxpsT0rKwvl5eUYNGiQ5AUDEREREVFv1O2KBgBYtmwZ\nRFHEpk2bUFJSon29srISMTExEAQBkZGRMkZIRERERNRzdLs1DQAwbdo0hIeHQ6lUYvbs2Zg4cSKs\nra2RkZGB2tpaTJkyBfPmzZM7TCIiIiKiHqFbFg0AsGbNGgQEBCA5ORk5OTnQaDTw9vZGWFgY5s6d\nK3d4REREREQ9RrctGgAgODgYwcHBcodBRERERNSjdcs1DURERERE1HlYNBARERERkVEsGoiIiIiI\nyCgWDUREREREZJRldHR0tNxBdDcjR45EYGAgRo4cKXco3R5zKS3mU1rMp3SYS2kxn9JiPqXFfEqn\nK+VSEEVRlDsIIiIiIiLqunh5EhERERERGcWigYiIiIiIjGLRQERERERERrFoICIiIiIio1g0EBER\nERGRUSwaiIiIiIjIKBYNRERERERklJXcAXSGxsZGZGdn49SpUzh79ixKS0tRXV0NZ2dnjB07FvPn\nz0dgYKDB/ocPH4ZSqcSlS5eg0Wjg7e2N0NBQhIeHQxAEg/2++OIL7N27FxcuXEB9fT28vLwQHByM\nxYsXw8bGxhyH2inam8/Vq1cjNTXV4Lje3t749NNP9W4TRRH79+9HSkoKfvjhB1haWsLHxwfh4eEI\nDg6W7NjkkpiYiNzcXFy6dAmVlZWora2Fo6MjFAoFQkJC8Lvf/U5vv47kpb3v666uPbmMiIhAdna2\nwTEnTZqEnTt36t3W0NCA3bt349NPP8XVq1fRp08fjB49GosWLcITTzwh2XF1FVu2bEFcXBwAYOXK\nlVi0aJHedvzcNE1r+eTnpmHtzQ0/N/VrTz752dm6+vp6JCQkIC0tDcXFxbh37x4GDhyI0aNHY+HC\nhfD399dp35Xfn72iaMjOzsaiRYsgCAJcXFwwevRo2Nvbo6ioCOnp6Th27BiWL1+Ol19+uUXfmJgY\nKJVK2NraIigoCNbW1sjIyMDatWuRmZmJ2NhYvf8jdu7cic2bN8PKygqBgYFwcnJCdnY23nvvPXz+\n+efYt28f+vTp0xmHL7mO5FMQBIwbNw5Dhw5tsc3V1VXv/pqamrB8+XJ89tlncHR0xKRJk9DQ0ICM\njAz85S9/QV5eHt544w3Jj7Mz7dq1C1VVVXjkkUcwbtw42Nvbo7S0FJmZmcjIyMCxY8ewdetWnT4d\nyUt739fdQXtyCdx/bz7xxBNwcXFpsc3Hx0fvvu7cuYM//elPyM/Px8CBAzF58mTU1NQgMzMTp0+f\nxqpVq7Bw4UKpD1E2586dw+7du2FhYQFjzwXl56ZpTM0nPzcNa2tu+LlpXHvea/zsNOzq1atYsmQJ\nSkpK4OLigsDAQNjY2KC0tBQnT57EyJEjdYqGLv/+FHuBjIwM8ZVXXhFzc3NbbPv0009FX19fUaFQ\niJmZmTrbjh49Kvr4+IiTJk0SS0pKtK9XVlaKM2fOFBUKhZiQkNBizPz8fFGhUIhjx44Vz507p329\nrq5OnD9/vqhQKMQNGzZIeISdq735XLVqlahQKMTU1NQ27W/37t2ij4+POGvWLLGyslL7enFxsfj4\n4+ry3ikAABLQSURBVI+LCoVCPHHiRPsOpovIzc0V79y50+L1oqIi7TGmpKTobGtvXtr7vu4u2pPL\n5r/LrKysNu3r7bffFn18fMQ//elPYl1dnfb1b7/9Vhw7dqw4cuRIsaCgoH0H0sXU19eLM2fOFJ98\n8klxxYoVokKhEOPj41u04+emaUzNJz83DWtPbvi5aVh78snPTsPq6urEZ555RlQoFOI//vEPsbGx\nUWd7dXW1eOXKFZ3Xuvr7s1esaQgKCkJsbCzGjRvXYtuMGTMQEhICADh06JDOth07dkAQBERFRcHL\ny0v7urOzM6KjoyGKonZa+UHNr0VGRsLPz0/7up2dHdavXw9BELB//36o1WpJjq+ztTef7dHU1IRd\nu3ZBEARER0fD2dlZu23o0KGIioqCKIrYvn17h/clp3HjxsHW1rbF6w8//DDCw8MhiiJOnz6tfb0j\neWnv+7q7aGsu2+v27dv48MMPYWlpifXr18POzk67bcyYMViyZAmampqwY8eODu+rK4iNjcUPP/yA\nmJgYODg4GGzHz03TmJrP9ugtn5ttxc/NrqG3fHZu27YNV69exbPPPosVK1bA0tJSZ3u/fv0wbNgw\n7e/d4f3ZK4qG1owcORKiKKK8vFz7WkVFBVQqFaytrTF9+vQWfcaPHw83NzfcvHkTeXl52tfv3buH\nL7/8EgAwa9asFv28vLwwduxY3Lt3D6dOnTLD0chPXz7b6+zZs6iqqoK7uzsCAgJabJ8+fTqsrKyQ\nn5+PGzdudHh/XZGV1f2rCB+8LKO9efm/9u49pqn7/QP4+0BBvFFEQESFIbpUxdummco2dc5pTFy8\nMN3ES9R5iXGaTRyDZSoOb4AXXNyyOLkojGxmwKKbiSJOM6MBhvNSS4xRBh1epnJxgBTb8/3DX/uj\ntj1tj85SeL8SE+3n8ymnDw8PPu35nCM3r9sLa7GU6/Tp03j8+DFGjhyJPn36WIwb906cPn0aer3+\nmb+eK128eBGZmZmYPn06JkyYYHMe66ZjHI2nXKyb1rFutg0doXa2tLTg8OHDEAQBy5cvd2iNO+Rn\nh9jTYE9FRQUAIDAw0PTY1atXAQADBgywuflu6NChOHnyJK5evYoRI0YAAG7evImmpib4+fmZdXtP\nr7tw4QKuXr3aLjajPc1aPI1EUcT58+dRXl6OxsZG9OzZE6+++iqioqKsnmun0WgAwOydx9Z8fHww\ncOBAlJeXQ6PR2Dzn0l1VVVUhNzcXgiBg4sSJpsflxkVuXrcHrWP51ltvWZ1z/PhxHD9+HDqdDkFB\nQXjttdcwatQoq3PtfQ9CQ0OhVCpRX1+PiooKREREPJ8X8oLpdDrExcXBz8/P7jnwrJv2ORNPI9ZN\n25yJDeumfc7mmhFrpzm1Wo3a2lqEhIQgPDwcZWVlOH36NGpqahAYGIg33njDIk/cIT87fNNw7949\nFBQUQBAETJkyxfS4VqsFAKtdsFHv3r3N5rb+e0hIiOQ6URTN1rUXreNpreMVBAE///yz2WOiKGLA\ngAHYtWsXXn75ZbMxR+NZXl7eLuKZl5eHkpIStLS04M6dO7hw4QJEUcSKFSvw9ttvm+bJjYvcvHZH\nUrGcNGmS1TXZ2dlm//7qq6/wyiuvYNeuXQgODjYb02q1EARB8nsQHByM+vp6aLVat/zFBzy5us9f\nf/2F3bt3Q6lUSs5l3bTPmXgasW7a5kxsWDftczbXjFg7zV27dg0AEBYWZroqVeuma9++fXjnnXeQ\nmppq+o++O+Rnh24a9Ho9YmNj8fDhQ0RFRZl9TNzY2AgAZufaPa1Lly4QRRENDQ1OrevatSsAmK1r\nD56O5/jx483GBw0ahMjISIwZMwZ9+vTBv//+C7VajT179kCj0WDJkiXIy8sze9ersbERgiDY/T4A\n7SOeZWVlKCgoMP3b09MTa9eutbiKhNy4yM1rd+RoLIEnH9/OnDkTo0aNQnBwMB48eICysjLs3r0b\nZWVlWLx4MfLz8832SjgaS8B9c7OsrAwHDx7E5MmTrb4J8DTWTWnOxhNg3ZTibGxYN6XJyTXWTutq\na2sBPLnapMFgwIcffoi5c+eiR48eKCkpQWJiIk6cOIHExERs2bIFgHvkZ4fe07BhwwacP38eISEh\nSE5ONhsT/+/yd85enkruuvZAKp4AsHDhQsTExCAiIgI+Pj4ICAjA+PHjcfjwYYwYMQL379+32KjT\n0eKZlJQEjUaDixcv4ujRo1i0aBH27t2LOXPm4J9//jHNY37a52gsAWDNmjWYNWsWQkND4e3tjeDg\nYEybNg35+fno168fKioqkJuba7amvceyubkZ8fHx6N69OzZu3OjQGualbXLiCbBuSnE2NsxPaXJy\njbXTOuNr1Ov1iI6ONm1Q7tatGyZOnGi67HdBQYHp3X93yM8O2zQkJSXhp59+QlBQELKystCzZ0+z\nceO7WsYOzhpjV2ic6+g6Y6fXep27sxdPKQqFAsuXL4coihabHLt27QpRFO1+H4xz2wtvb29ERERg\n/fr1WLduHcrLy/Hll1+axuXGRW5euzN7sZTSrVs3LFy40GZuAvZj2XquO9m5cycqKyvx2WefOfzz\nzLppm5x4SmHdtM1WbFg35ZHKNVs6cu0EzI/7vffesxiPjIzEkCFDYDAYUFxcbFrT1vOzQ56etH37\ndmRnZyMgIACZmZlWN94Zzw37+++/bT6P8epArc8jM/69urpacp0gCJLnn7kTR+JpT//+/QE8uQpA\na47GEwD69u3r9Nd1B7NmzcKOHTtQVFQEvV4PT09P2XGRm9fthbVY2iOVm6IoOvQ9cMdYFhYWwsPD\nA3l5ecjLyzMbu3nzJgDg+++/R1FREcLCwpCUlMS6KUFOPO1h3bTNWmxYN+WzlWty1rT32gmYH7et\nn7G+fftCrVbj3r17Zmvacn52uKYhOTkZmZmZ8Pf3R3p6uimpnzZ48GAAwPXr16HT6azuSL98+bLZ\nXODJD4mPjw/q6upQVVVl9T/Qly5dsljnrhyNpz3G8/+M5+sZGWNkjPXTHj16ZNpwNGjQIFlfu63z\n9fWFQqGAXq9HXV0d/P39ZcdFbl63F9ZiaY/c3KysrERdXR06d+6Ml1566dkO3EUMBgNKS0ttjmu1\nWmi1WtOnAKyb0pyNpz2sm7ZZiw3rpny2ck3Omo5QO1vnQW1tLXr06GExp6amBsD/x8cd8rNDnZ6U\nmpqK9PR0+Pn5IT093eZVAIAnO/cHDx6MlpYWHDt2zGK8uLgYt2/fRmBgoNktwL28vPDmm28CAI4c\nOWKxrqqqCn/++Se8vLz+k+tzv0jOxNOeX3/9FcCTG7u0NnLkSPTs2RO3b9+2+sv22LFjePz4MYYN\nG+bWlw2UUlxcjMePH8PX19dUeOTGRW5etxfWYmmPrdwcP348FAoFLly4YPUdHuPNDSdOnGi6P4Q7\nKSoqgkajsfpnxowZAIC4uDhoNBrTO+esm7bJiac9rJu2WYsN66Z8tnJNzpr2XjsBoFevXhg+fDgA\n4Ny5cxbj9fX1pkulRkZGAnCP/OwwTcOePXvw3XffQalUIj09HSqVyu6aFStWQBRFpKamorKy0vT4\n/fv3kZiYaPOmHcuWLQMA7N+/3/TuGPDknLKEhASIooiYmJjnfhfQF8nZeJaXl+O3336DwWAwe1yv\n1yMjIwPZ2dkQBMHiyjYeHh5YunQpRFFEYmIiHjx4YBqrqKjAzp07IQgCVq5c+dxe24tWWlqKI0eO\nQKfTWYz98ccf+PzzzyEIAqKjo00bnZ4lLnLz2h3IiWVxcTFKSkos5j969AjJyck4efIkFAoF5s+f\nbzauVCoxd+5c6PV6JCQkmJ1PevHiRRw4cAAeHh5uG0tHGDfgtca6Kd/T8WTdtE1ObFg3bZMTT9ZO\naStXroQoivj6669RXl5uelyn02Hjxo14+PAhIiMjTfdNcIf8FERrVb+dKSoqwqpVqyAIAiIjIzFg\nwACr88LDwy2CunnzZuTm5sLb2xtjx46Fl5cXzp07h4aGBkyePBlpaWlWd6wfOHAAqamp8PDwwJgx\nY9C9e3eUlJTgwYMHGD58OLKysp7LXWldQU48CwsLsXr1aiiVSoSHh6NXr15oaGjAtWvXcPfuXXh6\nemLdunVYsmSJxfMYDAasXr0ap06dQteuXTF27Fi0tLTg3Llz0Ol0WLBgARISEv7T1/xfys/PR3x8\nPHx9fTF48GAEBASgoaEBVVVVuH79OgRBwIQJE5CWlmb2seOzxEVuXrd1cmKZlZWFbdu2ISAgAGFh\nYQgKCkJtbS00Gg1qa2vRqVMnbN261eoNxZqamrBo0SJcvnwZ/v7+GD16NB4+fIjz58/DYDAgLi7O\n6iVe3Z3xuuNxcXFYvHixxTjrpnNsxZN10za5sWHdtE5OPFk77UtJSUF6ejoUCgWGDx8OPz8/XLp0\nCXfv3kXv3r2RlZWF0NBQ0/y2np8domnIz893qDiOHj0aBw8etHj8l19+QU5ODq5duwa9Xo/+/fsj\nOjoaH3zwgeTz/f7778jIyMCVK1fQ3NyMfv36Yfr06Vi8eDG8vLxkvx5XkxNPrVaLQ4cO4dKlS6iu\nrkZtbS0EQUCvXr0wevRozJs3z+65djk5OcjLy8ONGzfg6ekJlUqFefPmYdq0ac/ldbmKVqtFfn4+\nSktLUVlZiZqaGoiiiICAAAwdOhTvvvuuzTsYA/LjIjev2zI5sdRoNPjxxx9x5coV3Lp1C3V1dVAo\nFOjbty/GjBmD+fPnIywszObX1Ol0SE9Px9GjR6HVatGpUycMHToUS5Yswbhx4/7rl+wS8fHxKCgo\nwKeffmq1aQBYN51hK56sm7Y9a2xYN83JiSdrp2MKCwuRnZ0NjUaDpqYm9O7dG5MmTcKyZctsnibb\nVvOzQzQNREREREQkX4fZ00BERERERPKwaSAiIiIiIklsGoiIiIiISBKbBiIiIiIiksSmgYiIiIiI\nJLFpICIiIiIiSWwaiIiIiIhIEpsGIiIiIiKSxKaBiIiIiIgksWkgIiIiIiJJbBqIiIiIiEgSmwYi\nIiIiIpLEpoGIiIiIiCSxaSAiIiIiIklsGoiIyKVWrVoFlUoFlUqF+Ph4Vx8OERFZoXD1ARARUcdV\nWFiIoqIiCILg6kMhIiIJ/KSBiIhcorGxEVu2bEH37t3Rv39/Vx8OERFJYNNAREQusWfPHty+fRtr\n166Fv7+/qw+HiIgksGkgIiKn7Nq1CyqVCuPGjcP9+/etzlm6dClUKhVmz54NvV5vMa5Wq5GTk4NB\ngwYhJibmvz5kIiJ6RmwaiIjIKWvWrMGQIUNQU1ODhIQEi/Hs7GycPXsWnTt3RmpqKjw9Pc3GRVHE\nhg0bIIoiNm3axP0MRERugE0DERE5RaFQIDk5GZ06dcKZM2eQm5trGrtx4wZSU1MhCAJiY2MRHh5u\nsf7QoUNQq9WIjo7GsGHDXuShExGRTGwaiIjIaREREYiNjYUoikhOTkZFRQX0ej3Wr1+P5uZmREVF\nWT3t6M6dO0hLS0OPHj2wbt06Fxw5ERHJwaaBiIhkmT9/Pl5//XU0NTUhNjYWe/fuhVqthlKpxLZt\n26yuSUpKQmNjI2JjY6FUKl/wERMRkVxsGoiISLZt27bBz88ParUa3377LQRBQGJiIgIDAy3mnjp1\nCidOnMCIESMwe/ZsFxwtERHJxaaBiIhkCwwMxCeffAJRFCEIAqZOnYopU6ZYzGtqasLmzZuhUCiw\nceNGFxwpERE9C94RmoiIZDMYDMjPzwfw5KpIGo0Gjx49go+Pj9m8/fv349atW5gzZw5CQ0PR2Nho\nGhNFEQaDAQCg1+tNY126dHlBr4KIiOwRRFEUXX0QRETknr755hukpaXB19cX3bp1Q3V1Nd5//31s\n2rTJbF58fLypuXBUUVERQkJCnuPREhGRXDw9iYiIZFGr1di3bx8EQcAXX3yB7du3QxAE/PDDDzhz\n5ozFfEEQJP+0nuPhwV9PRERtCT9pICIipzU3N2PmzJm4efMmpk6dit27dwMAduzYgYyMDAQGBuLI\nkSPw8/Nz6PkWLFiA0tJSzJgxw+aVl4iIyHX4Vg4RETktJSUFN27cQFBQkNmpSB9//DEGDhyIe/fu\nYcOGDa47QCIieq7YNBARkVPOnj2LnJwcCIKArVu3mt1vwdvbGykpKVAoFDhx4oRT+xj4wTcRUdvF\npoGIiBxWX1+PhIQEAEBMTAyioqIs5qhUKnz00UcAgK1bt6K6utqh5269t4GIiNoW7mkgIiIiIiJJ\n/KSBiIiIiIgksWkgIiIiIiJJbBqIiIiIiEgSmwYiIiIiIpLEpoGIiIiIiCSxaSAiIiIiIklsGoiI\niIiISBKbBiIiIiIiksSmgYiIiIiIJLFpICIiIiIiSWwaiIiIiIhIEpsGIiIiIiKSxKaBiIiIiIgk\nsWkgIiIiIiJJbBqIiIiIiEgSmwYiIiIiIpLEpoGIiIiIiCT9D5VTAtjQb+SuAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75ac851250\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 167,
              "width": 390
            },
            "tags": [
              "id4_content_1",
              "outputarea_id4",
              "user_output"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"9625abde-a254-11e9-86b7-b3b4ddf7ea5c\"] = google.colab.output.setActiveOutputArea(window[\"95696c58-a254-11e9-86b7-b3b4ddf7ea5c\"]);\n",
              "//# sourceURL=js_c4f8425fb5"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75adfd8f10\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_1",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"962632e8-a254-11e9-86b7-b3b4ddf7ea5c\"] = google.colab.output.getActiveOutputArea();\n",
              "//# sourceURL=js_7decddbfdb"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75acf29b90\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_2",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"962661fa-a254-11e9-86b7-b3b4ddf7ea5c\"] = document.querySelector(\"#id4_content_2\");\n",
              "//# sourceURL=js_3c7656f4a7"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75adfd8410\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_2",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"96268aae-a254-11e9-86b7-b3b4ddf7ea5c\"] = google.colab.output.setActiveOutputArea(window[\"962661fa-a254-11e9-86b7-b3b4ddf7ea5c\"]);\n",
              "//# sourceURL=js_8f8ab63579"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75adfd8390\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_2",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"9626bdbc-a254-11e9-86b7-b3b4ddf7ea5c\"] = window[\"id4\"].setSelectedTabIndex(2);\n",
              "//# sourceURL=js_f4ecf74aa0"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75adfd8f10\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_2",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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upVKJ2bNn45133lG/ZmVlhZEjRwK4e2Xl+vXr6uWIVVcTBEFAaGgo7OzsEB0d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\n7t27p7fd0LcaD3+zYKiPZn/Fo/slfv75ZwDtS5/q6+sNzk2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            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75ac65eb50\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 167,
              "width": 390
            },
            "tags": [
              "id4_content_2",
              "outputarea_id4",
              "user_output"
            ]
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "application/javascript": [
              "window[\"9656e8f2-a254-11e9-86b7-b3b4ddf7ea5c\"] = google.colab.output.setActiveOutputArea(window[\"962632e8-a254-11e9-86b7-b3b4ddf7ea5c\"]);\n",
              "//# sourceURL=js_9a005382d3"
            ],
            "text/plain": [
              "\u003cIPython.core.display.Javascript at 0x7f75acc0f450\u003e"
            ]
          },
          "metadata": {
            "tags": [
              "id4_content_2",
              "outputarea_id4"
            ]
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def show_hist(name):\n",
        "  plt.figure(figsize=(6, 2))\n",
        "  plt.hist(\n",
        "      df.loc[df['treatment'] == 1, name],\n",
        "      bins=20,\n",
        "      alpha=0.4,\n",
        "      color='#00BFC4',\n",
        "      label='treated',\n",
        "      edgecolor='none')\n",
        "  plt.hist(\n",
        "      df.loc[df['treatment'] == 0, name],\n",
        "      bins=20,\n",
        "      alpha=0.4,\n",
        "      color='#F8766D',\n",
        "      label='control',\n",
        "      edgecolor='none')\n",
        "  plt.xlabel(name)\n",
        "  plt.legend(loc='upper left', prop={'size': 12})\n",
        "  plt.show()\n",
        "\n",
        "tb = widgets.TabBar(['covariates', 'transformed_covariates', 'outcome'])\n",
        "with tb.output_to('covariates'):\n",
        "  for name in [\"z1\", \"z2\", \"z3\", \"z4\"]:\n",
        "    show_hist(name)\n",
        "\n",
        "with tb.output_to('transformed_covariates'):\n",
        "  for name in [\"x1\", \"x2\", \"x3\", \"x4\"]:\n",
        "    show_hist(name)\n",
        "\n",
        "with tb.output_to('outcome'):\n",
        "  show_hist(\"outcome\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "X1D4OBiEZhnT"
      },
      "source": [
        "## Correctly Specified Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "5gUCcNuhcSBf"
      },
      "source": [
        "We run the simulation $1000$ times under correctly specified logistic propensity score. For each simulation, the treatment group was weighted so that it matches the population in terms of their covariate distributions.\n",
        "The estimator is the weighted value of $y$ in the treatment group."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "0lcgAuqwiVLv"
      },
      "outputs": [],
      "source": [
        "def estimate_mean(formula):\n",
        "  simulation = ec.data.kang_schafer.Simulation(size=1000)\n",
        "\n",
        "  t = simulation.treatment\n",
        "  y = simulation.outcome\n",
        "\n",
        "  df = pd.DataFrame(\n",
        "      np.column_stack(\n",
        "          [simulation.covariates, simulation.transformed_covariates]))\n",
        "  df.columns = [\"z1\", \"z2\", \"z3\", \"z4\", \"x1\", \"x2\", \"x3\", \"x4\"]\n",
        "  x = patsy.dmatrix(formula, df, return_type=\"dataframe\").values\n",
        "\n",
        "  weights = ec.from_formula(formula=formula,\n",
        "                            df=df.loc[t==1],\n",
        "                            target_df=df)[0]\n",
        "\n",
        "  return np.mean(np.sum(y[t == 1] * weights))\n",
        "\n",
        "def show_estimates(estimates):\n",
        "  estimates = pd.Series(estimates)\n",
        "  ax = estimates.hist(bins=20, alpha=0.8, edgecolor='none')\n",
        "  plt.axvline(estimates.mean(), linestyle='dashed', color='red')\n",
        "  # True population mean is 210.\n",
        "  print('bias is {}'.format(estimates.mean() - 210.))\n",
        "  print('rmse is {}'.format(np.sqrt(np.mean((estimates - 210.) ** 2))))\n",
        "\n",
        "estimates_correct = [estimate_mean(\"-1 + z1 + z2 + z3 + z4\") for i in xrange(1000)]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "f0VIHhXycouh"
      },
      "source": [
        "With correctly specified covariates to match ($Z1, \\dots, Z4$),\n",
        "the bias is smaller and the RMSE is better than any of the methods in the Kang \u0026 Schafer paper, where the best RMSE was 1.17."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "height": 313
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 648,
          "status": "ok",
          "timestamp": 1562683458497,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "th6PXxYBnK6M",
        "outputId": "4f70f806-ab4f-4852-927a-8ecffcc09e98"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "bias is 0.0350477677586\n",
            "rmse is 1.13484576048\n"
          ]
        },
        {
          "data": {
            "image/png": 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ra6vmz5+vN954Q4WFhdqwYYO3T1lZmTwej2JjY1VSUuKd4T958qTy8vK0detW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\nERFpCAt8IiIiIiIN+R/6cEJJc1vadwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75b0b10fd0\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 262,
              "width": 380
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "show_estimates(estimates_correct)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "0zuCvTGVdMVj"
      },
      "source": [
        "## Misspecified Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "sA_480Flh5gz"
      },
      "source": [
        "If the transformed covariates are observed in place of the true covariates, aka the propensity score model is misspecified, the estimate is no long un-biased."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "ReZeU-vUdk-j"
      },
      "outputs": [],
      "source": [
        "estimates_miss = [estimate_mean(\"-1 + x1 + x2 + x3 + x4\") for i in xrange(1000)]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "height": 313
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 505,
          "status": "ok",
          "timestamp": 1562683625422,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "O1mUMQqFq4XI",
        "outputId": "c80cbe21-47a9-41d9-b505-ee8a351d56e3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "bias is -1.96987818018\n",
            "rmse is 2.48825392824\n"
          ]
        },
        {
          "data": {
            "image/png": 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SvvGNb+gb3/jGefWZPXu2Zs+eHaCKAAAAgL4pJAI+AMB8G9LnOl0CAIQFAj4A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\nSUVORK5CYII=\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75ad202790\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 262,
              "width": 380
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "show_estimates(estimates_miss)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "y4uYEPCnoUzG"
      },
      "source": [
        "## Adding transformations of covariates\n",
        "\n",
        "One reasonable strategy is to expand the set of balancing covariates and hope it will make the model less \"misspecified\". If we additional balance the two-way interactions and the log transformation, the bias indeed reduces."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "eY4OL0uFmbgk"
      },
      "outputs": [],
      "source": [
        "formula = (\"-1 + (x1 + x2 + x3 + x4)**2 + I(np.log(x1)) + I(np.log(x2)) + \"\n",
        "           \"I(np.log(x3)) + I(np.log(x4))\")\n",
        "estimates_expanded = [estimate_mean(formula) for i in xrange(1000)]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "height": 313
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 591,
          "status": "ok",
          "timestamp": 1562683799445,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "o9TjJbMIq8dv",
        "outputId": "093e5796-fb0e-48c0-c71b-37702fee6473"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "bias is -0.84544280528\n",
            "rmse is 1.59210353659\n"
          ]
        },
        {
          "data": {
            "image/png": 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oOTlZYWFhqqys1PLly7V3716tWbOG4AAAAAB4iW2hweFwKDU1VQsX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\nQmCC\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75b3e84f10\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 262,
              "width": 390
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "show_estimates(estimates_expanded)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "1Ji6iROgDYfv"
      },
      "source": [
        "## Adding extra covariates\n",
        "If the model is misspecified in the sense that more covariates are included than necessary, the causal estimate remains unbiased."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "8ZsBSFkVB6-E"
      },
      "outputs": [],
      "source": [
        "formula = \"-1 + z1 + z2 + z3 + z4 + x1 + x2 + x3 + x4\"\n",
        "estimates_redundant = [estimate_mean(formula) for i in xrange(1000)]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "height": 313
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 607,
          "status": "ok",
          "timestamp": 1562683896766,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "gG0ToCi4rUzx",
        "outputId": "88c5d386-8349-4c48-e2cb-68b537f54e9b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "bias is -0.0523106606256\n",
            "rmse is 1.10923646003\n"
          ]
        },
        {
          "data": {
            "image/png": 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AABgRGgAAAAAYERoAAAAAGPH0JHQJ83M3q76hQZIU+sZmn+yTZzID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\nGFEaAAAAABhRGgAAAAAYURoAAAAAGL0DKZ6bQI0TiSwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7f75acb1f3d0\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 262,
              "width": 390
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "show_estimates(estimates_redundant)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ITCnSqDiyjIx"
      },
      "source": [
        "## Benchmark Execution Time"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "IknZ8jA51hbE"
      },
      "source": [
        "The execution time is generally linear with respect to the sample size."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 35
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 5883,
          "status": "ok",
          "timestamp": 1543857037021,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 300
        },
        "id": "gJ2OIBsxIxLk",
        "outputId": "a0c5423c-af21-4188-8c35-59bdef6b39e5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1000 loops, best of 3: 1.42 ms per loop\n"
          ]
        }
      ],
      "source": [
        "np.random.seed(123)\n",
        "simulation = ec.data.kang_schafer.Simulation(size=2000)\n",
        "x1 = simulation.covariates[simulation.treatment == 1]\n",
        "x0 = simulation.covariates[simulation.treatment == 0]\n",
        "%timeit weights = ec.maybe_exact_calibrate(x0, x1)[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 35
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 3943,
          "status": "ok",
          "timestamp": 1543857041017,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 300
        },
        "id": "pIdIjcpi077X",
        "outputId": "ce6d7d80-c030-44f3-88e9-a01946a0936c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "100 loops, best of 3: 9.51 ms per loop\n"
          ]
        }
      ],
      "source": [
        "np.random.seed(123)\n",
        "simulation = ec.data.kang_schafer.Simulation(size=20000)\n",
        "x1 = simulation.covariates[simulation.treatment == 1]\n",
        "x0 = simulation.covariates[simulation.treatment == 0]\n",
        "%timeit weights = ec.maybe_exact_calibrate(x0, x1)[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 35
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 4451,
          "status": "ok",
          "timestamp": 1543857045531,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 300
        },
        "id": "PlH1wW8Z1KIr",
        "outputId": "67ced1af-1322-4886-d90e-460ee1b097b1"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "10 loops, best of 3: 103 ms per loop\n"
          ]
        }
      ],
      "source": [
        "np.random.seed(123)\n",
        "simulation = ec.data.kang_schafer.Simulation(size=200000)\n",
        "x1 = simulation.covariates[simulation.treatment == 1]\n",
        "x0 = simulation.covariates[simulation.treatment == 0]\n",
        "%timeit weights = ec.maybe_exact_calibrate(x0, x1)[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "height": 35
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 6375,
          "status": "ok",
          "timestamp": 1543857051962,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 300
        },
        "id": "jik1dMgh1TRw",
        "outputId": "62d88767-94a1-44b0-b110-6d2c9d00b294"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1 loops, best of 3: 1.42 s per loop\n"
          ]
        }
      ],
      "source": [
        "np.random.seed(123)\n",
        "simulation = ec.data.kang_schafer.Simulation(size=2000000)\n",
        "x1 = simulation.covariates[simulation.treatment == 1]\n",
        "x0 = simulation.covariates[simulation.treatment == 0]\n",
        "%timeit weights = ec.maybe_exact_calibrate(x0, x1)[0]"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "last_runtime": {
        "build_target": "//research/colab/notebook:notebook_backend",
        "kind": "private"
      },
      "name": "kang_schafer_population_mean.ipynb",
      "provenance": [],
      "version": "0.3.2"
    },
    "kernelspec": {
      "display_name": "Python 2",
      "name": "python2"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}