Box Cox transformation.ipynb

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    "## Box Cox Transformation\n",
    "\n",
    "A Box Cox transformation is a transformation of non-normal dependent variables into a normal shape. \n",
    "Box and Cox proposed a parametric power transformation technique defined by a single parameter λ, aimed at reducing anomalies in the data and ensuring that the usual assumptions for a linear model hold. This transformation results from modifying the family of power transformations defined by Tukey  to account for the discontinuity at λ = 0.\n",
    "\n",
    "Let $y=(y_1,y_2,…,y_n)$ be the data on which the Box–Cox transformation is to be applied. Box and Cox defined their transformation as\n",
    "\n",
    "for $\\lambda \\neq 0$:\n",
    "\n",
    "$$\n",
    "y{(i)}^{\\lambda}=\\frac{1}{\\lambda}*(y_{i}^{\\lambda}-1)    \n",
    "$$\n",
    "\n",
    "for $\\lambda = 0$\n",
    "\n",
    "$$\n",
    "log(y_i)  \n",
    "$$\n",
    "\n",
    "such that, for unknown $\\lambda$,\n",
    "\n",
    "$$\n",
    "y^\\lambda=X* \\beta + \\epsilon\n",
    "$$\n",
    "\n",
    "where $y^{(\\lambda)}$ is the $\\lambda$-transformed data, X is the design matrix (possible covariates of interest), $\\beta$ is the set of parameters associated with the $\\lambda$-transformed data, and ϵ = (ϵ1, ϵ2, …, ϵn) is the error term. Since the aim of Equation (1) is that\n",
    "\n",
    "$$\n",
    "y^{(\\lambda)} \\epsilon ~ N(X* \\beta, \\sigma^2*I_n),    (3)\n",
    "$$\n",
    "then $\\epsilon ~ N(0, \\sigma^2)$. Note that the transformation in Equation (1) is only valid for $y_i$ > 0, i = 1, 2, …, n, and modifications have to be made when negative observations are present."
   ]
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from scipy.stats import boxcox"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c98c234a",
   "metadata": {},
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "plt.figure(figsize = (4, 4))\n",
    "data = np.random.beta(1, 3, 5000) # we create random non normal data (from beta distribution)\n",
    "sns.distplot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "50669b91",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Transformed data into normal distibution: [-2.01054071 -1.79406199 -1.0597953  ... -1.65388475 -0.92313735\n",
      " -1.69962455]\n",
      "================================================================================\n",
      "Lambda that maximizes the log-likelihood function for normal distribution: 0.39321032751806273\n"
     ]
    }
   ],
   "source": [
    "data_transformed, lambda_ = boxcox(data) #If the lambda parameter is None, the second returned argument is the \n",
    "# lambda that maximizes the log-likelihood function.\n",
    "print('Transformed data into normal distibution:', data_transformed)\n",
    "print(40*'==')\n",
    "print('Lambda that maximizes the log-likelihood function for normal distribution:', lambda_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "466f6d23",
   "metadata": {},
   "outputs": [],
   "source": [
    "manually_transformed = [(i**lambda_ -1)/lambda_ for i in data] # manual implementation of the formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5b3846ec",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "warnings.filterwarnings('ignore')\n",
    "plt.figure(figsize = (4, 4))\n",
    "sns.distplot(data_transformed)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2c3060cd",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "warnings.filterwarnings('ignore')\n",
    "plt.figure(figsize = (4, 4))\n",
    "sns.distplot(manually_transformed) # manually transformed vector with the calculatet best lambda parameter\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9b7d845f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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h1CxFWcJBiddiEDVExGpgNYCk9ohozvD+o5I/3+g2lj+fpPYsdVl2K0rAjIrl6cDeQdSY2SiSJRy2AI2SZkn6BXA5sL5PzXrg6vJZi7OAAxGxr++GzGz0qLpbERGHJa0AXgPGA09ExG5JN5TXtwIbgYuBTuAgsDzDe68edNejgz/f6DaWP1+mz6aIow4NmJl5hqSZpTkczCyp0HCQ9J+SPilPuV4raXKR/eRN0j9K2i3p/ySNidNi1abSj3aSnpD09VicgyNphqQ2SR3lf5e3Hqu+6JHD68DciPh74H+Afyu4n7ztAv4B2FR0I3momEp/EXA6cIWk04vtKndPARcW3USNHAZuj4jZwFnAzcf6+ys0HCLivyPicHnxfXrmR4wZEdEREZ8W3UeOskylH9UiYhPwTdF91EJE7IuIbeXn3wEd9MxkTip65FDpn4FXi27Cjqm/afI2ykhqAM4APuivpuaXiZP0BnBSYtXvImJdueZ39Ax51tS6n7xl+XxjSKZp8jaySZoEvAjcFhHf9ldX83CIiF8fa72kfwKWAotjFE66qPb5xhhPkx/lJNXREwxrIuKlY9UWfbbiQuBfgd9GxMEie7FMskyltxFKkoDHgY6IeKhafdHHHFYBxwOvS9ouqbXgfnIl6VJJJeBsYIOk14ruaSjKB4+PTKXvAP4YEbuL7Spfkp4F3gNOlVSS9C9F95Sjc4CrgEXl/2/bJV3cX7GnT5tZUtEjBzMboRwOZpbkcDCzJIeDmSU5HMwsyeFgZkkOBzNL+n/nDrqxk5REVAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambde = [-4,-2,-1,0.5,1,2,4] # only for lambda 0.5 we got transformed distribution that is normal\n",
    "x = np.linspace(data.min(), data.max(), 5000)\n",
    "for l in lambde:\n",
    "    transformed = [(i**l -1)/l for i in data]\n",
    "    plt.figure(figsize=(4,4))\n",
    "    plt.hist(data, bins=20, density=True)\n",
    "    plt.hist(transformed, bins=30, density=True, label = f'lambda: {l}')\n",
    "    plt.xlim(-2, 2)\n",
    "    plt.legend()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}