josef-pkt/ex_gam_bs_autos_cleaned.ipynb

## ex_gam_bs_autos_cleaned.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GAM example: Autos miles per gallon\n",
    "\n",
    "based on statsmodels.gam.tests.test_gam.TestGAMMPG\n",
    "\n",
    "This contains now the basic working version.\n",
    "\n",
    "\n",
    "We are here working with fixed penalization weights `alpha`. Selection of penalization weights is still incomplete."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import os\n",
    "\n",
    "import numpy as np\n",
    "from numpy.testing import assert_allclose\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "import patsy\n",
    "import patsy.splines as bspl\n",
    "import patsy.mgcv_cubic_splines as cspl\n",
    "\n",
    "from statsmodels.regression.linear_model import OLS\n",
    "from statsmodels.discrete.discrete_model import Poisson, Logit, Probit\n",
    "from statsmodels.genmod.generalized_linear_model import GLM\n",
    "from statsmodels.genmod.families import family\n",
    "from statsmodels.sandbox.regression.penalized import TheilGLS\n",
    "from statsmodels.base._penalized import PenalizedMixin\n",
    "import statsmodels.base._penalties as smpen\n",
    "\n",
    "from statsmodels.gam.smooth_basis import (BSplines, CubicSplines,\n",
    "                                          CyclicCubicSplines)\n",
    "from statsmodels.gam.gam import GLMGam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from statsmodels.gam.tests import test_gam\n",
    "from statsmodels.gam.tests.results import results_mpg_bs as res_mgcv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cur_dir = os.path.dirname(os.path.abspath(test_gam.__file__))\n",
    "\n",
    "file_path = os.path.join(cur_dir, \"results\", \"autos.csv\")\n",
    "df_autos_ = pd.read_csv(file_path)\n",
    "df_autos = df_autos_[['city_mpg', 'fuel', 'drive', 'weight', 'hp']].dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "file_path = os.path.join(cur_dir, \"results\", \"autos_predict.csv\")\n",
    "res_pred = pd.read_csv(file_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>city_mpg</th>\n",
       "      <th>fuel</th>\n",
       "      <th>drive</th>\n",
       "      <th>weight</th>\n",
       "      <th>hp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>21</td>\n",
       "      <td>gas</td>\n",
       "      <td>rwd</td>\n",
       "      <td>2548</td>\n",
       "      <td>111.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>21</td>\n",
       "      <td>gas</td>\n",
       "      <td>rwd</td>\n",
       "      <td>2548</td>\n",
       "      <td>111.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19</td>\n",
       "      <td>gas</td>\n",
       "      <td>rwd</td>\n",
       "      <td>2823</td>\n",
       "      <td>154.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>24</td>\n",
       "      <td>gas</td>\n",
       "      <td>fwd</td>\n",
       "      <td>2337</td>\n",
       "      <td>102.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18</td>\n",
       "      <td>gas</td>\n",
       "      <td>4wd</td>\n",
       "      <td>2824</td>\n",
       "      <td>115.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   city_mpg fuel drive  weight     hp\n",
       "0        21  gas   rwd    2548  111.0\n",
       "1        21  gas   rwd    2548  111.0\n",
       "2        19  gas   rwd    2823  154.0\n",
       "3        24  gas   fwd    2337  102.0\n",
       "4        18  gas   4wd    2824  115.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_autos.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "      <th>Row.names</th>\n",
       "      <th>fit</th>\n",
       "      <th>se_fit</th>\n",
       "      <th>fit_fuel</th>\n",
       "      <th>fit_drive</th>\n",
       "      <th>fit_s_weight_</th>\n",
       "      <th>fit_s_hp.</th>\n",
       "      <th>se.fit_fuel</th>\n",
       "      <th>se.fit_drive</th>\n",
       "      <th>se.fit_s_weight_</th>\n",
       "      <th>se.fit_s_hp.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td>-5.508351</td>\n",
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       "      <td>0.869684</td>\n",
       "      <td>1.132888</td>\n",
       "      <td>0.396038</td>\n",
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       "      <th>4</th>\n",
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       "   Row.names        fit    se_fit  fit_fuel  fit_drive  fit_s_weight_  \\\n",
       "0          1  21.004549  0.649519 -5.508351   0.349134      -0.902276   \n",
       "1          2  21.004549  0.649519 -5.508351   0.349134      -0.902276   \n",
       "2          3  17.547334  0.709550 -5.508351   0.349134      -0.884486   \n",
       "3          4  23.823625  0.549217 -5.508351   2.264275      -0.282829   \n",
       "4          5  20.597137  1.201011 -5.508351   0.000000      -0.886322   \n",
       "\n",
       "   fit_s_hp.  se.fit_fuel  se.fit_drive  se.fit_s_weight_  se.fit_s_hp.  \n",
       "0  -1.694105     0.869684      1.169621          0.488886      0.430747  \n",
       "1  -1.694105     0.869684      1.169621          0.488886      0.430747  \n",
       "2  -5.169110     0.869684      1.169621          0.607747      0.669556  \n",
       "3  -1.409616     0.869684      1.132888          0.396038      0.413609  \n",
       "4  -1.768336     0.869684      0.000000          0.607941      0.484633  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_pred.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The general model with a linear link function is\n",
    "\n",
    "$y = X \\beta + \\sum_k f_k(x_k) = X \\beta + \\sum_k \\sum_j b_{j,k} g_{j, k}(x_k)$\n",
    "\n",
    "Each nonparametric function $f_k$ is modeled as a linear combination of basis functions $g_{j, k}$\n",
    "\n",
    "$f_k(x_k) = \\sum_j b_{j,k} g_{j, k}(x_k)$\n",
    "\n",
    "The overall model is linear in parameters and can be estimated by a standard model like OLS or GLM. Patsy provides basis function for several types of splines that can be used with the formula interface in statsmodels. However, in this case we can use only a small number of basis functions relative to the number of observations to avoid overfitting.\n",
    "\n",
    "As alternative we can use penalization to avoid overfitting and impose more smoothness while at the same time increasing the number of knots. The importance of the spline basis function for the fit of the data then depends on the smoothing or penalization parameters and less on the total number of basis functions.\n",
    "\n",
    "This notebook illustrates the basic use case of a new class in statsmodels to fit generalized additive models, GAM, and penalized splines. The penalization is quadratic and similar to Ridge Regression, except that we penalize in most cases the integrated square of the second derivative of the function, and thus penalizing large fluctuations.\n",
    "\n",
    "The implementation is based on maximum penalized loglikeliood estimation. The full GAM features are currently only implemented for GLM, but a generic penalized MLE framework can use it for any type of models that directly minimize the negative loglikelihood.\n",
    "\n",
    "Currently two types of splines, B-splines and cyclic cubic splines, are available with similar features as and verfied against `mgcv` R package.\n",
    "\n",
    "**Current status:**  \n",
    "The core features are now verified against R mgcv, but currently only for linear Gaussian GLM.  \n",
    "API is still experimental, and some parts will still change, especially also in the internal API, i.e. API for penalization and spline classes.  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model that we are using has miles per gallon in city traffic `city_mpg` as the dependent variable.\n",
    "The first two explanatory variable, 'fuel' and 'drive' are treated as linear effects, both arecategorical variables.\n",
    "The effect of two continuous variables, 'weight' and horse power 'hp' are modeled by penalized B-splines.\n",
    "\n",
    "In the following we use patsy to create a design matrix for the constant and the categorical variables.\n",
    "The model will be estimated by GLMGam which takes an instance of an additive spline class as argument, so we need to create it first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# penalization weights are taken from mgcv to match up its results\n",
    "sp = np.array([0.830689464223685, 425.361212061649])\n",
    "s_scale = np.array([2.443955e-06, 0.007945455])\n",
    "\n",
    "\n",
    "x_spline = df_autos[['weight', 'hp']].values\n",
    "exog = patsy.dmatrix('fuel + drive', data=df_autos)\n",
    "\n",
    "# TODO: set `include_intercept=True` automatically if constraints='center'\n",
    "bs = BSplines(x_spline, df=[12, 10], degree=[3, 3], variable_names=['weight', 'hp'], \n",
    "              constraints='center', include_intercept=True)\n",
    "alpha = 1 / s_scale * sp / 2\n",
    "gam_bs = GLMGam(df_autos['city_mpg'], exog=exog, smoother=bs,\n",
    "                alpha=alpha)\n",
    "res1a = gam_bs.fit()  # default is pirls with use_t=False\n",
    "\n",
    "res1b = gam_bs.fit(method='newton', use_t=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The overall design matrix, `model.exog` has 24 columns, 4 for the linear component, 11 for the first and 9 for the second spline component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(203, 24)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gam_bs.exog.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'fuel[T.gas]', 'drive[T.fwd]', 'drive[T.rwd]']"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(exog.design_info)\n",
    "exog.design_info.column_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11, 9)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k_smooth0 = res1a.model.smoother.smoothers_[0].basis_.shape[1]\n",
    "k_smooth1 = res1a.model.smoother.smoothers_[1].basis_.shape[1]\n",
    "k_smooth0, k_smooth1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Currently the name handling is not finished. We create our own list of variable names and attach it to the model overwriting the automatically created names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept',\n",
       " 'fuel[T.gas]',\n",
       " 'drive[T.fwd]',\n",
       " 'drive[T.rwd]',\n",
       " 'weight0',\n",
       " 'weight1',\n",
       " 'weight2',\n",
       " 'weight3',\n",
       " 'weight4',\n",
       " 'weight5',\n",
       " 'weight6',\n",
       " 'weight7',\n",
       " 'weight8',\n",
       " 'weight9',\n",
       " 'weight10',\n",
       " 'hp0',\n",
       " 'hp1',\n",
       " 'hp2',\n",
       " 'hp3',\n",
       " 'hp4',\n",
       " 'hp5',\n",
       " 'hp6',\n",
       " 'hp7',\n",
       " 'hp8']"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xnames = exog.design_info.column_names + res1a.model.smoother.col_names\n",
    "xnames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Generalized Linear Model Regression Results                  \n",
      "==============================================================================\n",
      "Dep. Variable:               city_mpg   No. Observations:                  203\n",
      "Model:                         GLMGam   Df Residuals:                   185.10\n",
      "Model Family:                Gaussian   Df Model:                        16.90\n",
      "Link Function:               identity   Scale:                          4.7065\n",
      "Method:                         PIRLS   Log-Likelihood:                -435.89\n",
      "Date:                Tue, 13 Nov 2018   Deviance:                       871.17\n",
      "Time:                        12:24:38   Pearson chi2:                     871.\n",
      "No. Iterations:                     3   Covariance Type:             nonrobust\n",
      "================================================================================\n",
      "                   coef    std err          z      P>|z|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------\n",
      "Intercept       29.6273      1.107     26.755      0.000      27.457      31.798\n",
      "fuel[T.gas]     -6.2137      0.731     -8.501      0.000      -7.646      -4.781\n",
      "drive[T.fwd]     1.4399      0.803      1.794      0.073      -0.133       3.013\n",
      "drive[T.rwd]     1.0113      0.827      1.223      0.221      -0.610       2.632\n",
      "weight0         20.1054      3.459      5.812      0.000      13.325      26.886\n",
      "weight1         -1.2601      1.723     -0.731      0.465      -4.638       2.118\n",
      "weight2         -5.2687      1.346     -3.914      0.000      -7.907      -2.630\n",
      "weight3         -4.5440      1.129     -4.026      0.000      -6.756      -2.332\n",
      "weight4         -7.6006      1.238     -6.138      0.000     -10.027      -5.174\n",
      "weight5         -5.0104      1.251     -4.006      0.000      -7.462      -2.559\n",
      "weight6         -6.9623      1.326     -5.252      0.000      -9.560      -4.364\n",
      "weight7         -9.0672      1.463     -6.199      0.000     -11.934      -6.200\n",
      "weight8         -8.8183      2.087     -4.226      0.000     -12.908      -4.728\n",
      "weight9         -7.9146      2.448     -3.233      0.001     -12.713      -3.116\n",
      "weight10        -6.2807      1.577     -3.984      0.000      -9.371      -3.191\n",
      "hp0              5.0931      0.706      7.211      0.000       3.709       6.477\n",
      "hp1              1.9085      0.340      5.608      0.000       1.241       2.575\n",
      "hp2             -0.6462      0.439     -1.471      0.141      -1.507       0.215\n",
      "hp3             -1.5024      0.476     -3.157      0.002      -2.435      -0.570\n",
      "hp4             -4.1924      0.682     -6.151      0.000      -5.528      -2.857\n",
      "hp5             -5.7299      0.863     -6.641      0.000      -7.421      -4.039\n",
      "hp6             -6.8332      1.297     -5.268      0.000      -9.376      -4.291\n",
      "hp7             -5.7709      2.010     -2.871      0.004      -9.711      -1.831\n",
      "hp8             -4.2911      1.897     -2.262      0.024      -8.009      -0.573\n",
      "================================================================================\n"
     ]
    }
   ],
   "source": [
    "xnames = exog.design_info.column_names + res1a.model.smoother.col_names\n",
    "res1a.model.exog_names[:] = xnames\n",
    "\n",
    "# Note, we could also specify the parameter names directly for summary.\n",
    "# print(res1a.summary(xname=xnames))\n",
    "print(res1a.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The summary shows the usual GLM results. The parameters for the linear components can be interpreted as usually. However, the parameters for the spline basis functions do not have any clear interpretation. Specifically the original spline basis functions have been transformed to impose that the average prediction for each spline component is zero. However we can see that all except for two spline components are statistically significant and contribute to the fit.\n",
    "\n",
    "Even though we have 24 explanatory variables or columns in the design matrix, the effective number is smaller because of the penalization. In this case we see that the effective degrees of freedom, df_model plus 1 for the constant, is 17.9.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(185.09998586957269, 17.900014130427309)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1a.df_resid, res1a.df_model + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partial Prediction\n",
    "\n",
    "A better way to see the effect of the variable that underlies the spline is to look at partial prediction. The contribution of each spline component to the linear prediction is our estimate of the nonlinear function `f` in the description of the model.\n",
    "\n",
    "Partial prediction at the sample point can be obtained through the `partial_values` method. Instead of looking at those numbers we will provide the equivalent plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "part0, part0_se = res1a.partial_values(0)\n",
    "part1, part1_se = res1a.partial_values(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Partial Prediction Plot with CPR\n",
    "`cpr` is component plus residual. The following plots corresponds to a CCPR regression plot, available in statsmodels.graphics.\n",
    "\n",
    "This includes also the constant, so we get the additional uncertainty. Otherwise the confidence interval of the B-splines is zero at the first point because the first basis function has been dropped to have a nonsingular design matrix.\n",
    "\n",
    "We use resid_working for GLM. I'm not sure whether that makes sense for some link functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JiCTD+doWCKjtBM69AHzuvZ8aYV9TLOdhlPf+hSivLwRKhw8fTsuwn5LFxcUU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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb932e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = res1a.plot_partial(0, cpr=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6zZgqhP8RKeckOOfqOeeOAxoDU4G+QDnwZuA13vuvgAXAgDTbKXlut93gvPMS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\nAIApIQEAmBISAICp3+htmoURoEzkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x76c5f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = res1a.plot_partial(1, cpr=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot without cpr\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UX/XqtrjV/PnQtau9docOlvOwd2/pnlNEREqmpDkNTYBnsLyGGVithv7e+4+A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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf850be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = res1a.plot_partial(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/wZo1VgPmgw+sty8TKCRI0g0ZAocfbrs5Jnq3ROesJPKhh9rtVatsKOKXXxL7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf911da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = res1a.plot_partial(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Wald test\n",
    "\n",
    "Default is using normal and chisquare distribution, i.e. `use_t=False`.  \n",
    "\n",
    "We can use wald_test_terms for joint hypothesis when parameters that belong to the same explanatory variable can be identified by name.\n",
    "\n",
    "**Warning:** generic wald test, i.e. those inherited from the base classes do not yet take effective degrees of freedom into account.\n",
    "\n",
    "A model specific method, `test_significane` is available for testing whether a component modeled by the spline is zero or constant. This method takes `edf` into account. `test_significance` is a standard Wald test except that degrees of freedom have been replaced by effective degrees of freedom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.contrast.WaldTestResults'>\n",
       "              chi2                  P>chi2  df constraint\n",
       "fuel     72.260652  1.8857012798855524e-17              1\n",
       "drive     3.509491     0.17295123773359317              2\n",
       "weight  131.205902   9.923257765194286e-23             11\n",
       "hp       70.116213  1.4448532927533344e-11              9"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1a.wald_test_terms(skip_single=True, combine_terms=['fuel', 'drive', 'weight', 'hp'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "results when use_t is True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.contrast.WaldTestResults'>\n",
       "                F                     P>F  df constraint    df denom\n",
       "fuel    72.260652    6.17307890496181e-15              1  185.099986\n",
       "drive    1.754746     0.17581588475526833              2  185.099986\n",
       "weight  11.927809   9.135620948653085e-17             11  185.099986\n",
       "hp       7.790690  1.0522812964137523e-09              9  185.099986"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1b.wald_test_terms(skip_single=True, combine_terms=['fuel', 'drive', 'weight', 'hp'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.contrast.ContrastResults'>\n",
       "<F test: F=array([[ 12.79612043]]), p=4.10817312103462e-17, df_denom=185, df_num=10.3>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1b.test_significance(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<class 'statsmodels.stats.contrast.ContrastResults'>\n",
       "<F test: F=array([[ 19.22864809]]), p=1.9378091125595854e-12, df_denom=185, df_num=3.65>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1b.test_significance(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare results with mgcv. \n",
    "\n",
    "Our values are close to those of mgcv but there is a difference where it is not clear where it comes from. statsmodels and mgcv have the same edf, but mgcv might be using `Ref.df`. H the p-values are very small in this example and there might be only minor differences for larger p-values resulting from small differences in the df or edf used in the hypothesis test.\n",
    "\n",
    "\n",
    "\n",
    "```\n",
    "> summary(gam_a)\n",
    "\n",
    "Family: gaussian \n",
    "Link function: identity \n",
    "\n",
    "Formula:\n",
    "city.mpg ~ fuel + drive + s(weight, bs = \"bs\", k = 12) + s(hp, \n",
    "    bs = \"bs\", k = 10)\n",
    "\n",
    "Parametric coefficients:\n",
    "            Estimate Std. Error t value Pr(>|t|)    \n",
    "(Intercept)  29.6273     1.1074  26.755  < 2e-16 ***\n",
    "fuelgas      -6.2137     0.7310  -8.501 6.17e-15 ***\n",
    "drivefwd      1.4399     0.8027   1.794   0.0745 .  \n",
    "driverwd      1.0113     0.8272   1.223   0.2230    \n",
    "---\n",
    "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
    "\n",
    "Approximate significance of smooth terms:\n",
    "             edf Ref.df     F  p-value    \n",
    "s(weight) 10.254 10.806 12.22  < 2e-16 ***\n",
    "s(hp)      3.646  4.395 15.78 6.22e-12 ***\n",
    "---\n",
    "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
    "\n",
    "R-sq.(adj) =  0.891   Deviance explained =   90%\n",
    "GCV = 5.1616  Scale est. = 4.7065    n = 203\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0, dtype=int64)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1a.model.data.const_idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xf9d5668>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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yoX35uQj27IFXfKW6rEBhvPnz9PVVH5sktRsbBJpRQ0MT4+4LZxPM27cP1qyp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf964240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res1a.fittedvalues, res1a.model.endog, '.')\n",
    "plt.plot(res1a.fittedvalues, res1a.fittedvalues, '-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xfa3ff60>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5qJDQ7fzz52enMbPWVfiquioffU6AciM4iNyyZdnpZqHb+YeHpeOOk+bOTV6Hh/M9fi8I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\nACkEBwAAIIXgAAAApPx/iHHQQunxoS4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf89cd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res1a.model.endog, res1a.resid_response, '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variable addition score test\n",
    "\n",
    "We can use the score test to test whether the restricted model with only linear terms is appropriate or whether that model is rejected in favor of adding splines.\n",
    "\n",
    "The problem here is that the spline basis also includes an implicit linear term. The score_test does not take this into account and reports the number of constraints equal to the number of columns instead of the dimension of the subspace that is in addition to the already included exog.\n",
    "\n",
    "**Warning:** GLM.score_test is currently a \"hidden\", not-advertised method, which means it is a prototype for experimental use but will be replaced by an official GLMResults method, which is currently waiting in a pull request.\n",
    "\n",
    "In the following we estimate a GLM with linear components, and then test whether adding spline components is statistically significant.  \n",
    "However the current score test does not take the linear dependence of the spline component with already included variables into account when computing the degrees of freedom for the constraint. As workaround we use two helper functions, `partial_project` and `pca`, to compute the contribution of the spline component that is orthogonal to the already included linear term. This does not change the test chi-square statistic but reduces the degrees of freedom for the constraint to 18.\n",
    "\n",
    "As we can see from the results, the score_test for variable addition and therefore the linear specification is rejected, and we should add the spline component.\n",
    "\n",
    "**Note** This is a test with the alternative of adding all spline basis functions to the model and not a hypothesis test of adding a penalized version of it. Effective degrees of freedom are not used.\n",
    "\n",
    "As in the Wald test, the hypothesis that the linear specification is correct is strongly rejected.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mod_glm = GLM.from_formula('city_mpg ~ fuel + drive + weight + hp', df_autos)\n",
    "res_glm = mod_glm.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 108.91677455]), array([  3.09383926e-14]), 20)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_glm.model.score_test(res_glm.params, exog_extra=bs.basis_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(203, 20)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bs.basis_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.multivariate_tools import partial_project\n",
    "projection_resid = partial_project(bs.basis_, res_glm.model.exog)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18, 20)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_rank(projection_resid.resid), projection_resid.resid.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 108.91677455]), array([  3.09383926e-14]), 20)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_glm.model.score_test(res_glm.params, exog_extra=bs.basis_)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from statsmodels.sandbox.tools.tools_pca import pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 108.91677455]), array([  5.00598345e-15]), 18)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "red = pca(projection_resid.resid, keepdim=18, demean=False)[1]\n",
    "res_glm.model.score_test(res_glm.params, exog_extra=red)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prediction for new observations\n",
    "\n",
    "Prediction currently requires the design matrix for the linear part and the variables that are used for the spline parts.\n",
    "Full formula support with automatic design matrix creation is still missing.\n",
    "\n",
    "First we construct a new dataframe for the observations for which we compute the prediction, i.e. conditional expectation. In this example we consider a car that uses gasoline as fuel and has a front wheel drive. We use five percentiles for each of the smooth terms, weight and horse power.\n",
    "\n",
    "Next we use patsy.dmatrix to create our new design matrix for the linear part. Note that this is a stateful transform and we need to provide the original design matrix, so patsy can correctly convert the categorical variables to dummy variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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>weight</th>\n",
       "      <th>hp</th>\n",
       "      <th>fuel</th>\n",
       "      <th>drive</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.10</th>\n",
       "      <td>1946.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>gas</td>\n",
       "      <td>fwd</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.25</th>\n",
       "      <td>2145.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>gas</td>\n",
       "      <td>fwd</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.50</th>\n",
       "      <td>2414.0</td>\n",
       "      <td>95.0</td>\n",
       "      <td>gas</td>\n",
       "      <td>fwd</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.75</th>\n",
       "      <td>2943.5</td>\n",
       "      <td>116.0</td>\n",
       "      <td>gas</td>\n",
       "      <td>fwd</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.90</th>\n",
       "      <td>3230.0</td>\n",
       "      <td>160.0</td>\n",
       "      <td>gas</td>\n",
       "      <td>fwd</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      weight     hp fuel drive\n",
       "0.10  1946.0   68.0  gas   fwd\n",
       "0.25  2145.0   70.0  gas   fwd\n",
       "0.50  2414.0   95.0  gas   fwd\n",
       "0.75  2943.5  116.0  gas   fwd\n",
       "0.90  3230.0  160.0  gas   fwd"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new = df_autos[['weight', 'hp']].quantile([0.1, 0.25, 0.5, 0.75, 0.9])\n",
    "df_new['fuel'] = 'gas'\n",
    "df_new['drive'] = 'fwd'\n",
    "df_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# note stateful transform\n",
    "exog_linear_new = patsy.dmatrix(exog.design_info, df_new, return_type=\"dataframe\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 32.4405619 ,  29.71396177,  24.02805174,  21.11556954,  17.37701468])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO: smooth x cannot be a dataframe\n",
    "res1b.predict(exog_linear_new, df_new[['weight', 'hp']].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We varied both smooth terms at the same time. Instead we can vary only one smooth term and keep the other term at its mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 27.47259444,  27.15972987,  23.80511056,  22.08912555,  20.02775013])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new2 = df_new.copy()\n",
    "df_new2['weight'] = df_new['weight'].mean()\n",
    "res1b.predict(exog_linear_new, df_new2[['weight', 'hp']].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 28.08722431,  25.67348875,  23.34219804,  22.14570084,  20.4685214 ])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_new3 = df_new.copy()\n",
    "df_new3['hp'] = df_new['hp'].mean()\n",
    "res1b.predict(exog_linear_new, df_new3[['weight', 'hp']].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`predict` only computes the expected value for a new observations. Instead, we can use the `get_prediction` method which returns a prediction results instance with additional attributes and methods such as standard errors and confidence intervals for the predicted mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 28.08722431,  25.67348875,  23.34219804,  22.14570084,  20.4685214 ])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred = res1b.get_prediction(exog_linear_new, df_new3[['weight', 'hp']].values)\n",
    "pred.predicted_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.71039517,  0.63746064,  0.4644517 ,  0.63797194,  0.79398475])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred.se_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 26.68571202,  29.4887366 ],\n",
       "       [ 24.41586629,  26.93111121],\n",
       "       [ 22.42589849,  24.25849758],\n",
       "       [ 20.88706965,  23.40433203],\n",
       "       [ 18.90209832,  22.03494447]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred.conf_int()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choosing the smoothing or penalty parameter\n",
    "\n",
    "At the moment there is no built-in method to choose the penalty parameters `alpha`.\n",
    "\n",
    "In the following we use scipy optimizers to minimize several selection criteria, gcv, aic and bic which are available as attributes of the results instance.  \n",
    "The code below investigates the possibility of multiple local minima or near minima at which optimizers end up and differences across selection criteria.\n",
    "\n",
    "\n",
    "see https://github.com/statsmodels/statsmodels/issues/5381 which includes the following\n",
    "\n",
    "It can be difficult to minimize aic, bic or gcv to find the optimial smoothing or penalty parameter in GAM.\n",
    "\n",
    "I looked at the behavior of scipy optimizers when only the objective function is provided. (mgcv also has approximate derivative but I have not included any.)\n",
    "The example is miles per gallon in city traffic depending on 2 categorical variable and 2 smooth, B-spline terms, weight and horse power. The correlation between weight and horse power is 0.75 and both variables have a similar downward sloping effect on mpg.\n",
    "\n",
    "- Penalization parameters have to be positive or non-negative, so it is best to use a log-link, i.e. use exp(alpha) for the  optimization\n",
    "- The penalty parameter estimates depends on starting values and optimization method, nelder-mead, bfgs or basinhopping.\n",
    "using basinhopping with nelder-mead seems to converge resonably well to the same values from different start_params. Using default lbfgsb with basinhopping did not look good.\n",
    "- none of the estimated penalty parameters are close to those of mgcv. But mgcv values are large and there does not seem to be much effect of varying the penalty parameter in that range.\n",
    "- aic undersmooths for some penalty parameter estimates, often undersmooths only one component\n",
    "- gcv has very smooth estimate, and likely oversmooths\n",
    "- using the average between aic and gcv estimate looks good in graph.\n",
    "\n",
    "This means we/users need to check the results in case the optimizer gets ends in local optima or near-optima.\n",
    "One possibility is to start gcv minimization at the aic estimate and vice-versa to avoid that those are in different local optima.\n",
    "Another possibility in case of high correlation would be to change the penalty parameters in opposite direction for new starting values, eg. double one and half the other. This would help in case when a local minimum has one spline function oversmoothed and the other undersmoothed.\n",
    "\n",
    "**visual inspection**  \n",
    "using the plot_partial method can be used to quickly see the smoothness of the estimated partial prediction\n",
    "fig = res_aic.plot_partial(0, cpr=True)\n",
    "\n",
    "**current computational structure:**\n",
    "\n",
    "we can use the internal fit_pirls to change the penalization parameter alpha during the optimization.\n",
    "The fit method currently does not have an alpha argument and we need to create a new model with the chosen alpha. The smoother or spline instance can be reused when creating a new model.  \n",
    "Currently we cannot have several results instances that are based on different alpha and hold the same model instance because the alpha is a model attribute and not a results parameter.  \n",
    "This structure will likely change in future versions.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import fmin, fmin_bfgs, minimize, basinhopping\n",
    "x = np.array([0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 169947.7822267,   26767.5804634])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha  # mgcv equivalent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 907.347699\n",
      "         Iterations: 36\n",
      "         Function evaluations: 67\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([ 11.22682894,   9.86966346]),\n",
       " array([ 75119.01041465,  19334.83085966]))"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fun = lambda p: gam_bs._fit_pirls(alpha=[np.exp(p[0]), np.exp(p[1])]).aic\n",
    "x = x_aic = fmin(fun, np.log(alpha).tolist())\n",
    "x, np.exp(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 5.653825\n",
      "         Iterations: 34\n",
      "         Function evaluations: 65\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([ 12.39068244,  10.79505194]),\n",
       " array([ 240549.80518384,   48778.84240277]))"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fun = lambda p: gam_bs._fit_pirls(alpha=[np.exp(p[0]), np.exp(p[1])]).gcv\n",
    "x = x_gcv = fmin(fun, x_aic)\n",
    "x, np.exp(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#x = np.array([1, 1])\n",
    "history = []\n",
    "history_params = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 907.347699\n",
      "         Iterations: 35\n",
      "         Function evaluations: 68\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([ 11.2268819 ,   9.86965926]), array([ 75122.9888025,  19334.7496646]))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def fun(p, objective='aic'): \n",
    "    res = gam_bs._fit_pirls(alpha=[np.exp(p[0]), np.exp(p[1])])\n",
    "    history_params.append(p)\n",
    "    history.append([res.aic, res.gcv, res.bic, res.cv])\n",
    "    \n",
    "    return getattr(res, objective)\n",
    "\n",
    "x_aic = x = fmin(fun, x)\n",
    "x, np.exp(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "hist_p = np.asarray(history_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "hist = np.asarray(history)\n",
    "hist_res = np.column_stack((hist_p, hist))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "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>p0</th>\n",
       "      <th>p1</th>\n",
       "      <th>aic</th>\n",
       "      <th>gcv</th>\n",
       "      <th>bic</th>\n",
       "      <th>cv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.390682</td>\n",
       "      <td>10.795052</td>\n",
       "      <td>908.158316</td>\n",
       "      <td>5.653825</td>\n",
       "      <td>-107.714598</td>\n",
       "      <td>7.082931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.010217</td>\n",
       "      <td>10.795052</td>\n",
       "      <td>908.832263</td>\n",
       "      <td>5.656113</td>\n",
       "      <td>-103.213774</td>\n",
       "      <td>6.639704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12.390682</td>\n",
       "      <td>11.334805</td>\n",
       "      <td>908.847521</td>\n",
       "      <td>5.660265</td>\n",
       "      <td>-103.506104</td>\n",
       "      <td>7.103010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.010217</td>\n",
       "      <td>10.255299</td>\n",
       "      <td>908.547175</td>\n",
       "      <td>5.661834</td>\n",
       "      <td>-105.761468</td>\n",
       "      <td>6.636342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>12.390682</td>\n",
       "      <td>10.255299</td>\n",
       "      <td>907.849184</td>\n",
       "      <td>5.658978</td>\n",
       "      <td>-110.331291</td>\n",
       "      <td>7.072854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12.080915</td>\n",
       "      <td>9.985423</td>\n",
       "      <td>907.572446</td>\n",
       "      <td>5.665391</td>\n",
       "      <td>-112.809554</td>\n",
       "      <td>7.328070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>11.461381</td>\n",
       "      <td>10.525176</td>\n",
       "      <td>907.546826</td>\n",
       "      <td>5.660812</td>\n",
       "      <td>-112.569566</td>\n",
       "      <td>8.050819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>10.686964</td>\n",
       "      <td>10.660114</td>\n",
       "      <td>907.673366</td>\n",
       "      <td>5.669177</td>\n",
       "      <td>-112.464454</td>\n",
       "      <td>9.643831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>11.151614</td>\n",
       "      <td>9.715547</td>\n",
       "      <td>907.357574</td>\n",
       "      <td>5.681645</td>\n",
       "      <td>-115.707177</td>\n",
       "      <td>8.488434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10.532080</td>\n",
       "      <td>9.175794</td>\n",
       "      <td>907.563087</td>\n",
       "      <td>5.709325</td>\n",
       "      <td>-116.730225</td>\n",
       "      <td>9.852919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10.532080</td>\n",
       "      <td>10.255299</td>\n",
       "      <td>907.474491</td>\n",
       "      <td>5.675351</td>\n",
       "      <td>-114.365265</td>\n",
       "      <td>10.018856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>10.222313</td>\n",
       "      <td>9.445670</td>\n",
       "      <td>907.519285</td>\n",
       "      <td>5.701741</td>\n",
       "      <td>-116.371429</td>\n",
       "      <td>10.904747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>10.532080</td>\n",
       "      <td>9.715547</td>\n",
       "      <td>907.420259</td>\n",
       "      <td>5.689017</td>\n",
       "      <td>-115.931137</td>\n",
       "      <td>9.923837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>11.151614</td>\n",
       "      <td>9.175794</td>\n",
       "      <td>907.499900</td>\n",
       "      <td>5.701865</td>\n",
       "      <td>-116.511036</td>\n",
       "      <td>8.460044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>10.686964</td>\n",
       "      <td>9.985423</td>\n",
       "      <td>907.395768</td>\n",
       "      <td>5.679438</td>\n",
       "      <td>-115.256848</td>\n",
       "      <td>9.529465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>11.306498</td>\n",
       "      <td>9.985423</td>\n",
       "      <td>907.354276</td>\n",
       "      <td>5.671985</td>\n",
       "      <td>-114.877777</td>\n",
       "      <td>8.247512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>11.693707</td>\n",
       "      <td>10.120361</td>\n",
       "      <td>907.427836</td>\n",
       "      <td>5.664720</td>\n",
       "      <td>-113.731706</td>\n",
       "      <td>7.728103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>11.771148</td>\n",
       "      <td>9.715547</td>\n",
       "      <td>907.437162</td>\n",
       "      <td>5.675080</td>\n",
       "      <td>-114.593134</td>\n",
       "      <td>7.628920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>10.958010</td>\n",
       "      <td>9.917954</td>\n",
       "      <td>907.361171</td>\n",
       "      <td>5.677979</td>\n",
       "      <td>-115.361047</td>\n",
       "      <td>8.878529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>11.500102</td>\n",
       "      <td>9.783016</td>\n",
       "      <td>907.368351</td>\n",
       "      <td>5.675498</td>\n",
       "      <td>-115.093865</td>\n",
       "      <td>7.956680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>11.093533</td>\n",
       "      <td>9.884219</td>\n",
       "      <td>907.351126</td>\n",
       "      <td>5.677256</td>\n",
       "      <td>-115.364833</td>\n",
       "      <td>8.606332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>11.248416</td>\n",
       "      <td>10.154096</td>\n",
       "      <td>907.380943</td>\n",
       "      <td>5.668787</td>\n",
       "      <td>-114.413306</td>\n",
       "      <td>8.353475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>11.175815</td>\n",
       "      <td>9.825184</td>\n",
       "      <td>907.348953</td>\n",
       "      <td>5.677958</td>\n",
       "      <td>-115.441301</td>\n",
       "      <td>8.453391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>10.962850</td>\n",
       "      <td>9.723980</td>\n",
       "      <td>907.367540</td>\n",
       "      <td>5.683684</td>\n",
       "      <td>-115.818831</td>\n",
       "      <td>8.850353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>11.220586</td>\n",
       "      <td>9.920062</td>\n",
       "      <td>907.348704</td>\n",
       "      <td>5.674724</td>\n",
       "      <td>-115.157752</td>\n",
       "      <td>8.383219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>11.302868</td>\n",
       "      <td>9.861027</td>\n",
       "      <td>907.348955</td>\n",
       "      <td>5.675396</td>\n",
       "      <td>-115.215430</td>\n",
       "      <td>8.245674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>11.250534</td>\n",
       "      <td>9.866825</td>\n",
       "      <td>907.347818</td>\n",
       "      <td>5.675849</td>\n",
       "      <td>-115.263067</td>\n",
       "      <td>8.329937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>11.295305</td>\n",
       "      <td>9.961703</td>\n",
       "      <td>907.351974</td>\n",
       "      <td>5.672727</td>\n",
       "      <td>-114.959054</td>\n",
       "      <td>8.263715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>11.205687</td>\n",
       "      <td>9.859314</td>\n",
       "      <td>907.347828</td>\n",
       "      <td>5.676601</td>\n",
       "      <td>-115.329366</td>\n",
       "      <td>8.404318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>11.235635</td>\n",
       "      <td>9.806077</td>\n",
       "      <td>907.349259</td>\n",
       "      <td>5.677808</td>\n",
       "      <td>-115.426041</td>\n",
       "      <td>8.350661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>11.227957</td>\n",
       "      <td>9.872373</td>\n",
       "      <td>907.347702</td>\n",
       "      <td>5.675961</td>\n",
       "      <td>-115.273709</td>\n",
       "      <td>8.367650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>11.212658</td>\n",
       "      <td>9.868901</td>\n",
       "      <td>907.347740</td>\n",
       "      <td>5.676243</td>\n",
       "      <td>-115.298371</td>\n",
       "      <td>8.393138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>11.231164</td>\n",
       "      <td>9.869099</td>\n",
       "      <td>907.347703</td>\n",
       "      <td>5.676015</td>\n",
       "      <td>-115.278532</td>\n",
       "      <td>8.362085</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>11.237086</td>\n",
       "      <td>9.875780</td>\n",
       "      <td>907.347735</td>\n",
       "      <td>5.675755</td>\n",
       "      <td>-115.255322</td>\n",
       "      <td>8.352678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>11.225797</td>\n",
       "      <td>9.868214</td>\n",
       "      <td>907.347700</td>\n",
       "      <td>5.676105</td>\n",
       "      <td>-115.286449</td>\n",
       "      <td>8.370987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>11.222590</td>\n",
       "      <td>9.871489</td>\n",
       "      <td>907.347704</td>\n",
       "      <td>5.676050</td>\n",
       "      <td>-115.281591</td>\n",
       "      <td>8.376577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>11.229021</td>\n",
       "      <td>9.869696</td>\n",
       "      <td>907.347700</td>\n",
       "      <td>5.676024</td>\n",
       "      <td>-115.279316</td>\n",
       "      <td>8.365698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>11.226862</td>\n",
       "      <td>9.865538</td>\n",
       "      <td>907.347706</td>\n",
       "      <td>5.676169</td>\n",
       "      <td>-115.292028</td>\n",
       "      <td>8.369032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>11.227683</td>\n",
       "      <td>9.870664</td>\n",
       "      <td>907.347700</td>\n",
       "      <td>5.676013</td>\n",
       "      <td>-115.278302</td>\n",
       "      <td>8.367995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>11.230906</td>\n",
       "      <td>9.872146</td>\n",
       "      <td>907.347705</td>\n",
       "      <td>5.675932</td>\n",
       "      <td>-115.271143</td>\n",
       "      <td>8.362715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>11.227075</td>\n",
       "      <td>9.869197</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676062</td>\n",
       "      <td>-115.282633</td>\n",
       "      <td>8.368916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>11.225737</td>\n",
       "      <td>9.870165</td>\n",
       "      <td>907.347700</td>\n",
       "      <td>5.676050</td>\n",
       "      <td>-115.281614</td>\n",
       "      <td>8.371217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>11.225129</td>\n",
       "      <td>9.868698</td>\n",
       "      <td>907.347700</td>\n",
       "      <td>5.676099</td>\n",
       "      <td>-115.285940</td>\n",
       "      <td>8.372138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>11.227044</td>\n",
       "      <td>9.870173</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676034</td>\n",
       "      <td>-115.280214</td>\n",
       "      <td>8.369030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>11.228382</td>\n",
       "      <td>9.869205</td>\n",
       "      <td>907.347700</td>\n",
       "      <td>5.676046</td>\n",
       "      <td>-115.281229</td>\n",
       "      <td>8.366732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>11.226398</td>\n",
       "      <td>9.869925</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676049</td>\n",
       "      <td>-115.281519</td>\n",
       "      <td>8.370094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>11.226428</td>\n",
       "      <td>9.868950</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676076</td>\n",
       "      <td>-115.283938</td>\n",
       "      <td>8.369980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>11.226890</td>\n",
       "      <td>9.869867</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676045</td>\n",
       "      <td>-115.281145</td>\n",
       "      <td>8.369268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>11.226214</td>\n",
       "      <td>9.870595</td>\n",
       "      <td>907.347700</td>\n",
       "      <td>5.676032</td>\n",
       "      <td>-115.280030</td>\n",
       "      <td>8.370447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>11.226859</td>\n",
       "      <td>9.869547</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676054</td>\n",
       "      <td>-115.281983</td>\n",
       "      <td>8.369298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>11.227352</td>\n",
       "      <td>9.869489</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676050</td>\n",
       "      <td>-115.281608</td>\n",
       "      <td>8.368472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>11.227113</td>\n",
       "      <td>9.869598</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676050</td>\n",
       "      <td>-115.281586</td>\n",
       "      <td>8.368877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>11.227082</td>\n",
       "      <td>9.869277</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676059</td>\n",
       "      <td>-115.282424</td>\n",
       "      <td>8.368908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>11.226938</td>\n",
       "      <td>9.869720</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676048</td>\n",
       "      <td>-115.281465</td>\n",
       "      <td>8.369178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>11.226684</td>\n",
       "      <td>9.869669</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676053</td>\n",
       "      <td>-115.281862</td>\n",
       "      <td>8.369599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>11.226792</td>\n",
       "      <td>9.869651</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676052</td>\n",
       "      <td>-115.281793</td>\n",
       "      <td>8.369418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>11.226713</td>\n",
       "      <td>9.869478</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676058</td>\n",
       "      <td>-115.282311</td>\n",
       "      <td>8.369539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>11.226882</td>\n",
       "      <td>9.869659</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676051</td>\n",
       "      <td>-115.281676</td>\n",
       "      <td>8.369268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>11.226814</td>\n",
       "      <td>9.869763</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676049</td>\n",
       "      <td>-115.281486</td>\n",
       "      <td>8.369388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>11.226848</td>\n",
       "      <td>9.869601</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676053</td>\n",
       "      <td>-115.281859</td>\n",
       "      <td>8.369321</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>68 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           p0         p1         aic       gcv         bic         cv\n",
       "0   12.390682  10.795052  908.158316  5.653825 -107.714598   7.082931\n",
       "1   13.010217  10.795052  908.832263  5.656113 -103.213774   6.639704\n",
       "2   12.390682  11.334805  908.847521  5.660265 -103.506104   7.103010\n",
       "3   13.010217  10.255299  908.547175  5.661834 -105.761468   6.636342\n",
       "4   12.390682  10.255299  907.849184  5.658978 -110.331291   7.072854\n",
       "5   12.080915   9.985423  907.572446  5.665391 -112.809554   7.328070\n",
       "6   11.461381  10.525176  907.546826  5.660812 -112.569566   8.050819\n",
       "7   10.686964  10.660114  907.673366  5.669177 -112.464454   9.643831\n",
       "8   11.151614   9.715547  907.357574  5.681645 -115.707177   8.488434\n",
       "9   10.532080   9.175794  907.563087  5.709325 -116.730225   9.852919\n",
       "10  10.532080  10.255299  907.474491  5.675351 -114.365265  10.018856\n",
       "11  10.222313   9.445670  907.519285  5.701741 -116.371429  10.904747\n",
       "12  10.532080   9.715547  907.420259  5.689017 -115.931137   9.923837\n",
       "13  11.151614   9.175794  907.499900  5.701865 -116.511036   8.460044\n",
       "14  10.686964   9.985423  907.395768  5.679438 -115.256848   9.529465\n",
       "15  11.306498   9.985423  907.354276  5.671985 -114.877777   8.247512\n",
       "16  11.693707  10.120361  907.427836  5.664720 -113.731706   7.728103\n",
       "17  11.771148   9.715547  907.437162  5.675080 -114.593134   7.628920\n",
       "18  10.958010   9.917954  907.361171  5.677979 -115.361047   8.878529\n",
       "19  11.500102   9.783016  907.368351  5.675498 -115.093865   7.956680\n",
       "20  11.093533   9.884219  907.351126  5.677256 -115.364833   8.606332\n",
       "21  11.248416  10.154096  907.380943  5.668787 -114.413306   8.353475\n",
       "22  11.175815   9.825184  907.348953  5.677958 -115.441301   8.453391\n",
       "23  10.962850   9.723980  907.367540  5.683684 -115.818831   8.850353\n",
       "24  11.220586   9.920062  907.348704  5.674724 -115.157752   8.383219\n",
       "25  11.302868   9.861027  907.348955  5.675396 -115.215430   8.245674\n",
       "26  11.250534   9.866825  907.347818  5.675849 -115.263067   8.329937\n",
       "27  11.295305   9.961703  907.351974  5.672727 -114.959054   8.263715\n",
       "28  11.205687   9.859314  907.347828  5.676601 -115.329366   8.404318\n",
       "29  11.235635   9.806077  907.349259  5.677808 -115.426041   8.350661\n",
       "..        ...        ...         ...       ...         ...        ...\n",
       "38  11.227957   9.872373  907.347702  5.675961 -115.273709   8.367650\n",
       "39  11.212658   9.868901  907.347740  5.676243 -115.298371   8.393138\n",
       "40  11.231164   9.869099  907.347703  5.676015 -115.278532   8.362085\n",
       "41  11.237086   9.875780  907.347735  5.675755 -115.255322   8.352678\n",
       "42  11.225797   9.868214  907.347700  5.676105 -115.286449   8.370987\n",
       "43  11.222590   9.871489  907.347704  5.676050 -115.281591   8.376577\n",
       "44  11.229021   9.869696  907.347700  5.676024 -115.279316   8.365698\n",
       "45  11.226862   9.865538  907.347706  5.676169 -115.292028   8.369032\n",
       "46  11.227683   9.870664  907.347700  5.676013 -115.278302   8.367995\n",
       "47  11.230906   9.872146  907.347705  5.675932 -115.271143   8.362715\n",
       "48  11.227075   9.869197  907.347699  5.676062 -115.282633   8.368916\n",
       "49  11.225737   9.870165  907.347700  5.676050 -115.281614   8.371217\n",
       "50  11.225129   9.868698  907.347700  5.676099 -115.285940   8.372138\n",
       "51  11.227044   9.870173  907.347699  5.676034 -115.280214   8.369030\n",
       "52  11.228382   9.869205  907.347700  5.676046 -115.281229   8.366732\n",
       "53  11.226398   9.869925  907.347699  5.676049 -115.281519   8.370094\n",
       "54  11.226428   9.868950  907.347699  5.676076 -115.283938   8.369980\n",
       "55  11.226890   9.869867  907.347699  5.676045 -115.281145   8.369268\n",
       "56  11.226214   9.870595  907.347700  5.676032 -115.280030   8.370447\n",
       "57  11.226859   9.869547  907.347699  5.676054 -115.281983   8.369298\n",
       "58  11.227352   9.869489  907.347699  5.676050 -115.281608   8.368472\n",
       "59  11.227113   9.869598  907.347699  5.676050 -115.281586   8.368877\n",
       "60  11.227082   9.869277  907.347699  5.676059 -115.282424   8.368908\n",
       "61  11.226938   9.869720  907.347699  5.676048 -115.281465   8.369178\n",
       "62  11.226684   9.869669  907.347699  5.676053 -115.281862   8.369599\n",
       "63  11.226792   9.869651  907.347699  5.676052 -115.281793   8.369418\n",
       "64  11.226713   9.869478  907.347699  5.676058 -115.282311   8.369539\n",
       "65  11.226882   9.869659  907.347699  5.676051 -115.281676   8.369268\n",
       "66  11.226814   9.869763  907.347699  5.676049 -115.281486   8.369388\n",
       "67  11.226848   9.869601  907.347699  5.676053 -115.281859   8.369321\n",
       "\n",
       "[68 rows x 6 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort_idx = hist_p[:,0].argsort(0)\n",
    "#hist_res[sort_idx]\n",
    "col_names = 'p0 p1 aic gcv bic cv'.split()\n",
    "df_hist = pd.DataFrame(hist_res, columns=col_names)\n",
    "df_hist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([65,  0,  9,  3], dtype=int64)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min_idx = np.argmin(hist, 0)\n",
    "min_idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[ 11.2268819 ,   9.86965926],\n",
       "        [ 12.39068244,  10.79505194],\n",
       "        [ 10.53208007,   9.17579415],\n",
       "        [ 13.01021656,  10.25529934]]),\n",
       " array([[  75122.9888025 ,   19334.7496646 ],\n",
       "        [ 240549.80518384,   48778.84240277],\n",
       "        [  37499.39474376,    9660.43685657],\n",
       "        [ 446956.50254215,   28432.81865686]]))"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist_p[min_idx], np.exp(hist_p[min_idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10ee4a90>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JUnYGjB5QqVTa3YSOYB2WWIuCdVhiLQrWoXWaEjAi4kkRcX1E3BMRD0fEbRFx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\nQykjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xfa4e278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(hist_p[:,0], hist_p[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "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>p0</th>\n",
       "      <th>p1</th>\n",
       "      <th>aic</th>\n",
       "      <th>gcv</th>\n",
       "      <th>bic</th>\n",
       "      <th>cv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>65</th>\n",
       "      <td>11.226882</td>\n",
       "      <td>9.869659</td>\n",
       "      <td>907.347699</td>\n",
       "      <td>5.676051</td>\n",
       "      <td>-115.281676</td>\n",
       "      <td>8.369268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12.390682</td>\n",
       "      <td>10.795052</td>\n",
       "      <td>908.158316</td>\n",
       "      <td>5.653825</td>\n",
       "      <td>-107.714598</td>\n",
       "      <td>7.082931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10.532080</td>\n",
       "      <td>9.175794</td>\n",
       "      <td>907.563087</td>\n",
       "      <td>5.709325</td>\n",
       "      <td>-116.730225</td>\n",
       "      <td>9.852919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.010217</td>\n",
       "      <td>10.255299</td>\n",
       "      <td>908.547175</td>\n",
       "      <td>5.661834</td>\n",
       "      <td>-105.761468</td>\n",
       "      <td>6.636342</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           p0         p1         aic       gcv         bic        cv\n",
       "65  11.226882   9.869659  907.347699  5.676051 -115.281676  8.369268\n",
       "0   12.390682  10.795052  908.158316  5.653825 -107.714598  7.082931\n",
       "9   10.532080   9.175794  907.563087  5.709325 -116.730225  9.852919\n",
       "3   13.010217  10.255299  908.547175  5.661834 -105.761468  6.636342"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_hist.iloc[min_idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# some previous results with different starting values and optimizers\n",
    "a_minaic = [ 112487.6132559 ,     129.89530824]\n",
    "a_minaic = [  75122.9888025 ,   19334.7496646 ]\n",
    "a_minaic = [  1.84554244e+00,   1.95130433e+04] # basinhopping default\n",
    "a_minaic = [112486.36013144413, 129.8919251893982] # basinhopping nm\n",
    "a_mingcv = [19643062.097191658, 49251.418095354195] # basinhopping nm\n",
    "a_minbic = [73696.07497684428, 62.55870150328582]  # basinhopping nm\n",
    "\n",
    "a_mingcv = np.exp(x_gcv)\n",
    "a_minaic = np.exp(x_aic)\n",
    "a = a_minaic\n",
    "a = a_mingcv\n",
    "a = a_minbic\n",
    "\n",
    "# use average of aic and gcv estimate\n",
    "a = (a_minaic + a_mingcv) / 2\n",
    "gam_bs_aic = GLMGam(df_autos['city_mpg'], exog=exog, smoother=bs,\n",
    "                alpha=a)\n",
    "res1_aic = gam_bs_aic.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 157836.39699317,   34056.79603368]),\n",
       " array([ 75122.9888025,  19334.7496646]),\n",
       " array([ 240549.80518384,   48778.84240277]))"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a, a_minaic, a_mingcv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.762842296343244"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1_aic.edf.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ViPwiItkA/gjgamPMOQFrMUWEvn2B9u2Bd95xfUy9evb34+O9O0d8PPDaazrF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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef6400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = res1_aic.plot_partial(0, cpr=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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B6W+65JLu3W1mwm23xXcHHTl0UF4eHMr4+mvrsXj2WXsusL7DL79YF/7KlcmP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\nJSEBACgJCQBASUgAAEpCAgBQ+gLqMP+Jl53hjAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f2ca90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = res1_aic.plot_partial(1, cpr=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                        fun: 907.34769921075156\n",
       " lowest_optimization_result:  final_simplex: (array([[ 11.22684271,   9.8696653 ],\n",
       "       [ 11.22684067,   9.8696088 ],\n",
       "       [ 11.22691188,   9.86962771]]), array([ 907.34769921,  907.34769921,  907.34769921]))\n",
       "           fun: 907.34769921075156\n",
       "       message: 'Optimization terminated successfully.'\n",
       "          nfev: 58\n",
       "           nit: 29\n",
       "        status: 0\n",
       "       success: True\n",
       "             x: array([ 11.22684271,   9.8696653 ])\n",
       "                    message: ['requested number of basinhopping iterations completed successfully']\n",
       "      minimization_failures: 0\n",
       "                       nfev: 654\n",
       "                        nit: 10\n",
       "                          x: array([ 11.22684271,   9.8696653 ])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basinhopping(fun, x, minimizer_kwargs={'method': 'Nelder-Mead'}, niter=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.845542440551041, 19513.043336567418]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(np.array([ 0.61277324,  9.87883841])).tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[112486.36013144413, 129.8919251893982]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(np.array([11.63058725,   4.86670276])).tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                        fun: 5.6538245393041597\n",
       " lowest_optimization_result:  final_simplex: (array([[ 12.39062742,  10.79502202],\n",
       "       [ 12.39058025,  10.7950683 ],\n",
       "       [ 12.39066756,  10.79508847]]), array([ 5.65382454,  5.65382454,  5.65382454]))\n",
       "           fun: 5.6538245393041597\n",
       "       message: 'Optimization terminated successfully.'\n",
       "          nfev: 62\n",
       "           nit: 31\n",
       "        status: 0\n",
       "       success: True\n",
       "             x: array([ 12.39062742,  10.79502202])\n",
       "                    message: ['requested number of basinhopping iterations completed successfully']\n",
       "      minimization_failures: 0\n",
       "                       nfev: 681\n",
       "                        nit: 10\n",
       "                          x: array([ 12.39062742,  10.79502202])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basinhopping(lambda p: fun(p, objective='gcv'), x, minimizer_kwargs={'method': 'Nelder-Mead'}, niter=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[19643062.097191658, 49251.418095354195]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# min gcv\n",
    "np.exp(np.array([16.79323476,  10.80469344])).tolist()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                        fun: -127.34066179693878\n",
       " lowest_optimization_result:  final_simplex: (array([[ 11.20770641,   4.13606207],\n",
       "       [ 11.20773554,   4.13609134],\n",
       "       [ 11.20767237,   4.13615912]]), array([-127.3406618 , -127.3406618 , -127.34066179]))\n",
       "           fun: -127.34066179693878\n",
       "       message: 'Optimization terminated successfully.'\n",
       "          nfev: 64\n",
       "           nit: 33\n",
       "        status: 0\n",
       "       success: True\n",
       "             x: array([ 11.20770641,   4.13606207])\n",
       "                    message: ['requested number of basinhopping iterations completed successfully']\n",
       "      minimization_failures: 0\n",
       "                       nfev: 703\n",
       "                        nit: 10\n",
       "                          x: array([ 11.20770641,   4.13606207])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basinhopping(lambda p: fun(p, objective='bic'), x, minimizer_kwargs={'method': 'Nelder-Mead'}, niter=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[73696.07497684428, 62.55870150328582]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# min bic\n",
    "np.exp(np.array([11.20770482,   4.13610534])).tolist()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "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>city_mpg</th>\n",
       "      <th>weight</th>\n",
       "      <th>hp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>city_mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.758145</td>\n",
       "      <td>-0.803620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>weight</th>\n",
       "      <td>-0.758145</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.751034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hp</th>\n",
       "      <td>-0.803620</td>\n",
       "      <td>0.751034</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          city_mpg    weight        hp\n",
       "city_mpg  1.000000 -0.758145 -0.803620\n",
       "weight   -0.758145  1.000000  0.751034\n",
       "hp       -0.803620  0.751034  1.000000"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_autos.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### basic recipe for penality parameter optimization\n",
    "\n",
    "The following code summarizes the basic current pattern for choosing the penalization parameter and visualizing the estimated smooth function.\n",
    "\n",
    "This just uses Nelder-Mead as optimizer which could be replaced by other optimizers like basinhopping."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 907.222821\n",
      "         Iterations: 116\n",
      "         Function evaluations: 216\n",
      "[ 11.63059839   4.8667288 ] [ 112487.6132559      129.89530824]\n"
     ]
    },
    {
     "data": {
      "image/png": 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g7/3ZcfYtxmZNSB457zwLHD79FH75JfoxzZrBzyHVOryHW2+1Ggzp1KoV3HGH\nBRBnnAEDBsCTT9q0zUwIFCMC6/U49ti652+IiGST1p6QOjn8cOtxuOceS3IM5Zz1Juy0U/XH/fGP\nNnyRCb/6lS20tfPOludw/fWwdWv6X1fFiESkoVHQIHXSuLGVjC4ttVyCoiJLgCwqsuGBDz6oXr0R\nYPZsq7mQKZ07w6RJlrx5ww22+NbSpel9TRUjEpGGRkGD1NlZZ9kUzE8+sVoJmzfbv7vuavtjXSyv\nvhoqKjLXzsaN4dpr4e23Yd486N/fEibTRcWIRKShUdAgddaxo9VECCRERoq8eB5yiG1fssR++dck\n1QmF++9vwxVDh9rQxeWXW6CTiGTaomJEItLQKGiQlDjvPPjqq/DiTgGRF8977rHkSLBExWnT4j93\n5OqG3brVPXho29YKQd16q9WaOOigmpffjtYWrbQoIvlEQYOkxEEHQe/eNa9HAfYr/dpr7e/KSltu\nO94wRWQC4caNqblgN2oEl10G775rpagHDrS8h3iU3Cgi+UxBg6REo0Zw8sk2pbFHj5p7Ai67DPba\ny/6ePx8uuCD2sbFyIlJ1wR4+3CpJDhxoC3HFm12h5EYRyWcKGiRlXn/dchoWLIjdExDICejb16Zc\ntmxp2x97DO6+O/y4oUNtGOOTT6zmQmFh+HOl8oLdti28+ipcd50FDUceGb0YlJIbRSSfJVXcSSSe\nVavC70+bZgHCxInBJMDQgkdgtRPmzbO/L7wQunaFUaPsuE8+CR63aRMMGQJNm1oPQ8eOqb9gN25s\niZn77GO9JgMHwvPPB3tEIJifISKSj9TTICkT+ct/y5bqPQ6RQwpbtsDvf29/V1bCiSfCxx9HH3r4\n7DP7d+pUu3CnYpntaA45xGZXdOsGBxwAzzyTmucVEanvFDRIygS67iOFBgCRgUXr1nDvvcElrNev\nt4t2ZHVJqB6EpHMmQ6dOVs9hzBgLZG68Mfp0UhGRfKKgQVIm0HUfWTY6NFCIzAn45hubORF6Qa6o\ngLlzrQchEEyECgQh6Z7J0KyZ5VrccIMNW5x2ms3cEBHJV8ppkJR76y274DdvbktTh+YeROYENGkS\n/ljnLIDYssVmVWyzTfjS2hAMQjp2tF6GyO2p5JxVrtx5Zzj9dFi8GF54AbbdNvWvJSKS69TTICnX\ntSv86U9WZfGll+JXQgwUeQpo2RJ+85vg/ciAoagoGIREm8mQruWoTzzRgqGZM+21vv8+Nc8rIlKf\nKGiQtDh0vVpVAAAgAElEQVTvPKt1cP/98Y/r3bv6/fvvh5tvttoPodq3h48+CgYh0co0pzPPYd99\nYcoUG6IYNsyWA8+GdAVGIiI1UdAgadGunVV6vPPO6Os6BC58s2aFb1+71oYEzjyzei9EoHbDhRfa\n7IZo0p3n0KePzd7o0cPWsPjPf1L7/IlQKWsRyRYFDZI2F18czAGIFLjwbdkSvv3bb61eQs+eNpMi\n0rp1MGGC1VAYPBjuuit8CCMyr2HBAvjyy7q/l1Dt2tnMisMOs4W6xo/P7MwKlbIWkWxR0CBp07+/\nrUkxblz1ffEudJWV0QOGjh3Dp2JOn27lpzt2tJkNkybBs89a0BGwdSvsvXft30MsLVrAc8/B2LF2\nO/ZY+PHH1L9ONCplLSLZoqBB0mrsWMtDeP/98O3JXuiKimxI4ocfbFGsPfcM7vvlF3j8cTj0UOt9\nqKwMf+yGDbVre025A40b2yqZ//43vPce7LorPPJI9ddP5LmSoVLWIpItzme5Yo1zbhBQVlZWxqBB\ng7LaFkk972HAAAsSXn89uH3FCvt1HigJPXVq9Ist2MV56dLqszBmzIAHH7SAYc2a2G0oKrJciWTt\nu294yevhw2OXkF682CpbPv205V3ccUd4+elknktEJFHTp09n8ODBAIO999PT/XrqaZC0cg6uvBLe\neAPKyoLbI2c+vPNO+LBCqC5dok/b7N/fLs5Ll9qwxFFHVa/7ADZEcfnldlwyIodQPv00dk9Bly7w\n1FPW4xCYXXH66fDVV7Z/0aLw4xcvTq4tIiK5QEGDpN3xx9tUyhtvjH3MiBGWFOl99VLUXbrEf/5m\nzeC442yY4IcfbLXMYcOC+9evh1tugR13hHPOge++S6zdkUMoGzcGZyyMGhX7fZSV2RDKpEk2ZHHE\nEdVXzMxU/kM6aeqnSP5R0CBp17gxXHstvPhieBd9LHUZs99+e6sRMXWqJUr+5je2MibYSpkPPGDL\nco8dG1yVM3Dx697d1sLo0cPu33tvsB2R5ay/+CL++/3tb60A1GOP2cU0Mq9iu+0Sf0+5SlM/RfKP\nchokIyorLUmxeXO7wERbUyJdli2D22+36ZmhuQ1FRXDFFVZr4aOPqj8uNO+gWbPq604EApp4FS8h\nmNcRGmg0a2Z1LIYPtwCld+/MnpNU6NUrvIx3z5423CQimZPpnAYFDZIxkybZDIfnn8/Or9Lychum\nuO228F/+jRrFTsIsLLR/CwqsRkSkRBMaA4mfS5dawDB0qPWEzJplQcV221nhqI4dYYcdwm9t29oF\nescdrR25QsmdItmnoEEatCOOsF+nX34ZPWkxE5YutZUrH3jAkiQTVVRkwUZoQaq6/rr+6Sfr5fj4\nY1vxc8UKGzYJ3EIDlaZNbQXRfv0sd+LIIy2YyJbIGTCJ9LqISGopaJAGbcYMq+Y4YQKcf3522zJn\nDlx1VfSKldH07GkXx0z+ut6wwS7OX39t7Z092xbN+ugjK8+9006WBHraabDLLulrh4jkJk25lAat\nf3+7wF13HVRUZLctffvar+NJk2zp65oEfk1nsrBS8+aWoHnIIbbmxoQJMHkyrF5twc6IETZbpF8/\n2GcfeOKJ6rkX6ZZrsyhyrT0iDYmCBsm4G2+0gOHqq7PdEnPwwZakeMMNwZkWAY0bW17D0KE2jXLU\nKKvXsGRJ9IW4MqWoCI4+2oZYfvjB6lS0aAGnngrdutnS5JG1IdIl12ZR5Fp7RBqSpIIG59x5zrkZ\nzrnyqtsU59wRIfsLnXMTnHOrnHMVzrnnnHMa5ZQw3bpZ4HDHHbbUdC4oLLQg5ssv7dd7wNatloA4\nYYJN5fzkE/slv3Gj5SHkwgUpUKdi0iQbvjjxRDu3PXpY+956K70LauXaAlq51h6RhiTZnoZFwBXA\n4Krb28CLzrnAaOp4YCQwBhgBdAKeT01TpSG55BL79X7GGbUr8ZyI2nRT9+5t1Sn/8Y/gzIk5c6xY\nVKC6Y6hcuyD17WsBw5Iltiz5vHk2tNGvH/zzn+k518kuoJXO4YPly6sX0tKCXiIp5L2v0w1YDZwJ\ntAY2AseE7OsDVAJD4zx+EODLysq85Jevv/a+qMj744/3vrIy9c8/fLj39hvbbsOHJ/f4L7/0fo89\nwp8j8pbscyZr2TJ7jZ497d/ly5N7fGWl9+++a+e4cWPvW7Xy/vzzvZ81K3VtXL48uTbW9XNJ5rmL\nipI/ZyL1SVlZmQc8MMjX8XqeyK3WOQ3OuUbOuZOAFsBUrOehAHgrJCCZCywE0rA4sdR3vXvDQw/Z\nePydd6b++evaTd2vH7RqFX1fkybWU1LXRMiafnVHjs+PGpXcr3TnYP/94ZlnYOFCuOwyS6DcbTfr\nPbnllvACTbURuY5ITdMuUzl8EHr+hg61fJNQbdtqGqhIKiUdNDjndnPOVWC9CndhPQtzgA7AJu99\nZAfo8qp9ItUcd5yVdL7kktpdgONddGN1myfTPb5sWfTtmzdb0HPUUXXrZq8paS/ygvrFF7VP8uvU\nyWatLFxoQUSnTnDNNdb+AQNslc5XX7XaEemU7HBGPKHnL5BvkqrnFpEoku2awHoTemLDCn8BVgB9\ngRJgQ5TjPwZuivN8Gp7IM5Fd7kuXen/iid43ber9m28m91zxurpjdZsPHRr+mKFDE3/+HXao21BF\n5Hvv3j38OQoKwtsa+fqFheH3e/ZM7nxFqqjw/plnvD/9dO87dw4+70472WdyzTXeP/aY9x995P2q\nVakZRkp2OCOenj1jfx7OaWhCGr5MD0/UubiTc+5N4BvgGWASsK0P6W1wzn0PjPPe3x7j8YOAshEj\nRtCmTZuwfSUlJZSUlNSpfZJ7opUffvtt+9X+/vs2XHHkkYk9V23WP4hcR6KwEH75Jfqxs2ZZ/YMN\nG6xmwpQp1gV+4YXVy0oHXnv5cvsFHK1SYuR7LyqKXq8iUDQqsuri5s02ayPyuFTw3qpSTptmv9o/\n+8yKSoX2tjRpEixt3batlb9u0SJ4a97cSl07Z5UzN22yNse6Re7fssU+n1atbPGw3r1tKGW33eyz\njlw+PfJ8hor3uYrUR6WlpZSWloZtKy8vZ/LkyVBfKkI6594CFgCXACuBk7z3L1Tt2xmYAwzz3n8c\n4/GqCJlnYl3o16+Hk06CV16B8ePhootqfq7arH+QTNAQ+fyFhbDnnnDllTB6dPiaFdtsA59/bgtR\nRQYG33xjgUPke+/e3Zb+njYtsfLU2SjdXFFhbQkERCtXWjtWrrQlvjdssNv69XbbutUCkIICq3vR\npEn0W7R9BQX2Wfz8M6xZA3PnWiErsHO/yy5WIGz0aAss588PBnWVleGfx5Ah4QGWSEOU6YqQSS1/\n45z7C/AaNvWyCDgF2B84zHu/1jn3IHCbc24NUAHcAXwYK2CQ/NSxY/iFMzDu3KKFJeldcQX8v/9n\nNRNuu822xzJxYvWLaE322MN+SYfejyUyp2DjRgsISkqqL3L10092UWvWLHx7RQW0b28Xvcj1Nrp0\nsSAnMjiJNRYfSDrMpKIiy3kYMCCzrwsWfCxfbt+FL7+0np9p0+CRR6w3olmz8J6aoiLrAUn0uyAi\nyUl2zbz2wKNAR6Ac+AILGN6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QCP07NOm0cWObKdSjhyX39uhhr3/kkbk9YyhXKWgQSbNM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KAAAd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xfa6fa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0 = [0, 0]\n",
    "fun = lambda p: gam_bs._fit_pirls(alpha=[np.exp(p[0]), np.exp(p[1])]).aic\n",
    "a = fmin(fun, x0)\n",
    "print(a, np.exp(a))\n",
    "gam_bs_aic = GLMGam(df_autos['city_mpg'], exog=exog, smoother=bs,\n",
    "                alpha=np.exp(a))\n",
    "res_aic = gam_bs_aic.fit()\n",
    "\n",
    "fig = plt.figure(figsize=(6, 8))\n",
    "ax0 = fig.add_subplot(211)\n",
    "fig = res_aic.plot_partial(0, cpr=True, ax=ax0)\n",
    "ax1 = fig.add_subplot(212)\n",
    "fig = res_aic.plot_partial(1, cpr=True, ax=ax1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                        fun: 907.22282095619732\n",
       " lowest_optimization_result:  final_simplex: (array([[ 11.63059094,   4.8667184 ],\n",
       "       [ 11.63058094,   4.86666148],\n",
       "       [ 11.63050623,   4.86670023]]), array([ 907.22282096,  907.22282096,  907.22282096]))\n",
       "           fun: 907.22282095619732\n",
       "       message: 'Optimization terminated successfully.'\n",
       "          nfev: 66\n",
       "           nit: 34\n",
       "        status: 0\n",
       "       success: True\n",
       "             x: array([ 11.63059094,   4.8667184 ])\n",
       "                    message: ['requested number of basinhopping iterations completed successfully']\n",
       "      minimization_failures: 0\n",
       "                       nfev: 759\n",
       "                        nit: 10\n",
       "                          x: array([ 11.63059094,   4.8667184 ])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = [1, 1]\n",
    "basinhopping(fun, x0, minimizer_kwargs={'method': 'Nelder-Mead'}, niter=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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