pyGAM_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An example of additive model in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Xu Ren"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'm a graduate student in Statistics. Now I'm working on some additive models. Additive model is an extension of linear regression model. In linear regression we assume the effect of each variable is linear, while in additive model we are trying to model the nonlinear effect of variables. i.e.\n",
    "\n",
    "Linear regression: $\\text{E}[y|X] = \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ... + \\beta_p X_p$\n",
    "\n",
    "Additive model: $\\text{E}[y|X] = \\beta_0 + f_1(X_1) + f_2(X_2) + ... + f_p(X_p)$\n",
    "\n",
    "where $f_1$, $f_2$, ..., $f_p$ are nonlinear functions like spline or local regression.\n",
    "\n",
    "In this notebook, I'm trying to fit additive model on an example dataset, namely boston housing data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pygam import LinearGAM\n",
    "from pygam.utils import generate_X_grid\n",
    "import pandas as pd \n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'm going to use boston housing data as an example to fit an additive model. First import dataset and explore it a little bit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n",
       "       'TAX', 'PTRATIO', 'B', 'LSTAT'],\n",
       "      dtype='<U7')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston = load_boston()\n",
    "boston.feature_names  ## these are the independent variables (predictors) in boston dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.02985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.430</td>\n",
       "      <td>58.7</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.12</td>\n",
       "      <td>5.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.08829</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.012</td>\n",
       "      <td>66.6</td>\n",
       "      <td>5.5605</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>395.60</td>\n",
       "      <td>12.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.14455</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.172</td>\n",
       "      <td>96.1</td>\n",
       "      <td>5.9505</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>19.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.21124</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>5.631</td>\n",
       "      <td>100.0</td>\n",
       "      <td>6.0821</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>386.63</td>\n",
       "      <td>29.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.17004</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.004</td>\n",
       "      <td>85.9</td>\n",
       "      <td>6.5921</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>15.2</td>\n",
       "      <td>386.71</td>\n",
       "      <td>17.10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM    AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575   65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421   78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185   61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998   45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147   54.2  6.0622  3.0  222.0   \n",
       "5  0.02985   0.0   2.18   0.0  0.458  6.430   58.7  6.0622  3.0  222.0   \n",
       "6  0.08829  12.5   7.87   0.0  0.524  6.012   66.6  5.5605  5.0  311.0   \n",
       "7  0.14455  12.5   7.87   0.0  0.524  6.172   96.1  5.9505  5.0  311.0   \n",
       "8  0.21124  12.5   7.87   0.0  0.524  5.631  100.0  6.0821  5.0  311.0   \n",
       "9  0.17004  12.5   7.87   0.0  0.524  6.004   85.9  6.5921  5.0  311.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  \n",
       "5     18.7  394.12   5.21  \n",
       "6     15.2  395.60  12.43  \n",
       "7     15.2  396.90  19.15  \n",
       "8     15.2  386.63  29.93  \n",
       "9     15.2  386.71  17.10  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## convert predictors into a dataframe\n",
    "X_df = pd.DataFrame(boston.data)\n",
    "X_df.columns = boston.feature_names\n",
    "X_df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## This is the housing price. \n",
    "y = pd.Series(boston.target)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the dataset is ready, we are going to fit the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100% (11 of 11) |########################| Elapsed Time: 0:00:02 Time:  0:00:02\n"
     ]
    }
   ],
   "source": [
    "fit = LinearGAM().gridsearch(X_df, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a summary of fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LinearGAM                                                                                                 \n",
      "=============================================== ==========================================================\n",
      "Distribution:                        NormalDist Effective DoF:                                      89.441\n",
      "Link Function:                     IdentityLink Log Likelihood:                                  -1616.431\n",
      "Number of Samples:                          506 AIC:                                              3413.744\n",
      "                                                AICc:                                            3453.6419\n",
      "                                                GCV:                                                13.538\n",
      "                                                Scale:                                              9.3128\n",
      "                                                Pseudo R-Squared:                                   0.9092\n",
      "==========================================================================================================\n",
      "Feature Function   Data Type      Num Splines   Spline Order  Linear Fit  Lambda     P > x      Sig. Code \n",
      "================== ============== ============= ============= =========== ========== ========== ==========\n",
      "feature 1          numerical      25            3             False       3.9811     1.63e-12   ***       \n",
      "feature 2          numerical      25            3             False       3.9811     1.06e-01             \n",
      "feature 3          numerical      25            3             False       3.9811     1.20e-02   *         \n",
      "feature 4          categorical    2             0             False       3.9811     1.44e-01             \n",
      "feature 5          numerical      25            3             False       3.9811     1.11e-16   ***       \n",
      "feature 6          numerical      25            3             False       3.9811     1.11e-16   ***       \n",
      "feature 7          numerical      25            3             False       3.9811     8.67e-01             \n",
      "feature 8          numerical      25            3             False       3.9811     2.22e-15   ***       \n",
      "feature 9          numerical      25            3             False       3.9811     4.39e-03   **        \n",
      "feature 10         numerical      25            3             False       3.9811     5.80e-08   ***       \n",
      "feature 11         numerical      25            3             False       3.9811     1.53e-04   ***       \n",
      "feature 12         numerical      25            3             False       3.9811     9.13e-02   .         \n",
      "feature 13         numerical      25            3             False       3.9811     1.11e-16   ***       \n",
      "intercept                                                                            6.66e-16   ***       \n",
      "==========================================================================================================\n",
      "Significance codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "WARNING: Fitting splines and a linear function to a feature introduces a model identifiability problem\n",
      "         which can cause p-values to appear significant when they are not.\n",
      "\n",
      "WARNING: p-values calculated in this manner behave correctly for un-penalized models or models with\n",
      "         known smoothing parameters, but when smoothing parameters have been estimated, the p-values\n",
      "         are typically lower than they should be, meaning that the tests reject the null too readily.\n"
     ]
    }
   ],
   "source": [
    "fit.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### There are 13 variables in total, but here we only show the nonlinear relationship of 3 of them. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## generate X values for prediction and plots\n",
    "Xgrid = generate_X_grid(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# partial_dependence function returns the predicted values and confidence intervals\n",
    "# we make prediction on the first 3 predictors\n",
    "pred1,confi1 = fit.partial_dependence(Xgrid, feature = 1, width = 0.95)\n",
    "pred2,confi2 = fit.partial_dependence(Xgrid, feature = 2, width = 0.95)\n",
    "pred3,confi3 = fit.partial_dependence(Xgrid, feature = 3, width = 0.95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make plots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zVAAfA+jg8TnjUtu23Dz66afz2WtHCuboo7k6Z9gwYMECoHlztmCMoqIHCa+b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MGdfe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\nZwNdu/q4oUrz5sDixcD559ua/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1091d3b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(311)\n",
    "plt.plot(Xgrid[:,0], pred1, c = 'r')\n",
    "plt.plot(Xgrid[:,0], confi1[0][:, 0], c = 'b', ls = '--')\n",
    "plt.plot(Xgrid[:,0], confi1[0][:, 1], c = 'b', ls = '--')\n",
    "plt.xlabel(\"CRIM\")\n",
    "\n",
    "plt.subplot(312)\n",
    "plt.plot(Xgrid[:,1], pred2, c = 'r')\n",
    "plt.plot(Xgrid[:,1], confi2[0][:, 0], c = 'b', ls = '--')\n",
    "plt.plot(Xgrid[:,1], confi2[0][:, 1], c = 'b', ls = '--')\n",
    "plt.xlabel(\"ZN\")\n",
    "\n",
    "plt.subplot(313)\n",
    "plt.plot(Xgrid[:,2], pred3, c = 'r')\n",
    "plt.plot(Xgrid[:,2], confi3[0][:, 0], c = 'b', ls = '--')\n",
    "plt.plot(Xgrid[:,2], confi3[0][:, 1], c = 'b', ls = '--')\n",
    "plt.xlabel(\"INDUS\")\n",
    "\n",
    "f = plt.gcf()\n",
    "f.set_size_inches(6,20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plots, we can see that additive model allow us to model the nonlinear trend. It is more flexible than linear regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'm familiar with additive models, but this is my first time to run additive models in Python. I used to do it in R using mgcv package, but of course there are more things to explore in Python. This is just a start, and I will continue to do some more things in the future."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "1.Pablo Oberhauser.\n",
    "pyGAM : Getting Started with Generalized Additive Models in Python \n",
    "https://codeburst.io/pygam-getting-started-with-generalized-additive-models-in-python-457df5b4705f\n",
    "\n",
    "2.Daniel Servén, & Charlie Brummitt. (2018, March 27). \n",
    "pyGAM: Generalized Additive Models in Python. Zenodo. DOI: 10.5281/zenodo.1208723\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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