Phylogenetic Generalised least squares.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.stats.power as smp\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import linalg\n",
    "\n",
    "from numpy.linalg import inv\n",
    "\n",
    "# Install seaborn typing `conda install seaborn`\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x=np.array([[1,1.02],[1,1.06],[1,0.96],[1,0.92],[1,0.89]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y=np.array([1.38,1.41,1.36,1.22,1.13])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b=(inv(x.T.dot(x))).dot((x.T.dot(y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.22923469,  1.57653061])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C=np.array([[3,2,1,1,0],[2,3,1,1,0],[1,1,3,2,0],[1,1,2,3,0],[0,0,0,0,3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 2, 1, 1, 0],\n",
       "       [2, 3, 1, 1, 0],\n",
       "       [1, 1, 3, 2, 0],\n",
       "       [1, 1, 2, 3, 0],\n",
       "       [0, 0, 0, 0, 3]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b=inv(x.T.dot(inv(C).dot(x))).dot(x.T).dot(inv(C).dot(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.2759995 ,  1.61590229])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x105f42ad0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x105f42ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x[:,1],y,'ro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = pd.DataFrame({'x':x[:,1],'y':y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.02</td>\n",
       "      <td>1.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.06</td>\n",
       "      <td>1.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.96</td>\n",
       "      <td>1.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.92</td>\n",
       "      <td>1.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.89</td>\n",
       "      <td>1.13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      x     y\n",
       "0  1.02  1.38\n",
       "1  1.06  1.41\n",
       "2  0.96  1.36\n",
       "3  0.92  1.22\n",
       "4  0.89  1.13"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tVW8qoh19ze/itpQlgz0Rb/tgZyXkPubYfcxxc7TFih7uaqSLW29PtF63PrfE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\n+vPjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113d6a750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"x\", y=\"y\", data=df);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "expected matrix",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-25-562db4f6b536>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mr\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlstsq\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m//anaconda/lib/python2.7/site-packages/scipy/linalg/basic.pyc\u001b[0m in \u001b[0;36mlstsq\u001b[0;34m(a, b, cond, overwrite_a, overwrite_b, check_finite, lapack_driver)\u001b[0m\n\u001b[1;32m    822\u001b[0m     \u001b[0mb1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_asarray_validated\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcheck_finite\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcheck_finite\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    823\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 824\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'expected matrix'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    825\u001b[0m     \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ma1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    826\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: expected matrix"
     ]
    }
   ],
   "source": [
    "r=linalg.lstsq(x[:,1], y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.02,  1.06,  0.96,  0.92,  0.89]),\n",
       " array([ 1.38,  1.41,  1.36,  1.22,  1.13]))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:,1], y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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