notebooks/causal_inference_kang_schafer.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "cellView": "form",
        "id": "O7Smg5SYGqvY"
      },
      "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": {
        "id": "RYsS3JrpHaJI"
      },
      "source": [
        "# Causal Inference of Kang-Schafer simulation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s_FngMAZGxLG"
      },
      "source": [
        "<table align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/google/empirical_calibration/blob/master/notebooks/causal_inference_kang_schafer.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/google/empirical_calibration/blob/master/notebooks/causal_inference_kang_schafer.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "toc",
        "id": "FDLqKjdKKZMV"
      },
      "source": [
        ">[Causal Inference of Kang-Schafer simulation.](#scrollTo=RYsS3JrpHaJI)\n",
        "\n",
        ">>[Imports](#scrollTo=VGDMBD7TRIf4)\n",
        "\n",
        ">>[Correctly Specified Model](#scrollTo=X1D4OBiEZhnT)\n",
        "\n",
        ">>[Misspecified Model](#scrollTo=0zuCvTGVdMVj)\n",
        "\n",
        ">>[Benchmark Execution Time](#scrollTo=ITCnSqDiyjIx)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XhdK9tifRPYR"
      },
      "source": [
        "We illustrate empirical calibration to estimate the average treatment effect on the treated (ATT) on Kang-Schafer simulation under both correctly specified and misspecified models, and benchmark the execution time.  For details of simulation setup, please refer to [kang_schafer_population_mean.ipynb](./kang_schafer_population_mean.ipynb)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VGDMBD7TRIf4"
      },
      "source": [
        "## Imports"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "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",
        "import timeit\n",
        "\n",
        "# install and import ec\n",
        "!pip install -q git+https://github.com/google/empirical_calibration\n",
        "import empirical_calibration as ec\n",
        "\n",
        "sns.set_style('whitegrid')\n",
        "%config InlineBackend.figure_format='retina'\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X1D4OBiEZhnT"
      },
      "source": [
        "## Correctly Specified Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5gUCcNuhcSBf"
      },
      "source": [
        "We run the simulation 1000 times under correctly specified logistic propensity score and linear outcome regression. For each simulation we estimate the average treatment effect on the treated (ATT) using empirical calibration."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "0lcgAuqwiVLv"
      },
      "outputs": [],
      "source": [
        "def estimate_att(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",
        "\n",
        "  weights = ec.maybe_exact_calibrate(covariates=x[t == 0],\n",
        "                                     target_covariates=x[t == 1])[0]\n",
        "\n",
        "  return (np.mean(y[t == 1]) - np.mean(y[t == 0]),\n",
        "          np.mean(y[t == 1]) - np.sum(y[t == 0] * weights))\n",
        "\n",
        "\n",
        "def show_estimates(estimates, col='weighted'):\n",
        "  ax = estimates[col].hist(bins=20, alpha=0.8, edgecolor='none')\n",
        "  plt.axvline(estimates[col].mean(), linestyle='dashed', color='red')\n",
        "  print('bias of {} is {}'.format(col, estimates[col].mean()))\n",
        "  print('rmse of {} is {}'.format(col, np.sqrt(np.mean((estimates[col] - 0.) ** 2))))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "qgVOrpBNN0AP"
      },
      "outputs": [],
      "source": [
        "estimates = pd.DataFrame(\n",
        "    [estimate_att(\"-1 + z1 + z2 + z3 + z4\") for i in range(1000)])\n",
        "estimates.columns = ['raw', 'weighted']"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f0VIHhXycouh"
      },
      "source": [
        "The mean of the 1000 ATT estimates after weight correction is very close to the true zero ATT."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "height": 465,
          "base_uri": "https://localhost:8080/"
        },
        "id": "th6PXxYBnK6M",
        "outputId": "3f26f455-bea3-4cef-f189-59fb34e66ba6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "bias of raw is -20.091962742537778\n",
            "rmse of raw is 20.21367826477308\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 559,
              "height": 413
            }
          }
        }
      ],
      "source": [
        "show_estimates(estimates,'raw')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "height": 465,
          "base_uri": "https://localhost:8080/"
        },
        "id": "irPv3UCLLMeu",
        "outputId": "5b007331-ce6b-48ba-b50e-3fd13bc120ba"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "bias of weighted is 0.005794534933450649\n",
            "rmse of weighted is 0.08224360636460012\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 557,
              "height": 413
            }
          }
        }
      ],
      "source": [
        "show_estimates(estimates,'weighted')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0zuCvTGVdMVj"
      },
      "source": [
        "## Misspecified Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sA_480Flh5gz"
      },
      "source": [
        "If the transformed covariates are observed in place of the true covariates, both the propensity score model and outcome regression model become misspecified. We run 1000 simulations and for each simulation estimate the ATT by balancing the transformed covariates. The causal estimate is no longer unbiased."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "ReZeU-vUdk-j"
      },
      "outputs": [],
      "source": [
        "estimates_miss = pd.DataFrame([estimate_att(\"-1 + x1 + x2 + x3 + x4\") for i in range(1000)])\n",
        "estimates_miss.columns = ['raw', 'weighted']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "height": 465,
          "base_uri": "https://localhost:8080/"
        },
        "id": "O1mUMQqFq4XI",
        "outputId": "40b1279e-5c90-4ad6-eaf7-5742fc882583"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "bias of weighted is -6.162263108668607\n",
            "rmse of weighted is 6.272858880439236\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 552,
              "height": 413
            }
          }
        }
      ],
      "source": [
        "show_estimates(estimates_miss)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y4uYEPCnoUzG"
      },
      "source": [
        "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": 9,
      "metadata": {
        "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",
        "\n",
        "estimates_expanded = pd.DataFrame([estimate_att(formula) for i in range(1000)])\n",
        "estimates_expanded.columns = ['raw', 'weighted']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "height": 465,
          "base_uri": "https://localhost:8080/"
        },
        "id": "o9TjJbMIq8dv",
        "outputId": "05336858-7298-4a1f-9fed-fe756bc4f05f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "bias of weighted is -2.5052361452961387\n",
            "rmse of weighted is 2.7081656787473634\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 552,
              "height": 413
            }
          }
        }
      ],
      "source": [
        "show_estimates(estimates_expanded)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1Ji6iROgDYfv"
      },
      "source": [
        "If the model was misspecified in the sense that more covariates are included than necessary, the causal estimate remains unbiased."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "8ZsBSFkVB6-E"
      },
      "outputs": [],
      "source": [
        "formula = \"-1 + z1 + z2 + z3 + z4 + x1 + x2 + x3 + x4\"\n",
        "estimates_redundant = pd.DataFrame([estimate_att(formula) for i in range(1000)])\n",
        "estimates_redundant.columns = ['raw', 'weighted']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "height": 465,
          "base_uri": "https://localhost:8080/"
        },
        "id": "gG0ToCi4rUzx",
        "outputId": "84eac6a5-d2ff-4d02-b8a6-25596b4e17bc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "bias of weighted is -0.0012267953075457286\n",
            "rmse of weighted is 0.08620366239711337\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 552,
              "height": 413
            }
          }
        }
      ],
      "source": [
        "show_estimates(estimates_redundant)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ITCnSqDiyjIx"
      },
      "source": [
        "## Benchmark Execution Time"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IknZ8jA51hbE"
      },
      "source": [
        "The execution time is generally linear with respect to the sample size. With 1 million control units, it takes around 1 second to find the weights."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i21mXoaxywOn",
        "outputId": "a45574ae-ac01-45ac-9038-8c19148013b4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count    100.000000\n",
              "mean       0.001002\n",
              "std        0.000186\n",
              "min        0.000901\n",
              "25%        0.000933\n",
              "50%        0.000939\n",
              "75%        0.000974\n",
              "max        0.001920\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "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",
        "pd.Series(timeit.repeat(\n",
        "    'ec.maybe_exact_calibrate(x0, x1)',\n",
        "    setup='from __main__ import x1, x0, ec',\n",
        "    repeat=100,\n",
        "    number=1)).describe()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pIdIjcpi077X",
        "outputId": "ebf4ea66-dccd-42c8-fd53-4498b50cc7b5"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "count    100.000000\n",
              "mean       0.004682\n",
              "std        0.003315\n",
              "min        0.003733\n",
              "25%        0.003964\n",
              "50%        0.003999\n",
              "75%        0.004146\n",
              "max        0.035557\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "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",
        "pd.Series(timeit.repeat(\n",
        "    'ec.maybe_exact_calibrate(x0, x1)',\n",
        "    setup='from __main__ import x1, x0, ec',\n",
        "    repeat=100,\n",
        "    number=1)).describe()"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "bWxGbsZuFPgy"
      },
      "execution_count": 14,
      "outputs": []
    }
  ],
  "metadata": {
    "colab": {
      "name": "causal_inference_kang_schafer.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 2",
      "name": "python2"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}