{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BLM example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add PyTwoWay to system path (do not run this)\n",
    "# import sys\n",
    "# sys.path.append('../../..')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the PyTwoWay package\n",
    "\n",
    "Make sure to install it using `pip install pytwoway`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import bipartitepandas as bpd\n",
    "import pytwoway as tw\n",
    "from pytwoway import constraints as cons\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First, check out parameter options\n",
    "\n",
    "Do this by running:\n",
    "\n",
    "- BLM - `tw.blm_params().describe_all()`\n",
    "\n",
    "- Clustering - `bpd.cluster_params().describe_all()`\n",
    "\n",
    "- Cleaning - `bpd.clean_params().describe_all()`\n",
    "\n",
    "- Simulating - `bpd.sim_params().describe_all()`\n",
    "\n",
    "Alternatively, run `x_params().keys()` to view all the keys for a parameter dictionary, then `x_params().describe(key)` to get a description for a single key."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second, set parameter choices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "nl = 3 # Number of worker types\n",
    "nk = 4 # Number of firm types\n",
    "blm_params = tw.blm_params({\n",
    "    'nl': nl, 'nk': nk,\n",
    "    'a1_mu': 0, 'a1_sig': 1.5, 'a2_mu': 0, 'a2_sig': 1.5,\n",
    "    's1_low': 0.5, 's1_high': 1.5, 's2_low': 0.5, 's2_high': 1.5\n",
    "})\n",
    "cluster_params = bpd.cluster_params({\n",
    "    'measures': bpd.measures.CDFs(),\n",
    "    'grouping': bpd.grouping.KMeans(n_clusters=nk),\n",
    "    'is_sorted': True,\n",
    "    'copy': False\n",
    "})\n",
    "clean_params = bpd.clean_params({\n",
    "    'drop_returns': 'returners',\n",
    "    'copy': False\n",
    "})\n",
    "sim_params = bpd.sim_params({\n",
    "    'nl': nl, 'nk': nk,\n",
    "    'alpha_sig': 1, 'psi_sig': 1, 'w_sig': 0.6,\n",
    "    'c_sort': 0, 'c_netw': 0, 'c_sig': 1\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Extract data (we simulate for the example)\n",
    "\n",
    "`BipartitePandas` contains the class `SimBipartite` which we use here to simulate a bipartite network. If you have your own data, you can import it during this step. Load it as a `Pandas DataFrame` and then convert it into a `BipartitePandas DataFrame` in the next step.\n",
    "\n",
    "Note that `l` gives the true worker type and `k` gives the true firm type, while `alpha` gives the true worker effect and `psi` gives the true firm effect. We will save these columns separately.\n",
    "\n",
    "The BLM estimator uses the firm types computed via clustering, which are saved in columns `g1` and `g2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_data = bpd.SimBipartite(sim_params).simulate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare data\n",
    "\n",
    "This is exactly how you should prepare real data prior to running the BLM estimator.\n",
    "\n",
    "- First, we convert the data into a `BipartitePandas DataFrame`\n",
    "\n",
    "- Second, we clean the data (e.g. drop NaN observations, make sure firm and worker ids are contiguous, etc.)\n",
    "\n",
    "- Third, we cluster firms by their wage distributions, to generate firm classes (columns `g1` and `g2`). Alternatively, manually set the columns `g1` and `g2` to pre-estimated clusters (but make sure to [add them correctly!](https://tlamadon.github.io/bipartitepandas/notebooks/custom_columns.html#Adding-custom-columns-to-an-instantiated-DataFrame)).\n",
    "\n",
    "- Fourth, we collapse the data at the worker-firm spell level (taking mean wage over the spell)\n",
    "\n",
    "- Fifth, we convert the data into event study format\n",
    "\n",
    "Further details on `BipartitePandas` can be found in the package documentation, available [here](https://tlamadon.github.io/bipartitepandas/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "checking required columns and datatypes\n",
      "sorting rows\n",
      "dropping NaN observations\n",
      "generating 'm' column\n",
      "keeping highest paying job for i-t (worker-year) duplicates (how='max')\n",
      "dropping workers who leave a firm then return to it (how='returners')\n",
      "making 'i' ids contiguous\n",
      "making 'j' ids contiguous\n",
      "computing largest connected set (how=None)\n",
      "sorting columns\n",
      "resetting index\n"
     ]
    }
   ],
   "source": [
    "# Convert into BipartitePandas DataFrame\n",
    "sim_data = bpd.BipartiteDataFrame(sim_data)\n",
    "# Clean and collapse\n",
    "sim_data = sim_data.clean(clean_params).collapse(is_sorted=True, copy=False)\n",
    "# Cluster\n",
    "sim_data = sim_data.cluster(cluster_params)\n",
    "# Convert to event study format\n",
    "sim_data = sim_data.to_eventstudy(is_sorted=True, copy=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Separate observed and unobserved data\n",
    "\n",
    "Some of the simulated data is not observed, so we separate out that data during estimation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_data_observed = sim_data.loc[:, ['i', 'j1', 'j2', 'y1', 'y2', 't11', 't12', 't21', 't22', 'g1', 'g2', 'w1', 'w2', 'm']]\n",
    "sim_data_unobserved = sim_data.loc[:, ['alpha1', 'alpha2', 'k1', 'k2', 'l1', 'l2', 'psi1', 'psi2']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Separate movers and stayers data\n",
    "\n",
    "We need to distinguish movers and stayers for the estimator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "movers = sim_data_observed.get_worker_m(is_sorted=True)\n",
    "jdata = sim_data_observed.loc[movers, :]\n",
    "sdata = sim_data_observed.loc[~movers, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check the data\n",
    "\n",
    "Let's check the cleaned data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Movers data\n"
     ]
    },
    {
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       "      <td>15</td>\n",
       "      <td>15</td>\n",
       "      <td>-0.318783</td>\n",
       "      <td>-0.318783</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</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",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20111</th>\n",
       "      <td>9820</td>\n",
       "      <td>177</td>\n",
       "      <td>177</td>\n",
       "      <td>0.865980</td>\n",
       "      <td>0.865980</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20155</th>\n",
       "      <td>9840</td>\n",
       "      <td>111</td>\n",
       "      <td>111</td>\n",
       "      <td>1.149045</td>\n",
       "      <td>1.149045</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20213</th>\n",
       "      <td>9866</td>\n",
       "      <td>187</td>\n",
       "      <td>187</td>\n",
       "      <td>1.390672</td>\n",
       "      <td>1.390672</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20259</th>\n",
       "      <td>9885</td>\n",
       "      <td>17</td>\n",
       "      <td>17</td>\n",
       "      <td>-1.266577</td>\n",
       "      <td>-1.266577</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20272</th>\n",
       "      <td>9892</td>\n",
       "      <td>47</td>\n",
       "      <td>47</td>\n",
       "      <td>0.795123</td>\n",
       "      <td>0.795123</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>641 rows × 14 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          i   j1   j2        y1        y2  t11  t12  t21  t22 g1  g2  w1  w2  \\\n",
       "16        9  183  183  1.775003  1.775003    0    4    0    4  0   0   5   5   \n",
       "101      55   36   36 -0.154698 -0.154698    0    4    0    4  1   1   5   5   \n",
       "127      65  192  192  0.476397  0.476397    0    4    0    4  0   0   5   5   \n",
       "131      67  123  123 -0.268389 -0.268389    0    4    0    4  3   3   5   5   \n",
       "152      78   15   15 -0.318783 -0.318783    0    4    0    4  1   1   5   5   \n",
       "...     ...  ...  ...       ...       ...  ...  ...  ...  ... ..  ..  ..  ..   \n",
       "20111  9820  177  177  0.865980  0.865980    0    4    0    4  0   0   5   5   \n",
       "20155  9840  111  111  1.149045  1.149045    0    4    0    4  3   3   5   5   \n",
       "20213  9866  187  187  1.390672  1.390672    0    4    0    4  0   0   5   5   \n",
       "20259  9885   17   17 -1.266577 -1.266577    0    4    0    4  1   1   5   5   \n",
       "20272  9892   47   47  0.795123  0.795123    0    4    0    4  2   2   5   5   \n",
       "\n",
       "       m  \n",
       "16     0  \n",
       "101    0  \n",
       "127    0  \n",
       "131    0  \n",
       "152    0  \n",
       "...   ..  \n",
       "20111  0  \n",
       "20155  0  \n",
       "20213  0  \n",
       "20259  0  \n",
       "20272  0  \n",
       "\n",
       "[641 rows x 14 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('Movers data')\n",
    "display(jdata)\n",
    "print('Stayers data')\n",
    "display(sdata)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize and run BLMEstimator\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Note\n",
    "\n",
    "The `BLMEstimator` class requires data to be formatted as a BipartitePandas DataFrame.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize BLM estimator\n",
    "blm_fit = tw.BLMEstimator(blm_params)\n",
    "# Fit BLM estimator\n",
    "blm_fit.fit(jdata=jdata, sdata=sdata, n_init=40, n_best=5, ncore=8)\n",
    "# Store best model\n",
    "blm_model = blm_fit.model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check that log-likelihoods are monotonic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-likelihoods monotonic (movers): True\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Change in log-likelihood')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "liks1 = blm_model.liks1\n",
    "\n",
    "print('Log-likelihoods monotonic (movers):', np.min(np.diff(liks1)) >= 0)\n",
    "\n",
    "x_axis = range(1, len(liks1))\n",
    "plt.plot(x_axis, np.diff(liks1), '.', label='liks1', color='red')\n",
    "plt.plot(x_axis, np.zeros(len(liks1) - 1))\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Change in log-likelihood')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-likelihoods monotonic (stayers): True\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Change in log-likelihood')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "liks0 = blm_model.liks0\n",
    "\n",
    "print('Log-likelihoods monotonic (stayers):', np.min(np.diff(liks0)) >= 0)\n",
    "\n",
    "x_axis = range(1, len(liks0))\n",
    "plt.plot(x_axis, np.diff(liks0), '.', label='liks0', color='red')\n",
    "plt.plot(x_axis, np.zeros(len(liks0) - 1))\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Change in log-likelihood')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now we can investigate the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEGCAYAAABy53LJAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAaxUlEQVR4nO3dfbRV1Xnv8e9PEPAFUAFfQQ5VjJ4Yqs2W+BILkmGudjS+Ya00wzZJ1cREE5urLQwzxjU0RmtMmhK9Jt5EU62Jsd7YYohiFNSY+sJBAUWEIhoFvHo0vkSJvOhz/1jzwHZzOGct2evsfc75fcbYg7XmnGvtZ06HPMy11p5LEYGZmVleOzQ6ADMz612cOMzMrBAnDjMzK8SJw8zMCnHiMDOzQgY2OoCeMHLkyGhpaWl0GGZmvcrChQtfiYhRteX9InG0tLTQ1tbW6DDMzHoVSb/trNyXqszMrBAnDjMzK8SJw8zMCnHiMDOzQpw4uvDW+k08+uzveKb9rUaHYmbWNPrFU1UfxA2/eZav3/EU+w8X62MQ40buwqxph7Pn0CGNDs3MrKGcODox+cp7ee537wDw/BsBrOfNP2zgwlsW8ZNzjmxscGZmDeZLVTUefbZ9c9I44/B9+Z+fGA/AHzYGC555ld+++nYjwzMzazjPOGqc8YNHAbjpbydy7PjsB5MXHH8QLdPnsBF4bd1Gxo5oYIBmZg3mGcc2zF60ttPyg/ce2sORmJk1F884tmHektV8NYI/n7APy1e/url8yI4DGhiVmVnjOXHUeOCij/OnVz3IqxthzuI13LFoDRvfy+q+ffqhjQ3OzKwJ+FJVjf1HDufTldEArH+XzUnjyJbdmFoZ28DIzMyagyKi0TGUrlKphFfHNTMrRtLCiKjUlnvGYWZmhThxmJlZIU4cZmZWSKmJQ9IJkpZLWilpeif1YyXdK2mJpPskja6qu1LSUknLJM2SpJpjZ0t6ssz4zcxsa6UlDkkDgGuAE4FWYJqk1ppmVwE3RsQEYCZweTr2aOAYYAJwKHAEMKnq3KcBXrLWzKwBypxxTARWRsSqiNgA3AKcXNOmFZiXtudX1QcwBBgEDAZ2BF4CkLQr8FXgGyXGbmZm21Bm4tgPeKFqf3Uqq7YYOC1tnwoMlTQiIh4iSyQvps/ciFiW2v0j8G1gXVdfLulcSW2S2trb27evJ2Zmtlmjb45fBEyS9DjZpag1wLuSDgQOAUaTJZspko6VdBhwQETc3t2JI+K6iKhERGXUqFHl9cDMrJ8pc8mRNcCYqv3RqWyziFhLmnGkS1BTI+J1SecAD0fEW6nuTuAo4PdARdJzKfY9Jd0XEZNL7IeZmVUpc8axABgvaZykQcCZwOzqBpJGSuqIYQZwfdp+nmwmMlDSjmSzkWURcW1E7BsRLcDHgRVOGmZmPau0xBERm4DzgbnAMuDWiFgqaaakk1KzycBySSuAvYDLUvltwDPAE2T3QRZHxB1lxWpmZvl5rSozM+uU16oyM7O6cOIwM7NCnDjMzKwQJw4zMyvEicPMzApx4jAzs0KcOMzMrBAnDjMzK8SJw8zMCnHiMDOzQpw4zMysECcOMzMrxInDzMwKceIwM7NCnDjMzKwQJw4zMyvEicPMzApx4jAzs0KcOMzMrBAnDjMzK8SJw8zMCnHiMDOzQpw4zMysECcOMzMrpNTEIekEScslrZQ0vZP6sZLulbRE0n2SRlfVXSlpqaRlkmYps7OkOZKeTnVXlBm/mZltrbTEIWkAcA1wItAKTJPUWtPsKuDGiJgAzAQuT8ceDRwDTAAOBY4AJnUcExEHA4cDx0g6saw+mJnZ1sqccUwEVkbEqojYANwCnFzTphWYl7bnV9UHMAQYBAwGdgReioh1ETEfIJ3zMWA0ZmbWY8pMHPsBL1Ttr05l1RYDp6XtU4GhkkZExENkieTF9JkbEcuqD5S0G/Ap4N7OvlzSuZLaJLW1t7dvb1/MzCxp9M3xi4BJkh4nuxS1BnhX0oHAIWSzif2AKZKO7ThI0kDgp8CsiFjV2Ykj4rqIqEREZdSoUWX3w8ys3xhY4rnXAGOq9kenss0iYi1pxiFpV2BqRLwu6Rzg4Yh4K9XdCRwF/Dodeh3w3xHx3RLjNzOzTpQ541gAjJc0TtIg4ExgdnUDSSMldcQwA7g+bT9PNhMZKGlHstnIsnTMN4DhwIUlxm5mZttQWuKIiE3A+cBcsr/0b42IpZJmSjopNZsMLJe0AtgLuCyV3wY8AzxBdh9kcUTckR7XvYTspvpjkhZJOrusPpiZ2dYUEY2OoXSVSiXa2toaHYaZWa8iaWFEVGrLG31z3MzMehknDjMzK8SJw8zMCnHiMDOzQpw4zMysECcOMzMrxInDzMwKceIwM7NCnDjMzKwQJw4zMyvEicPMzApx4jAzs0IKJw5JO0gaVkYwZmbW/HIlDkk/kTRM0i7Ak8BTki4uNzQzM2tGeWccrRHxJnAKcCcwDjirrKDMzKx55U0cO6Y38Z0CzI6IjUDff5GHmZltJW/i+AHwHLAL8ICkscCbZQVlZmbNa2CeRhExC5hVVfRbSceVE5KZmTWzvDfHv5JujkvSjyQ9BkwpOTYzM2tCeS9VfS7dHP8ksDvZjfErSovKzMyaVt7EofTnnwE3RcTSqjIzM+tH8iaOhZLuJksccyUNBd4rLywzM2tWuW6OA38LHAasioh1kkYAny0tKjMza1p5ZxwBtAJfTvu7AENKicjMzJpa3sTxv4GjgGlp//fANd0dJOkEScslrZQ0vZP6sZLulbRE0n2SRlfVXSlpqaRlkmZJUir/qKQn0jk3l5uZWc/Imzg+FhFfAt4BiIjXgEFdHSBpAFlyOZFstjJNUmtNs6uAGyNiAjATuDwdezRwDDABOBQ4ApiUjrkWOAcYnz4n5OyDmZnVQd7EsTElggCQNIrub45PBFZGxKqI2ADcApxc06YVmJe251fVB9mlsEHAYGBH4CVJ+wDDIuLhiAjgRrJlUMzMrIfkTRyzgNuBPSVdBjwIfLObY/YDXqjaX53Kqi0GTkvbpwJDJY2IiIfIEsmL6TM3Ipal41d3c04AJJ0rqU1SW3t7e3f9MzOznPIuOXKzpIXAJ8h+v3FK+ot8e10EXC3pM8ADwBrgXUkHAocAHfc8fiXpWOAPeU8cEdcB1wFUKhUvyGhmVid5H8cF+G+yhQ0HAkjaPyKe76L9GmBM1f7oVLZZRKwlzTgk7QpMjYjXJZ0DPBwRb6W6O8luzt/ElmTS6TnNzKxcedequgB4CfgV8AtgTvqzKwuA8ZLGSRoEnAnMrjnvSEkdMcwArk/bzwOTJA1My7lPApZFxIvAm5KOTE9T/TXwn3n6YGZm9ZF3xvEV4EMR8WreE0fEJknnA3OBAcD1EbFU0kygLSJmA5OByyUF2aWqL6XDbyNbRPEJshvld0XEHanui8CPgZ3IXip1Z96YzMxs+yl7OKmbRtJ84PiI2FR+SPVXqVSira2t0WGYmfUqkhZGRKW2PO+MYxVwn6Q5wPqOwoj4Tp3iMzOzXiJv4ng+fQbRzQ//zMysb8v7OO7Xyw7EzMx6hy4Th6Q7SL8W70xEnFT3iMzMrKl1N+O4Kv15GrA38G9pfxrZ47lmZtbPdJk4IuJ+AEnfrrmzfockP6ZkZtYP5V2rahdJf9SxI2kc2Ts5zMysn8n7VNXfkT2Ou4psraqxwOdLi8rMzJpW3qeq7pI0Hjg4FT0dEeu7OsbMzPqmvGtV7QxcDJwfEYuB/SX9eamRmZlZU8p7j+MGYAPZCrWQrUj7jVIiMjOzppY3cRwQEVcCGwEiYh3ZvQ4zM+tn8iaODZJ2YsurYw+gas0qMzPrP/I+VXUpcBcwRtLNwDHAZ8sKyszMmlfep6ruTq+OPZLsEtVXIuKVUiMzM7OmlPepqnsj4tWImBMRv4iIVyTdW3ZwZmbWfLpb5HAIsDMwUtLubLkhPgzYr+TYzMysCXV3qerzwIXAvsBCtiSON4GrywvLzMyaVXeLHP4L8C+SLoiI7/VQTGZm1sTyPo77nqTdOnYk7S7pi+WEZGZmzSxv4jgnIl7v2ImI14BzSonIzMyaWt7EMUDS5l+KSxqA3z1uZtYv5f0B4F3AzyT9IO1/PpWZmVk/kzdx/ANZsjgv7f8K+GEpEZmZWVPL+8vx9yT9GJgXEcvLDcnMzJpZ3l+OnwQsIl2eknSYpNk5jjtB0nJJKyVN76R+rKR7JS2RdJ+k0an8OEmLqj7vSDol1X1C0mOp/EFJB+bvrpmZba+8N8f/FzAReB0gIhYB47o6IN1AvwY4EWgFpklqrWl2FXBjREwAZgKXp/PPj4jDIuIwYAqwDrg7HXMt8OlU9xPgazn7YGZmdZA3cWyMiDdqyqKbYyYCKyNiVURsAG4BTq5p0wrMS9vzO6kHOB24M70DpON7h6Xt4cDaHPGbmVmd5E0cSyX9FdljueMlfQ/4r26O2Q94oWp/NVuvb7UYOC1tnwoMlTSips2ZwE+r9s8GfilpNXAWcEVnXy7pXEltktra29u7CdXMzPLKmzguAD5M9vKmn5KtVXVhHb7/ImCSpMeBSWSvpH23o1LSPsBHgLlVx/wd8GcRMZrslbbf6ezEEXFdRFQiojJq1Kg6hGpmZpD/qap1wCXpk9caYEzV/uhUVn3etaQZh6RdganVv1AHzgBuj4iNqc0o4I8j4pFU/zP8exIzsx6VK3FIOohsdtBSfUxETOnisAXAeEnjyBLGmcBf1Zx3JPC7iHgPmAFcX3OOaam8w2vAcEkHRcQK4HhgWZ4+mJlZfeT9AeC/A98n+9Hfu920BSAiNkk6n+wy0wDg+ohYKmkm0BYRs4HJwOWSAngA+FLH8ZJayGYs99ec8xzg/0p6jyyRfC5nH8zMrA4U0d3DUSBpYUR8tAfiKUWlUom2trZGh2Fm1qukv/srteV5b47fIemLkvaRtEfHp84xmplZL5D3UtXfpD8vrioL4I/qG46ZmTW7vE9VdfkrcTMz6z/yzjiQdDRbP1V1YwkxmZlZE8v7OO5NwAFkCx12PFUVgBOHmVk/k3fGUQFaI88jWGZm1qflfarqSWDvMgMxM7PeIe+MYyTwlKRHydarAiAiTiolKjMza1p5E8elZQZhZma9R97Hce+XtBdwRCp6NCJeLi8sMzNrVnlfHXsG8CjwF2Qr1j4i6fQyAzMzs+aU91LVJcARHbOMtLz5PcBtZQVmZmbNKe9TVTvUXJp6tcCxZmbWh+SdcdwlaS5bXuH6l8AvywnJzMyaWZeJQ9KBwF4RcbGk04CPp6qHgJvLDs7MzJpPdzOO75LewBcRPwd+DiDpI6nuUyXGZmZmTai7+xR7RcQTtYWprKWUiMzMrKl1lzh266JupzrGYWZmvUR3iaMtveP7fSSdDSwsJyQzM2tm3d3juBC4XdKn2ZIoKsAg4NQS4zIzsybVZeKIiJeAoyUdBxyaiudExLzSIzMzs6aUd62q+cD8kmMxM7NewL/+NjOzQpw4zMyskFITh6QTJC2XtFLS9E7qx0q6V9ISSfdJGp3Kj5O0qOrzjqRTUp0kXSZphaRlkr5cZh/MzOz98q5VVZikAcA1wPHAamCBpNkR8VRVs6uAGyPiXyVNAS4Hzkr3VA5L59kDWAncnY75DDAGODgi3pO0Z1l9MDOzrZU545gIrIyIVRGxAbgFOLmmTSvQ8YTW/E7qAU4H7oyIdWn/PGBmRLwH4BdKmZn1rDITx37AC1X7q1NZtcXAaWn7VGCopBE1bc5ky6q8AAcAfympTdKdksZ39uWSzk1t2trb2z9wJ8zM7P0afXP8ImCSpMeBScAa4N2OSkn7AB8B5lYdMxh4JyIqwP8Bru/sxBFxXURUIqIyatSosuI3M+t3SrvHQZYExlTtj05lm0XEWtKMQ9KuwNSIeL2qyRnA7RGxsapsNWmVXuB24Ib6hm1mZl0pc8axABgvaZykQWSXnGZXN5A0UlJHDDPYevYwjfdfpgL4D+C4tD0JWFHPoM3MrGulJY6I2AScT3aZaRlwa0QslTRT0kmp2WRguaQVwF7AZR3HS2ohm7HcX3PqK4Cpkp4gewrr7LL6YGZmW1NENDqG0lUqlWhra2t0GGZmvYqkhel+8vs0+ua4mZn1Mk4cZmZWiBOHmZkV4sRhZmaFOHGYmVkhThxmZlaIE4eZmRXixGFmZoU4cZiZWSFOHGZmVogTh5mZFeLEYWZmhThxmJlZIU4cZmZWiBOHmZkV4sRhZmaFOHGYmVkhThxmZlaIE4eZmRXixGFmZoU4cZiZWSFOHGZmVogTh5mZFeLEYWZmhZSaOCSdIGm5pJWSpndSP1bSvZKWSLpP0uhUfpykRVWfdySdUnPsLElvlRm/mZltrbTEIWkAcA1wItAKTJPUWtPsKuDGiJgAzAQuB4iI+RFxWEQcBkwB1gF3V527AuxeVuxmZrZtZc44JgIrI2JVRGwAbgFOrmnTCsxL2/M7qQc4HbgzItbB5oT0LeDvS4nazMy6VGbi2A94oWp/dSqrthg4LW2fCgyVNKKmzZnAT6v2zwdmR8SLXX25pHMltUlqa29vLxy8mZl1rtE3xy8CJkl6HJgErAHe7aiUtA/wEWBu2t8X+Avge92dOCKui4hKRFRGjRpVRuxmZv3SwBLPvQYYU7U/OpVtFhFrSTMOSbsCUyPi9aomZwC3R8TGtH84cCCwUhLAzpJWRsSBpfTAzMy2UuaMYwEwXtI4SYPILjnNrm4gaaSkjhhmANfXnGMaVZepImJOROwdES0R0QKsc9IwM+tZpSWOiNhEdj9iLrAMuDUilkqaKemk1GwysFzSCmAv4LKO4yW1kM1Y7i8rRjMzK04R0egYSlepVKKtra3RYZiZ9SqSFkZEpba80TfHzcysl3HiMDOzQpw4zMysECcOMzMrxInDzMwKceIwM7NCnDjMzKwQJw4zMyvEicPMzApx4jAzs0LKXB3XzMwa4Jgr7mHo609zw6BvcdSmKzjrowfzj1MPr9v5PeMwM+tDWmb8J+0D7uLmQZdz3pghDP3QN7lpwVpO+Of76vYdnnGYmfUhg/b4NYP3nMvkPfeoKt3E0y+9Xbfv8IzDzKyPmHLVPDa8Onmr8qGHfI2hh0znjfVv1OV7POMwM+sjxuw2hNeGXcqmTurefWdPhg0aVpfv8YzDzKyPmHXWh9k0+LVO6767ehPpldvbzYnDzKyPGL5xPUuefZ7Fq57fqu65PVbV7Xt8qcrMrK8YPAzt2crGP/wegP03vMfVL2zgnn134m9GfLRuX+PEYWbWV+w4BL74EIOAB9e/wbBBw5DEOXX+GicOM7M+aPjg4aWd2/c4zMysECcOMzMrxInDzMwKceIwM7NCFBGNjqF0ktqB31YVjQReaVA4zcjjsYXHYguPxfv1x/EYGxGjagv7ReKoJaktIiqNjqNZeDy28Fhs4bF4P4/HFr5UZWZmhThxmJlZIf01cVzX6ACajMdjC4/FFh6L9/N4JP3yHoeZmX1w/XXGYWZmH5ATh5mZFdKnEoekb0l6WtISSbdL2m0b7XaTdFtqu0zSUVV1F6TypZKurDluf0lvSbqo5K5st7LGQtJESYvSZ7GkU3uoSx9YiWNxvKSFkp5If07poS5tlxLHY4Sk+en/kat7qDvbpcy/MyTNkLRS0nJJ/6MHutNzIqLPfIBPAgPT9j8B/7SNdv8KnJ22BwG7pe3jgHuAwWl/z5rjbgP+Hbio0X1t1FgAO1eddx/g5Y79Zv2UOBaHA/um7UOBNY3ua4PHYxfg48AXgKsb3c8Gj0UrsBgYDIwDngEGNLq/9fr0qRlHRNwdER2v230YGF3bRtJw4E+BH6VjNkTE66n6POCKiFif6l6uOu4U4FlgaVnx11NZYxER66rOOwRo+qcrShyLxyNibWqzFNhJ0uDSOlInJY7H2xHxIPBOuT2onxL/zjgZuCUi1kfEs8BKYGJpHelhfSpx1PgccGcn5eOAduAGSY9L+qGkXVLdQcCxkh6RdL+kIwAk7Qr8A/D1ngi8BHUbCwBJH5O0FHgC+ELV/3i9QV3HospU4LGOv0B6kbLGozeq51jsB7xQdY7VqaxP6HWJQ9I9kp7s5HNyVZtLgE3AzZ2cYiDwJ8C1EXE48DYwvapuD+BI4GLgVkkCLgX+OSLeKq1jH0CDxoKIeCQiPgwcAcyQNKSsPubVqLFI5/0w2WWOz5fRtw+ikePRbDwWJWj0tbJ6f4DPAA8BO2+jfm/guar9Y4E5afsu4LiqumeAUcCvgefS53Xgd8D5je5rI8aik3PMAyqN7mujxoLs0sYK4JhG97EZxqPq3L3iHkdZYwHMAGZUlc8Fjmp0X+v16XUzjq5IOgH4e+CkiFjXWZuI+H/AC5I+lIo+ATyVtv+D7GYXkg4iuwn2SkQcGxEtEdECfBf4ZkQ09VMjZY2FpHGSBqbyscDBZAm1aZU4FrsBc4DpEfGb0jpQZ2WNR5kxl6XEsZgNnClpsKRxwHjg0bL60eManbnq/C+HlWTXFRelz/dT+b7AL6vaHQa0AUvI/sPvnsoHAf8GPAk8Bkzp5DsupXc8VVXKWABnkd0IXpTKT2l0Xxs4Fl8ju2yxqOqzZ0/2rZnGI9U9RzYjf4vsun5ro/vbwLG4hGwGshw4sdF9refHS46YmVkhfepSlZmZlc+Jw8zMCnHiMDOzQpw4zMysECcOMzMrxInDrAuStlotQNIXJP112r5PUiXnuVokPZm2K5Jmpe1LVcKKy2Wd12xgowMw620i4vt1OEcb2e8CzHodzzjMCursX/KSdpD0Y0nfkDRA2XseFih7z8NWa1hJmizpF1VFrWn2skrSl6vafbVqbaULc5RfImmFpAeBD2FWAs84zLbfQLLF8Z6MiMsknQu8ERFHKFtm/TeS7qbrJegPJlu6YiiwXNK1wATgs8DHAAGPSLqf7B982yo/k+xXzgPJfsm8sN6dNXPiMNt+PwBujYjL0v4ngQmSTk/7w8nWKlrRxTnmRLYk+3pJLwN7kb0U6faIeBtA0s/JFtjTNsp3SOXrUvnsOvbRbDNfqjLbfv8FHFe1vLyACyLisPQZFxF3d3OO6vd4vIv/UWdNzInDbPv9CPgl2bsYBpItoX2epB0hWzVVW178U8SvgVMk7ZyOPzWVbav8gVS+k6ShwKe2u2dmnfC/asy6trOk1VX73+msUUR8R9krRm8CPg20AI+ll/q0A6cU/eKIeEzSj9myHPcPI+JxgC7Kf0b2ruuXgQVFv9MsD6+Oa2ZmhfhSlZmZFeLEYWZmhThxmJlZIU4cZmZWiBOHmZkV4sRhZmaFOHGYmVkh/x/YEWKIO/rNoAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot likelihood vs. connectedness\n",
    "blm_fit.plot_liks_connectedness()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "blm_fit.plot_log_earnings()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEWCAYAAABrDZDcAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAAacklEQVR4nO3de7hVdZ3H8fdHLmoKmHFqlKs66ISaaUSW42RmBUxCjaViWBgTlZrO6NRY45iXbFKfscmySWdUvCs6ljjhmFOgaV6AvCKpRCogKuIFDG/gd/5YvzMtNntzFpyz9uac9Xk9z3pY9/XdC9ifvdZvXRQRmJlZdW3R6gLMzKy1HARmZhXnIDAzqzgHgZlZxTkIzMwqzkFgZlZxDgLrdiR9TtIvWl1HO0lbS7pJ0suSrmvididLuqNZ27Oey0FgAEh6QtKrkl6R9KykaZK23QzqGi4pJPVuHxcRV0bEx1tZV43PAO8C3hERn211MV1B0qmSrmh1HdYcDgLLOzgitgX2AUYBJ9fOkP9CLlszt9VJw4DHImJNszbYlfumG+1nK4mDwNYTEUuBm4E9ANIv8mMkPQ48nsZ9SdJCSS9ImiFpx/bl0/zHSVok6XlJ50jaIk3bQtLJkp6U9JykyyQNSNPaf/1PkfQU8Cvg9rTal9LRygdrT4lI+pCkOenUzBxJH8pNmy3pDEl3Slol6ReSBqZpW0m6QtIKSS+lZd9Vb59Ienda10uS5ksan8afBpwCHJbqm1Kz3FbpSKt9m/8kaY2k/mn4DEn/lvoHpP2xPO2fk3P7bXL6DN+XtAI4tU6N50i6I61ngKSLJC2TtFTSdyT1KrIuSWOAb+U+0wOSPitpXs18J0i6MfVPk/QTSbem/XybpGG5ef8iTXtB0qOSDs1NGyfpkbTcUkn/UO/vwEoUEe7cATwBHJT6hwDzgTPScAC3AtsDWwMHAs+THTlsCfwQuD23rgBmpfmHAo8Bf5umfRFYCOwMbAvcAFyepg1Py14GbJO21T6ud279k4E7Uv/2wIvAkUBvYGIafkeaPhv4PbBrWt9s4Htp2peBm4C3Ab2A9wH96+ybPqnmbwF90+dfBeyWpp8KXLGBfXs7cEjq/0WqZ2xu2qdT/2XAjUC/9LkfA6bkPvMa4Gvpc27dvh/IftD9B3AL8LY0/0+BC9J+fCdwL/DlRuuqU/M6nyn9Pb8AvDs37r7c55qW9slfpXl/kPs72gZYDByVtrc32b+fkWn6MmD/1P92YJ9W/3+oWtfyAtxtHh1ZELwCvAQ8Cfy4/QuC7Iv4wNy8FwFn54a3Bd4EhufmH5ObfjTwy9T/S+Do3LTd0rK9+dOX/s656e3jGgXBkcC9NZ/lLmBy6p8NnFxTy/+k/i8CvwHe08G+2R94BtgiN+5q4NTUv86XZp3lzwDOS5/xGeB44HvAVsCrwDvIguiN9i/HtNyXgdm5z/xUzXonA/cA1wL/BfRN498FvE7uC54sIGc1Wledmtf7TMC/A2em/t3JAnfLNDwNuKbm38Rash8VhwG/rlnXBcC3U/9T6bOuF8LumtP51JDlfSoitouIYRFxdES8mpu2ONe/I1lYABARrwArgEEN5n8yLbPesqm/N9mXV71lO1K7vvZ15mt5Jte/muxLCuBysl/R10h6WtLZkvo02MbiiHhrA9vYkNuAA8iOoB4iO7r6MLAvsDAiVgADyY48avdNo33a7s+BCcBpEfFGGjcsrWtZOpX1EtkX7zs7WFdHLgWOkCSyAJ4eEa/XW2f6N/EC2b4bBnygvZZUz+eAP0uzHwKMA55Mp5Q+uAm1WSc4CKyo/GNqnyb7zw2ApG3IftUuzc0zJNc/NC2z3rJp2hrg2Qbb6ujxuLXra1/n0jrzriMi3oyI0yJiJPAh4JPA5xtsY0j7+fqN2UbyG7Ijn08Dt0XEI2n5cWQhAdmpkjdZf9/kt1FvXywgO+Vys6Td0rjFZEcEA1OwbxcR/SNi9w7WxYamR8TdZEct+wNHkAVp3v//nSu74mx7sn23mOxzb5frto2Ir6b1zomICWRB9TNgege1WRdzENimuBo4StJ7JW0JfBe4JyKeyM3zdUlvlzSE7FTItbll/17STunL4rvAtdH4ipvlwFtkbQr1zAR2lXSEpN6SDgNGAv/d0YeQ9BFJe6ZG1JVkX8Rv1Zn1HrIjiW9I6iPpAOBg4JqOtgEQEauBecAx/OmL/zfAV9qHI2It2RfgmZL6pYbWE4AOL+GMiKvJ2i/+V9IuEbGMrC3iXyX1V9ZAv4ukDxepN3kWGF4TfpC1Y/wIeDMiau9hGCfpLyX1JTsddndELCb7u9hV0pFp//WR9P7UAN9X2X0hAyLiTbK/h3p/B1YiB4FttIj4X+Cfyc5LLwN2AQ6vme1Gsi+/+4Gfk7UrAFxM9kvyduAPwGtkjZaNtrUaOBO4M51W2Ldm+gqyX/Inkp2e+gbwyYh4vsBH+TPgerIvnwVkX8q1v3JJp1wOBsaS/XL/MfD5iPhdgW20u43sdM29ueF+/OmqKMj2wx+BRWSNwFeR7a8ORcSlwOnAryQNJzuy6Qs8QnYu/3pgh42ot/3GuBWSfpsbfznZ1WT1Auoq4Ntkp4TeB0xKta0CPk72b+RpslN1Z5E1KkN2mukJSSvJwvFzG1GndQFF+MU01rUkBTAiIha2uhbrWpK2Bp4ju7Ln8dz4acCSiFjv3hPb/PmIwMw2xleBOfkQsO7PdxSaWSGSngAEfKq1lVhX86khM7OK86khM7OK63anhgYOHBjDhw9vdRlmZt3KvHnzno+ItnrTul0QDB8+nLlz57a6DDOzbkVS7R34/8+nhszMKs5BYGZWcQ4CM7OKcxCYmVWcg8DMrOIcBGZmFVdaEEi6WNk7aR9uMF2SzlP23tsHJe1TVi1mZtZYmUcE04AxG5g+FhiRuqlkr8EzM7MmKy0IIuJ2sueSNzIBuCwydwPbSdqY56WbmVkXaOWdxYNY972pS9K4ZbUzSppKdtTA0KFDN3mDe1665yYv2xM89IWHOrW895/3X2d5H3ZOZ/dfI92isTgiLoyIURExqq2t7qMyzMxsE7UyCJay7gvOB1P8ZeBmZtZFWhkEM4DPp6uH9gVeTi/dNjOzJiqtjUDS1cABwEBJS8heat0HICJ+AswExgELgdXAUWXVYmZmjZUWBBExsYPpARxT1vbNzKyYbtFYbGZm5XEQmJlVnIPAzKziHARmZhXnIDAzqzgHgZlZxTkIzMwqzkFgZlZxDgIzs4pzEJiZVZyDwMys4hwEZmYV5yAwM6s4B4GZWcU5CMzMKs5BYGZWcQ4CM7OKcxCYmVWcg8DMrOIcBGZmFecgMDOrOAeBmVnFOQjMzCrOQWBmVnEOAjOzinMQmJlVnIPAzKziHARmZhXnIDAzqzgHgZlZxTkIzMwqzkFgZlZxpQaBpDGSHpW0UNJJdaYPlTRL0n2SHpQ0rsx6zMxsfaUFgaRewPnAWGAkMFHSyJrZTgamR8TewOHAj8uqx8zM6ivziGA0sDAiFkXEG8A1wISaeQLon/oHAE+XWI+ZmdVRZhAMAhbnhpekcXmnApMkLQFmAl+rtyJJUyXNlTR3+fLlZdRqZlZZrW4snghMi4jBwDjgcknr1RQRF0bEqIgY1dbW1vQizcx6sjKDYCkwJDc8OI3LmwJMB4iIu4CtgIEl1mRmZjXKDII5wAhJO0nqS9YYPKNmnqeAjwJIejdZEPjcj5lZE5UWBBGxBjgWuAVYQHZ10HxJp0san2Y7EfiSpAeAq4HJERFl1WRmZuvrXebKI2ImWSNwftwpuf5HgP3KrMHMzDas1Y3FZmbWYg4CM7OKcxCYmVWcg8DMrOIcBGZmFecgMDOrOAeBmVnFOQjMzCrOQWBmVnEOAjOzinMQmJlVnIPAzKziOgwCSftJ2ib1T5J0rqRh5ZdmZmbNUOSI4N+B1ZL2Ints9O+By0qtyszMmqZIEKxJ7wiYAPwoIs4H+pVblpmZNUuR9xGskvRNYBLwV+mdwn3KLcvMzJqlyBHBYcDrwJSIeIbs3cPnlFqVmZk1TYdHBOnL/9zc8FO4jcDMrMcoctXQ30h6XNLLklZKWiVpZTOKMzOz8hVpIzgbODgiFpRdjJmZNV+RIHjWIWBmm4OH/vBUq0vokYoEwVxJ1wI/I2s0BiAibiirKDMza54iQdAfWA18PDcuAAeBmVkPUOSqoaOaUUgz+LDSzGx9HQaBpMHAD4H90qhfA8dHxJIyC7PNj4O0c7z/bHNV5IayS4AZwI6puymNMzOzHqBIELRFxCURsSZ104C2kusyM7MmKRIEK9Ljp3ulbhKwouzCzMysOYoEwReBQ4FngGXAZ4Ae04BsZlZ1Ra4aehIY34RazMysBRoGgaRvRMTZkn5Idt/AOiLiuFIrMzOzptjQEUH7YyXmNqMQMzNrjYZBEBE3pd7VEXFdfpqkzxZZuaQxwA+AXsB/RsT36sxzKHAq2VHHAxFxRLHSzcysKxRpLP5mwXHrkNQLOB8YC4wEJkoaWTPPiLSu/SJid+DvCtRjZmZdaENtBGOBccAgSeflJvUH1hRY92hgYUQsSuu7huy9x4/k5vkScH5EvAgQEc9tXPlmZtZZGzoieJqsfeA1YF6umwF8osC6BwGLc8NL0ri8XYFdJd0p6e50KsnMzJpoQ20ED0h6GPhERFxa4vZHAAeQvQv5dkl7RsRL+ZkkTQWmAgwdOrSkUszMqmmDbQQRsRYYIqnvJqx7KTAkNzw4jctbAsyIiDcj4g/AY2TBUFvHhRExKiJGtbX56RZmZl2pyPsI/gDcKWkG8Mf2kRFxbuNFAJgDjJC0E1kAHA7UXhH0M2AicImkgWSnihYVK93MzLpCkSD4feq2APoVXXFErJF0LHAL2eWjF0fEfEmnA3MjYkaa9nFJjwBrga9HhJ9jZGbWREUeMXEagKRt0/ArRVceETOBmTXjTsn1B3BC6szMrAU6vI9A0h6S7gPmA/MlzZO0e/mlmZlZMxS5oexC4ISIGBYRw4ATgf8otywzM2uWIkGwTUTMah+IiNnANqVVZGZmTVWksXiRpH8GLk/Dk/CVPWZmPUbRF9O0ATekri2NMzOzHqDIVUMvAsdJGgC8FRGryi/LzMyapchVQ++X9BDwAPCQpAckva/80szMrBmKtBFcBBwdEb8GkPSXwCXAe8oszMzMmqNIG8Ha9hAAiIg7KPYYajMz6waKHBHcJukC4Gqyt4gdBsyWtA9ARPy2xPrMzKxkRYJgr/Tnt2vG700WDAd2aUVmZtZURa4a+kgzCjEzs9YoctXQAEnnSpqbun9Nl5KamVkPUKSx+GJgFXBo6laSXTVkZmY9QJE2gl0i4pDc8GmS7i+pHjMza7IiRwSvpnsHAJC0H/BqeSWZmVkzFTki+ApwWa5d4EXgC+WVZGZmzbTBIJDUCzgyIvaS1B8gIlY2pTIzM2uKDQZBRKxtPy3kADAz65mKnBq6T9IM4Drgj+0jI+KG0qoyM7OmKRIEWwErWPcO4iB7N4GZmXVzRe4sPqoZhZiZWWsUubN4Z0k3SVou6TlJN0raqRnFmZlZ+YrcR3AVMB3YAdiRrK3gmjKLMjOz5ikSBG+LiMsjYk3qriBrNzAzsx6gSGPxzZJOIjsKaH8fwUxJ2wNExAsl1mdmZiUrEgSHpj+/XDP+cLJg2LlLKzIzs6YqctWQG4bNzHqwIm0EZmbWgzkIzMwqzkFgZlZxRW4ok6RJkk5Jw0MljS6/NDMza4YiRwQ/Bj4ITEzDq4DzS6vIzMyaqkgQfCAijgFeA4iIF4G+RVYuaYykRyUtTPciNJrvEEkhaVShqs3MrMsUCYI30wtqAkBSG/BWRwulZc4HxgIjgYmSRtaZrx9wPHDPRtRtZmZdpEgQnAf8FHiXpDOBO4DvFlhuNLAwIhZFxBtkdyZPqDPfGcBZpCMOMzNrriI3lF0paR7w0TTqUxGxoMC6BwGLc8NLgA/kZ5C0DzAkIn4u6euNViRpKjAVYOjQoQU2bWZmRRW9fPRtQK80/9ZdsWFJWwDnAid2NG9EXBgRoyJiVFtbW1ds3szMkiKXj54CXApsDwwELpF0coF1LwWG5IYHp3Ht+gF7ALMlPQHsC8xwg7GZWXMVeejc54C9IuI1AEnfA+4HvtPBcnOAEeklNkvJHlJ3RPvEiHiZLFhI650N/ENEzN2I+s3MrJOKnBp6mnXfP7Al6/6yrysi1gDHArcAC4DpETFf0umSxm9KsWZm1vWKHBG8DMyXdCvZJaQfA+6VdB5ARBzXaMGImAnMrBl3SoN5DyhYs5mZdaEiQfDT1LWbXU4pZmbWCkWC4AXg5xHR4U1kZmbW/RRpIzgMeFzS2ZL+ouyCzMysuToMgoiYBOwN/B6YJukuSVPToyHMzKybK3RDWUSsBK4ne0zEDsCngd9K+lqJtZmZWRMUuaFsgqSfkjUS9wFGR8RYYC8K3BVsZmabtyKNxX8DfD8ibs+PjIjVkqaUU5aZmTVLkSB4pjYEJJ0VEf8YEb8sqa5SDH/tqlaX0FJPtLoAM9ssFWkj+FidcWO7uhAzM2uNhkcEkr4KHA3sIunB3KR+wJ1lF2ZmVstH9eXY0Kmhq4CbgX8B8q+ZXBURL5RUj23G/J/QrGdqGATp6aAv86eX1ptZJ1Q9SMFhurkq+mIaMzProRwEZmYV5yAwM6s4B4GZWcU5CMzMKs5BYGZWcQ4CM7OKcxCYmVWcg8DMrOIcBGZmFecgMDOrOAeBmVnFOQjMzCrOQWBmVnEOAjOzinMQmJlVnIPAzKziHARmZhXnIDAzqzgHgZlZxZUaBJLGSHpU0kJJJ9WZfoKkRyQ9KOmXkoaVWY+Zma2vtCCQ1As4HxgLjAQmShpZM9t9wKiIeA9wPXB2WfWYmVl9ZR4RjAYWRsSiiHgDuAaYkJ8hImZFxOo0eDcwuMR6zMysjjKDYBCwODe8JI1rZApwc70JkqZKmitp7vLly7uwRDMz2ywaiyVNAkYB59SbHhEXRsSoiBjV1tbW3OLMzHq43iWueykwJDc8OI1bh6SDgH8CPhwRr5dYj5mZ1VHmEcEcYISknST1BQ4HZuRnkLQ3cAEwPiKeK7EWMzNroLQgiIg1wLHALcACYHpEzJd0uqTxabZzgG2B6yTdL2lGg9WZmVlJyjw1RETMBGbWjDsl139Qmds3M7OObRaNxWZm1joOAjOzinMQmJlVnIPAzKziHARmZhXnIDAzqzgHgZlZxTkIzMwqzkFgZlZxDgIzs4pzEJiZVZyDwMys4hwEZmYV5yAwM6s4B4GZWcU5CMzMKs5BYGZWcQ4CM7OKcxCYmVWcg8DMrOIcBGZmFecgMDOrOAeBmVnFOQjMzCrOQWBmVnEOAjOzinMQmJlVnIPAzKziHARmZhXnIDAzqzgHgZlZxTkIzMwqzkFgZlZxpQaBpDGSHpW0UNJJdaZvKenaNP0eScPLrMfMzNZXWhBI6gWcD4wFRgITJY2smW0K8GJE/DnwfeCssuoxM7P6yjwiGA0sjIhFEfEGcA0woWaeCcClqf964KOSVGJNZmZWo3eJ6x4ELM4NLwE+0GieiFgj6WXgHcDz+ZkkTQWmpsFXJD1aSsXlG0jNZ2smdf/jLe+/zvM+7JzuvP+GNZpQZhB0mYi4ELiw1XV0lqS5ETGq1XV0V95/ned92Dk9df+VeWpoKTAkNzw4jas7j6TewABgRYk1mZlZjTKDYA4wQtJOkvoChwMzauaZAXwh9X8G+FVERIk1mZlZjdJODaVz/scCtwC9gIsjYr6k04G5ETEDuAi4XNJC4AWysOjJuv3prRbz/us878PO6ZH7T/4BbmZWbb6z2Mys4hwEZmYV5yBoAkkXS3pO0sOtrqU7kjRE0ixJj0iaL+n4VtfUnUjaStK9kh5I+++0VtfUHUnqJek+Sf/d6lq6moOgOaYBY1pdRDe2BjgxIkYC+wLH1HlciTX2OnBgROwFvBcYI2nf1pbULR0PLGh1EWVwEDRBRNxOdlWUbYKIWBYRv039q8j+Mw5qbVXdR2ReSYN9UuerRDaCpMHAXwP/2epayuAgsG4lPaF2b+CeFpfSraTTGvcDzwG3RoT338b5N+AbwFstrqMUDgLrNiRtC/wX8HcRsbLV9XQnEbE2It5Ldof/aEl7tLikbkPSJ4HnImJeq2spi4PAugVJfchC4MqIuKHV9XRXEfESMAu3WW2M/YDxkp4ge4rygZKuaG1JXctBYJu99Gjyi4AFEXFuq+vpbiS1Sdou9W8NfAz4XUuL6kYi4psRMTgihpM9/eBXETGpxWV1KQdBE0i6GrgL2E3SEklTWl1TN7MfcCTZL7H7Uzeu1UV1IzsAsyQ9SPYMsFsjosddAmmbzo+YMDOrOB8RmJlVnIPAzKziHARmZhXnIDAzqzgHgZlZxTkIrEeTdJykBZKulDRe0kklb++Asp5OKWm2pB734nRrvdJeVWm2mTgaOCgilqTh2vdmI6l3RKxpbllmmw8HgfVYkn4C7AzcLOli4EVgVEQcK2ka8BrZA+zulLQ98GoafifwReDzwAeBeyJicp31vx/4AbAN2aOeP1ozfXSavlVa91ER8aik3YFLgL5kR+WHAE8D08meBdQLOCMirm3wubYALgaWRMTJm7RzzHIcBNZjRcRXJI0BPhIRz0uaXDPLYOBDEbE2BcPbyb74x5MdOewH/C0wR9J7I+L+9gUl9QWuBQ6LiDmS+pN92ef9Dtg/ItZIOgj4LtmX/leAH0TElWk9vYBxwNMR8ddp/QMafKzewJXAwxFx5sbvFbP1uY3Aquy6iFibG74pslvtHwKejYiHIuItYD4wvGbZ3YBlETEHICJW1jm9NAC4Lr2Z7vvA7mn8XcC3JP0jMCwiXk3b/JiksyTtHxEvN6j5AhwC1sUcBFZlf6wZfj39+Vauv314U46ezwBmRcQewMFkp4iIiKvIjjpeBWZKOjAiHgP2IQuE70g6pcE6fwN8RNJWm1CPWV0OArNN8yiwQ2onQFI/SbVhMQBYmvont4+UtDOwKCLOA24E3iNpR2B1RFwBnEMWCvVcBMwEptfZntkmcRCYbYKIeAM4DPihpAeAW0m/+HPOBv5F0n2se0RxKPBwemPYHsBlwJ7AvWnct4HvbGDb5wL3AZenhmOzTvHTR83MKs6/JszMKs5BYGZWcQ4CM7OKcxCYmVWcg8DMrOIcBGZmFecgMDOruP8DaKC7p6z5KZ8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "blm_fit.plot_type_proportions()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finally, we can compare estimates to the truth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute true parameters\n",
    "true_A1 = np.expand_dims(sim_data_unobserved.groupby('l1')['alpha1'].mean().to_numpy(), 1) + np.tile(sim_data_unobserved.groupby('k1')['psi1'].mean().to_numpy(), (nl, 1))\n",
    "true_A2 = np.expand_dims(sim_data_unobserved.groupby('l2')['alpha2'].mean().to_numpy(), 1) + np.tile(sim_data_unobserved.groupby('k2')['psi2'].mean().to_numpy(), (nl, 1))\n",
    "\n",
    "# Sort estimated parameters (this is because the firm type order generated by clustering is random - this is automatically handled in the built-in plotting functions)\n",
    "A1, A2 = blm_model._sort_parameters(blm_model.A1, blm_model.A2, sort_firm_types=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(true_A1.flatten(), A1.flatten(), '.', label='A1', color='red')\n",
    "plt.plot(true_A2.flatten(), A2.flatten(), '.', label='A2', color='green')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrapped errors\n",
    "\n",
    "The package contains the class `BLMBootstrap`, which allows for the construction of bootstrapped error bars.\n",
    "\n",
    "In this example, we use the same simulated data and estimation parameters as in the previous example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize BLM bootstrap estimator\n",
    "blm_fit = tw.BLMBootstrap(blm_params)\n",
    "# Fit BLM estimator\n",
    "blm_fit.fit(\n",
    "    jdata=jdata, sdata=sdata,\n",
    "    blm_model=blm_model,\n",
    "    n_samples=20,\n",
    "    cluster_params=cluster_params,\n",
    "    ncore=8,\n",
    "    verbose=False\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now we can investigate the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "blm_fit.plot_log_earnings()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dCJwQEcMiYhhwIvAf5ZZlZmaNUiQItomIWe0DETEb2Ka0iszMrKGKNBYvkvTPwOVpeBK+ssfMrMco+mKaNuCG1LWlcWZm1gMUuWroReA4SQOAtyJiVfllmZlZoxS5auj9kh4CHgAekvSApPeVX5qZmTVCkTaCi4CjI+LXAJL+ErgEeE+ZhZmZWWMUaSNY2x4CABFxB8UeQ21mZi2gyBHBbZIuAK4me4vYYcBsSfsARMRvS6zPzMxKViQI9kp/frtm/N5kwXBgt1ZkZmYNVeSqoY80ohAzM2uOIlcNDZB0rqS5qfvXdCmpmZn1AEUaiy8GVgGHpm4l2VVDZmbWAxRpI9glIg7JDZ8m6f6S6jEzswYrckTwarp3AABJ+wGvlleSmZk1UpEjgq8Al+XaBV4EvlBeSWZm1kgbDAJJvYAjI2IvSf0BImJlQyozM7OG2GAQRMTa9tNCDgAzs56pyKmh+yTNAK4D/tg+MiJuKK0qMzNrmCJBsBWwgnXvIA6ydxOYmVmLK3Jn8VGNKMTMzJqjyJ3FO0u6SdJySc9JulHSTo0ozszMylfkPoKrgOnADsCOZG0F15RZlJmZNU6RIHhbRFweEWtSdwVZu4GZmfUARRqLb5Z0EtlRQPv7CGZK2h4gIl4osT4zMytZkSA4NP355Zrxh5MFw87dWpGZmTVUkauG3DBsZtaDFWkjMDOzHsxBYGZWcQ4CM7OKK3JDmSRNknRKGh4qaXT5pZmZWSMUOSL4MfBBYGIaXgWcX1pFZmbWUEWC4AMRcQzwGkBEvAj0LbJySWMkPSppYboXoaP5DpEUkkYVqtrMzLpNkSB4M72gJgAktQFvdbZQWuZ8YCwwEpgoaWSd+foBxwP3bETdZmbWTYoEwXnAT4F3SToTuAP4boHlRgMLI2JRRLxBdmfyhDrznQGcRTriMDOzxipyQ9mVkuYBH02jPhURCwqsexCwODe8BPhAfgZJ+wBDIuLnkr7e0YokTQWmAgwdOrTAps3MrKiil4++DeiV5t+6OzYsaQvgXODEzuaNiAsjYlREjGpra+uOzZuZWVLk8tFTgEuB7YGBwCWSTi6w7qXAkNzw4DSuXT9gD2C2pCeAfYEZbjA2M2usIg+d+xywV0S8BiDpe8D9wHc6WW4OMCK9xGYp2UPqjmifGBEvkwULab2zgX+IiLkbUb+ZmXVRkVNDT7Pu+we2ZN1f9nVFxBrgWOAWYAEwPSLmSzpd0vhNKdbMzLpfkSOCl4H5km4lu4T0Y8C9ks4DiIjjOlowImYCM2vGndLBvAcUrNnMzLpRkSD4aerazS6nFDMza4YiQfAC8POI6PQmMjMzaz1F2ggOAx6XdLakvyi7IDMza6xOgyAiJgF7A78Hpkm6S9LU9GgIMzNrcYVuKIuIlcD1ZI+J2AH4NPBbSV8rsTYzM2uAIjeUTZD0U7JG4j7A6IgYC+xFgbuCzcxs81aksfhvgO9HxO35kRGxWtKUcsoyM7NGKRIEz9SGgKSzIuIfI+KXJdVViuGvXdXsEprqiWYXYGabpSJtBB+rM25sdxdiZmbN0eERgaSvAkcDu0h6MDepH3Bn2YWZmdXyUX05NnRq6CrgZuBfgPxrJldFxAsl1WObMf8nNOuZOgyC9HTQl/nTS+vNrAuqHqTgMN1cFX0xjZmZ9VAOAjOzinMQmJlVnIPAzKziHARmZhXnIDAzqzgHgZlZxTkIzMwqzkFgZlZxDgIzs4pzEJiZVZyDwMys4hwEZmYV5yAwM6s4B4GZWcU5CMzMKs5BYGZWcQ4CM7OKcxCYmVWcg8DMrOJKDQJJYyQ9KmmhpJPqTD9B0iOSHpT0S0nDyqzHzMzWV1oQSOoFnA+MBUYCEyWNrJntPmBURLwHuB44u6x6zMysvjKPCEYDCyNiUUS8AVwDTMjPEBGzImJ1GrwbGFxiPWZmVkeZQTAIWJwbXpLGdWQKcHO9CZKmSporae7y5cu7sUQzM9ssGoslTQJGAefUmx4RF0bEqIgY1dbW1tjizMx6uN4lrnspMCQ3PDiNW4ekg4B/Aj4cEa+XWI+ZmdVR5hHBHGCEpJ0k9QUOB2bkZ5C0N3ABMD4iniuxFjMz60BpQRARa4BjgVuABcD0iJgv6XRJ49Ns5wDbAtdJul/SjA5WZ2ZmJSnz1BARMROYWTPulFz/QWVu38zMOrdZNBabmVnzOAjMzCrOQWBmVnEOAjOzinMQmJlVnIPAzKziHARmZhXnIDAzqzgHgZlZxTkIzMwqzkFgZlZxDgIzs4pzEJiZVZyDwMys4hwEZmYV5yAwM6s4B4GZWcU5CMzMKs5BYGZWcQ4CM7OKcxCYmVWcg8DMrOIcBGZmFecgMDOrOAeBmVnFOQjMzCrOQWBmVnEOAjOzinMQmJlVnIPAzKziHARmZhXnIDAzqzgHgZlZxZUaBJLGSHpU0kJJJ9WZvqWka9P0eyQNL7MeMzNbX2lBIKkXcD4wFhgJTJQ0sma2KcCLEfHnwPeBs8qqx8zM6ivziGA0sDAiFkXEG8A1wISaeSYAl6b+64GPSlKJNZmZWY3eJa57ELA4N7wE+EBH80TEGkkvA+8Ans/PJGkqMDUNviLp0VIqLt9Aaj5bI6n1j7e8/7rO+7BrWnn/DetoQplB0G0i4kLgwmbX0VWS5kbEqGbX0aq8/7rO+7Breur+K/PU0FJgSG54cBpXdx5JvYEBwIoSazIzsxplBsEcYISknST1BQ4HZtTMMwP4Qur/DPCriIgSazIzsxqlnRpK5/yPBW4BegEXR8R8SacDcyNiBnARcLmkhcALZGHRk7X86a0m8/7rOu/DrumR+0/+AW5mVm2+s9jMrOIcBGZmFecgaABJF0t6TtLDza6lFUkaImmWpEckzZd0fLNraiWStpJ0r6QH0v47rdk1tSJJvSTdJ+m/m11Ld3MQNMY0YEyzi2hha4ATI2IksC9wTJ3HlVjHXgcOjIi9gPcCYyTt29ySWtLxwIJmF1EGB0EDRMTtZFdF2SaIiGUR8dvUv4rsP+Og5lbVOiLzShrskzpfJbIRJA0G/hr4z2bXUgYHgbWU9ITavYF7mlxKS0mnNe4HngNujQjvv43zb8A3gLeaXEcpHATWMiRtC/wX8HcRsbLZ9bSSiFgbEe8lu8N/tKQ9mlxSy5D0SeC5iJjX7FrK4iCwliCpD1kIXBkRNzS7nlYVES8Bs3Cb1cbYDxgv6QmypygfKOmK5pbUvRwEttlLjya/CFgQEec2u55WI6lN0napf2vgY8DvmlpUC4mIb0bE4IgYTvb0g19FxKQml9WtHAQNIOlq4C5gN0lLJE1pdk0tZj/gSLJfYvenblyzi2ohOwCzJD1I9gywWyOix10CaZvOj5gwM6s4HxGYmVWcg8DMrOIcBGZmFecgMDOrOAeBmVnFOQisR5N0nKQFkq6UNF7SSSVv74Cynk4pabakHvfidGu+0l5VabaZOBo4KCKWpOHa92YjqXdErGlsWWabDweB9ViSfgLsDNws6WLgRWBURBwraRrwGtkD7O6UtD3wahp+J/BF4PPAB4F7ImJynfW/H/gBsA3Zo54/WjN9dJq+VVr3URHxqKTdgUuAvmRH5YcATwPTyZ4F1As4IyKu7eBzbQFcDCyJiJM3aeeY5TgIrMeKiK9IGgN8JCKelzS5ZpbBwIciYm0KhreTffGPJzty2A/4W2COpPdGxP3tC0rqC1wLHBYRcyT1J/uyz/sdsH9ErJF0EPBdsi/9rwA/iIgr03p6AeOApyPir9P6B3TwsXoDVwIPR8SZG79XzNbnNgKrsusiYm1u+KbIbrV/CHg2Ih6KiLeA+cDwmmV3A5ZFxByAiFhZ5/TSAOC69Ga67wO7p/F3Ad+S9I/AsIh4NW3zY5LOkrR/RLzcQc0X4BCwbuYgsCr7Y83w6+nPt3L97cObcvR8BjArIvYADiY7RUREXEV21PEqMFPSgRHxGLAPWSB8R9IpHazzN8BHJG21CfWY1eUgMNs0jwI7pHYCJPWTVBsWA4ClqX9y+0hJOwOLIuI84EbgPZJ2BFZHxBXAOWShUM9FwExgep3tmW0SB4HZJoiIN4DDgB9KegC4lfSLP+ds4F8k3ce6RxSHAg+nN4btAVwG7Ancm8Z9G/jOBrZ9LnAfcHlqODbrEj991Mys4vxrwsys4hwEZmYV5yAwM6s4B4GZWcU5CMzMKs5BYGZWcQ4CM7OK+z/4tbunncUTSgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "blm_fit.plot_type_proportions()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Control variables\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Hint\n",
    "\n",
    "Check out how to add custom columns to your BipartitePandas DataFrame [here](https://tlamadon.github.io/bipartitepandas/notebooks/custom_columns.html#)! If you don't add custom columns properly, they may not be handled during data cleaning and estimation how you want and/or expect!\n",
    "\n",
    "</div>\n",
    "\n",
    "## Simulating data with controls\n",
    "\n",
    "The package contains functions to simulate data from the BLM dgp. We use this here to see how to use control variables.\n",
    "\n",
    "In this example, we simulate a categorical, non-stationary, non-worker-type-interaction control variable. We use a low variance to ensure stability of the estimator.\n",
    "\n",
    "## Check out simulation parameter options\n",
    "\n",
    "Do this by running:\n",
    "\n",
    "- Simulating Categorical Controls - `tw.sim_categorical_control_params().describe_all()`\n",
    "\n",
    "- Simulating Continuous Controls - `tw.sim_continuous_control_params().describe_all()`\n",
    "\n",
    "Alternatively, run `x_params().keys()` to view all the keys for a parameter dictionary, then `x_params().describe(key)` to get a description for a single key."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set simulation parameter choices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_control = 2 # Number of types for control variable\n",
    "\n",
    "sim_cat_params = tw.sim_categorical_control_params({\n",
    "    'n': n_control,\n",
    "    'stationary_A': False, 'stationary_S': False,\n",
    "    'worker_type_interaction': False,\n",
    "    'a1_mu': -0.5, 'a1_sig': 0.25, 'a2_mu': 0.5, 'a2_sig': 0.25,\n",
    "    's1_low': 0, 's1_high': 0.01, 's2_low': 0, 's2_high': 0.01\n",
    "})\n",
    "sim_cts_params = tw.sim_continuous_control_params({\n",
    "    'stationary_A': True, 'stationary_S': True,\n",
    "    'worker_type_interaction': True,\n",
    "    'a1_mu': -0.15, 'a1_sig': 0.05, 'a2_mu': 0.15, 'a2_sig': 0.05,\n",
    "    's1_low': 0, 's1_high': 0.01, 's2_low': 0, 's2_high': 0.01\n",
    "})\n",
    "sim_blm_params = tw.sim_blm_params({\n",
    "    'nl': nl, 'nk': nk,\n",
    "    'a1_mu': -2, 'a1_sig': 0.25, 'a2_mu': 2, 'a2_sig': 0.25,\n",
    "    's1_low': 0, 's1_high': 0.01, 's2_low': 0, 's2_high': 0.01,\n",
    "    'categorical_controls': {'cat_control': sim_cat_params},\n",
    "    'continuous_controls': {'cts_control': sim_cts_params}\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating control variables\n",
    "\n",
    "PyTwoWay allows for categorical and continuous control variables.\n",
    "\n",
    "### Categorical\n",
    "\n",
    "To define a categorical control variable, construct an instance of the parameter dictionary `tw.categorical_control_params()`.\n",
    "\n",
    "Then, inside an instance of `blm_params()`, link the key `'categorical_controls'` to a dictionary linking column names to their associated parameter dictionaries.\n",
    "\n",
    "### Continuous\n",
    "\n",
    "To define a continuous control variable, construct an instance of the parameter dictionary `tw.continuous_control_params()`.\n",
    "\n",
    "Then, inside an instance of `blm_params()`, link the key `'continuous_controls'` to a dictionary linking column names to their associated parameter dictionaries.\n",
    "\n",
    "### Constraints\n",
    "\n",
    "Constraints can be specified for control variables. They are set through the `cons_a` and `cons_s` keys for a given control variable's parameter dictionary, except for `NoWorkerTypeInteraction()`. Constraint options are:\n",
    "- `Linear()` - for a fixed firm type, worker types effects must change linearly\n",
    "- `Monotonic()` - for a fixed firm type, worker types effects must increase (or decrease) monotonically\n",
    "- `NoWorkerTypeInteraction()` - for a fixed firm type, worker types effects must all be the same\n",
    "- `Stationary()` - worker-firm pair effects are the same in all periods\n",
    "- `StationaryFirmTypeVariation()` - firm type induced variation of worker-firm pair effects is the same in all periods. In particular, this is equivalent to setting `A2 = (np.mean(A2, axis=1) + A1.T - np.mean(A1, axis=1)).T`.\n",
    "- `BoundedBelow()` - worker-firm pair effects are bounded below\n",
    "- `BoundedAbove()` - worker-firm pair effects are bounded above\n",
    "\n",
    "`NoWorkerTypeInteraction()` is not specified through the `cons_a` and `cons_s` keys. Instead, if you want a control variable to interact with the unobserved worker types, this can be specified by setting `worker_type_interaction=True` in the control variable's parameter dictionary.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "Warning\n",
    "\n",
    "Be careful when adding constraints to categorical control variables (note that not interacting with worker types requires constraints). Because categorical control variables require normalization, the choice of how to normalize can alter parameter estimates. This may raise a warning if the normalization gets stuck in a cycle of changing how to normalize every loop and the estimator is not converging. The estimator will work if you set `force_min_firm_type=True` in your BLM parameter dictionary - the warning will also provide a reminder of this option.\n",
    "\n",
    "</div>\n",
    "\n",
    "## Check out estimation parameter options\n",
    "\n",
    "Do this by running:\n",
    "\n",
    "- Estimating Categorical Controls - `tw.categorical_control_params().describe_all()`\n",
    "\n",
    "- Estimating Continuous Controls - `tw.continuous_control_params().describe_all()`\n",
    "\n",
    "Alternatively, run `x_params().keys()` to view all the keys for a parameter dictionary, then `x_params().describe(key)` to get a description for a single key."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set estimation parameter choices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "cat_params = tw.categorical_control_params({\n",
    "    'n': n_control,\n",
    "    'worker_type_interaction': False,\n",
    "    'cons_a': None, 'cons_s': None,\n",
    "    'a1_mu': -0.5, 'a1_sig': 0.25, 'a2_mu': 0.5, 'a2_sig': 0.25,\n",
    "    's1_low': 0, 's1_high': 0.01, 's2_low': 0, 's2_high': 0.01\n",
    "})\n",
    "cts_params = tw.continuous_control_params({\n",
    "    'worker_type_interaction': True,\n",
    "    'cons_a': cons.Stationary(), 'cons_s': cons.Stationary(),\n",
    "    'a1_mu': -0.15, 'a1_sig': 0.05, 'a2_mu': 0.15, 'a2_sig': 0.05,\n",
    "    's1_low': 0, 's1_high': 0.01, 's2_low': 0, 's2_high': 0.01\n",
    "})\n",
    "blm_params = tw.blm_params({\n",
    "    'nl': nl, 'nk': nk,\n",
    "    'a1_mu': -2, 'a1_sig': 0.25, 'a2_mu': 2, 'a2_sig': 0.25,\n",
    "    's1_low': 0, 's1_high': 0.01, 's2_low': 0, 's2_high': 0.01,\n",
    "    'categorical_controls': {'cat_control': cat_params},\n",
    "    'continuous_controls': {'cts_control': cts_params},\n",
    "    'force_min_firm_type': True\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate data\n",
    "\n",
    "`sim_data` gives a dictionary where the key `'jdata'` gives simulated mover data and the key `'sdata'` gives simulated stayer data.\n",
    "\n",
    "`sim_params` gives a dictionary that links each type of control variable to the simulated parameter values for that type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "blm_true = tw.SimBLM(sim_blm_params)\n",
    "sim_data, sim_params = blm_true.simulate(return_parameters=True)\n",
    "jdata, sdata = sim_data['jdata'], sim_data['sdata']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Movers data\n"
     ]
    },
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       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>168</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-2.035432</td>\n",
       "      <td>2.368199</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.227607</td>\n",
       "      <td>0.600801</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>169</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-2.933966</td>\n",
       "      <td>2.556052</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.343777</td>\n",
       "      <td>1.315978</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>170</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.441650</td>\n",
       "      <td>2.437222</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.352137</td>\n",
       "      <td>-0.029504</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>171</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>-1.681946</td>\n",
       "      <td>2.603666</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.797169</td>\n",
       "      <td>-0.100233</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>172</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>-1.446450</td>\n",
       "      <td>2.115750</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.856424</td>\n",
       "      <td>-0.023039</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>173</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>-3.140376</td>\n",
       "      <td>2.507038</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2.209182</td>\n",
       "      <td>0.660209</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>174</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>-2.743617</td>\n",
       "      <td>2.046139</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.038795</td>\n",
       "      <td>-0.846242</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>175</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>-1.253390</td>\n",
       "      <td>1.997722</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-1.620871</td>\n",
       "      <td>-0.369944</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>176</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>-2.042038</td>\n",
       "      <td>1.745926</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-1.510300</td>\n",
       "      <td>0.903805</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>177</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>-1.678088</td>\n",
       "      <td>2.148858</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.876064</td>\n",
       "      <td>-0.305209</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>178</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.539851</td>\n",
       "      <td>2.806150</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.193820</td>\n",
       "      <td>-1.547240</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>179</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>-1.484411</td>\n",
       "      <td>2.540243</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.029680</td>\n",
       "      <td>-0.694832</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>180</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>-1.145073</td>\n",
       "      <td>1.938436</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.448419</td>\n",
       "      <td>1.062856</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>181</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>-1.976578</td>\n",
       "      <td>2.167116</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.051553</td>\n",
       "      <td>0.623657</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>182</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>-2.248826</td>\n",
       "      <td>2.782804</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.069256</td>\n",
       "      <td>-1.654039</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>183</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>-3.381418</td>\n",
       "      <td>2.342920</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.835689</td>\n",
       "      <td>-0.528370</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>184</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>-2.414065</td>\n",
       "      <td>1.897629</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.123666</td>\n",
       "      <td>0.956612</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>185</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>-3.131777</td>\n",
       "      <td>2.884738</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.767185</td>\n",
       "      <td>-0.904343</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>186</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>-3.342341</td>\n",
       "      <td>2.693796</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.726720</td>\n",
       "      <td>0.368079</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>187</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>-2.140324</td>\n",
       "      <td>2.530651</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.183305</td>\n",
       "      <td>-1.663274</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>188</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>-3.219936</td>\n",
       "      <td>2.662715</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.267946</td>\n",
       "      <td>0.635036</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>189</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>-2.813351</td>\n",
       "      <td>2.204771</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1.858780</td>\n",
       "      <td>-1.423794</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>190</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>-2.627046</td>\n",
       "      <td>2.341005</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.732658</td>\n",
       "      <td>-0.174954</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>191</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>-1.475745</td>\n",
       "      <td>1.854227</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.085931</td>\n",
       "      <td>-0.259650</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>192</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>-1.372760</td>\n",
       "      <td>1.618090</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.247395</td>\n",
       "      <td>1.038758</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>193</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>-1.396256</td>\n",
       "      <td>1.879039</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.298457</td>\n",
       "      <td>-0.415220</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>194</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>-1.349778</td>\n",
       "      <td>2.194202</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.641476</td>\n",
       "      <td>0.840362</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>195</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>-1.435867</td>\n",
       "      <td>1.505834</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.455100</td>\n",
       "      <td>1.541480</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>196</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>-2.786497</td>\n",
       "      <td>1.745557</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0.631748</td>\n",
       "      <td>0.769990</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>197</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>-1.450763</td>\n",
       "      <td>1.851792</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.047915</td>\n",
       "      <td>-0.048053</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>198</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>-2.567547</td>\n",
       "      <td>1.749243</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.018666</td>\n",
       "      <td>0.676466</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>199</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>-2.342840</td>\n",
       "      <td>2.728105</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1.548878</td>\n",
       "      <td>1.056820</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      i  j1  j2        y1        y2  g1  g2  m  cat_control1  cat_control2  \\\n",
       "0   160   0   0 -3.065299  2.939253   0   0  0             1             1   \n",
       "1   161   1   1 -3.308012  1.882332   0   0  0             1             0   \n",
       "2   162   1   1 -2.048957  2.500295   0   0  0             0             1   \n",
       "3   163   1   1 -1.647712  3.035064   0   0  0             0             1   \n",
       "4   164   0   0 -1.753908  2.028478   0   0  0             0             0   \n",
       "5   165   1   1 -1.838391  3.205352   0   0  0             0             1   \n",
       "6   166   0   0 -1.825758  2.394916   0   0  0             0             1   \n",
       "7   167   0   0 -3.162265  3.055979   0   0  0             1             1   \n",
       "8   168   0   0 -2.035432  2.368199   0   0  0             0             1   \n",
       "9   169   0   0 -2.933966  2.556052   0   0  0             1             1   \n",
       "10  170   2   2 -1.441650  2.437222   1   1  0             0             1   \n",
       "11  171   3   3 -1.681946  2.603666   1   1  0             0             1   \n",
       "12  172   3   3 -1.446450  2.115750   1   1  0             0             0   \n",
       "13  173   3   3 -3.140376  2.507038   1   1  0             1             1   \n",
       "14  174   2   2 -2.743617  2.046139   1   1  0             1             0   \n",
       "15  175   3   3 -1.253390  1.997722   1   1  0             0             0   \n",
       "16  176   3   3 -2.042038  1.745926   1   1  0             1             0   \n",
       "17  177   3   3 -1.678088  2.148858   1   1  0             0             0   \n",
       "18  178   2   2 -1.539851  2.806150   1   1  0             0             1   \n",
       "19  179   2   2 -1.484411  2.540243   1   1  0             0             1   \n",
       "20  180   5   5 -1.145073  1.938436   2   2  0             0             1   \n",
       "21  181   5   5 -1.976578  2.167116   2   2  0             0             0   \n",
       "22  182   5   5 -2.248826  2.782804   2   2  0             1             1   \n",
       "23  183   4   4 -3.381418  2.342920   2   2  0             1             0   \n",
       "24  184   5   5 -2.414065  1.897629   2   2  0             1             0   \n",
       "25  185   4   4 -3.131777  2.884738   2   2  0             1             1   \n",
       "26  186   4   4 -3.342341  2.693796   2   2  0             1             1   \n",
       "27  187   5   5 -2.140324  2.530651   2   2  0             0             0   \n",
       "28  188   4   4 -3.219936  2.662715   2   2  0             1             1   \n",
       "29  189   4   4 -2.813351  2.204771   2   2  0             1             0   \n",
       "30  190   6   6 -2.627046  2.341005   3   3  0             1             1   \n",
       "31  191   7   7 -1.475745  1.854227   3   3  0             0             0   \n",
       "32  192   7   7 -1.372760  1.618090   3   3  0             0             0   \n",
       "33  193   6   6 -1.396256  1.879039   3   3  0             0             0   \n",
       "34  194   6   6 -1.349778  2.194202   3   3  0             0             1   \n",
       "35  195   7   7 -1.435867  1.505834   3   3  0             0             0   \n",
       "36  196   6   6 -2.786497  1.745557   3   3  0             1             0   \n",
       "37  197   7   7 -1.450763  1.851792   3   3  0             0             0   \n",
       "38  198   6   6 -2.567547  1.749243   3   3  0             1             0   \n",
       "39  199   7   7 -2.342840  2.728105   3   3  0             1             1   \n",
       "\n",
       "    cts_control1  cts_control2  l  \n",
       "0       1.280102     -1.276638  1  \n",
       "1       0.673731      0.978745  2  \n",
       "2       0.188291     -0.354548  0  \n",
       "3       0.224408     -1.773956  1  \n",
       "4      -0.307819      0.595909  2  \n",
       "5      -0.034964     -1.680496  2  \n",
       "6      -0.045699      0.869568  2  \n",
       "7       0.174373     -1.324212  2  \n",
       "8       0.227607      0.600801  0  \n",
       "9       0.343777      1.315978  1  \n",
       "10     -0.352137     -0.029504  1  \n",
       "11      0.797169     -0.100233  0  \n",
       "12     -0.856424     -0.023039  0  \n",
       "13      2.209182      0.660209  0  \n",
       "14      0.038795     -0.846242  1  \n",
       "15     -1.620871     -0.369944  1  \n",
       "16     -1.510300      0.903805  2  \n",
       "17      0.876064     -0.305209  0  \n",
       "18     -0.193820     -1.547240  0  \n",
       "19      0.029680     -0.694832  1  \n",
       "20      0.448419      1.062856  2  \n",
       "21      0.051553      0.623657  0  \n",
       "22     -0.069256     -1.654039  2  \n",
       "23      0.835689     -0.528370  0  \n",
       "24     -0.123666      0.956612  1  \n",
       "25     -0.767185     -0.904343  0  \n",
       "26      0.726720      0.368079  0  \n",
       "27      1.183305     -1.663274  0  \n",
       "28     -0.267946      0.635036  0  \n",
       "29      1.858780     -1.423794  2  \n",
       "30     -0.732658     -0.174954  0  \n",
       "31      0.085931     -0.259650  0  \n",
       "32      0.247395      1.038758  2  \n",
       "33     -0.298457     -0.415220  0  \n",
       "34     -0.641476      0.840362  0  \n",
       "35      0.455100      1.541480  2  \n",
       "36      0.631748      0.769990  0  \n",
       "37     -0.047915     -0.048053  0  \n",
       "38     -0.018666      0.676466  2  \n",
       "39     -1.548878      1.056820  1  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated parameter values\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'A1': array([[-2.40434291, -1.93230882, -2.3641309 , -1.81931006],\n",
       "        [-1.99649895, -1.8539811 , -1.54271365, -1.67049293],\n",
       "        [-2.21882556, -1.59916272, -1.37328134, -1.69013257]]),\n",
       " 'A2': array([[1.85490342, 1.97296398, 2.15268324, 1.7112059 ],\n",
       "        [2.15476764, 1.81388297, 1.90973225, 2.26752212],\n",
       "        [2.0604013 , 1.90970787, 1.65698835, 1.84848259]]),\n",
       " 'S1': array([[6.24733520e-03, 3.25013934e-04, 9.95248435e-03, 7.88841644e-03],\n",
       "        [5.06607130e-04, 5.60070089e-05, 5.12086700e-03, 8.94274499e-03],\n",
       "        [1.15689335e-03, 3.52890499e-03, 3.17502080e-03, 9.56078356e-03]]),\n",
       " 'S2': array([[0.00106304, 0.00627278, 0.0096796 , 0.00626775],\n",
       "        [0.00905057, 0.00542163, 0.00412828, 0.00967574],\n",
       "        [0.00684023, 0.00786226, 0.00925993, 0.00867167]]),\n",
       " 'pk1': array([[0.22439344, 0.64001715, 0.13558941],\n",
       "        [0.30791439, 0.16101403, 0.53107158],\n",
       "        [0.13470115, 0.14758551, 0.71771334],\n",
       "        [0.15657995, 0.31968694, 0.5237331 ],\n",
       "        [0.08722402, 0.82393394, 0.08884205],\n",
       "        [0.81811766, 0.03811832, 0.14376401],\n",
       "        [0.13887305, 0.03062248, 0.83050447],\n",
       "        [0.44799947, 0.31514629, 0.23685424],\n",
       "        [0.42634457, 0.25005179, 0.32360364],\n",
       "        [0.41872874, 0.15005459, 0.43121667],\n",
       "        [0.36605   , 0.26067997, 0.37327004],\n",
       "        [0.38861717, 0.46752657, 0.14385626],\n",
       "        [0.81362141, 0.10810991, 0.07826868],\n",
       "        [0.66945685, 0.10447555, 0.2260676 ],\n",
       "        [0.29082898, 0.26732746, 0.44184356],\n",
       "        [0.28325089, 0.55597618, 0.16077293]]),\n",
       " 'pk0': array([[0.14716973, 0.33066942, 0.52216085],\n",
       "        [0.6236124 , 0.33471458, 0.04167301],\n",
       "        [0.34365961, 0.23123918, 0.42510121],\n",
       "        [0.71334724, 0.06543533, 0.22121742]]),\n",
       " 'A1_cat': {'cat_control': array([ 0.37500106, -0.88596277])},\n",
       " 'A2_cat': {'cat_control': array([0.12246111, 0.60852562])},\n",
       " 'S1_cat': {'cat_control': array([0.00785542, 0.00410917])},\n",
       " 'S2_cat': {'cat_control': array([0.00749964, 0.00787043])},\n",
       " 'A1_cts': {'cts_control': array([-0.14213511, -0.14125649, -0.30366185])},\n",
       " 'A2_cts': {'cts_control': array([-0.14213511, -0.14125649, -0.30366185])},\n",
       " 'S1_cts': {'cts_control': array([0.00774112, 0.00157575, 0.00477038])},\n",
       " 'S2_cts': {'cts_control': array([0.00774112, 0.00157575, 0.00477038])}}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('Movers data')\n",
    "display(jdata)\n",
    "print('Stayers data')\n",
    "display(sdata)\n",
    "print('Simulated parameter values')\n",
    "display(sim_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize and run BLMEstimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Initialize BLM estimator\n",
    "blm_fit = tw.BLMEstimator(blm_params)\n",
    "# Fit BLM estimator\n",
    "blm_fit.fit(jdata=jdata, sdata=sdata, n_init=80, n_best=5, ncore=8)\n",
    "# Store best model\n",
    "blm_model = blm_fit.model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check that log-likelihoods are monotonic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-likelihoods monotonic (movers): True\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Change in log-likelihood')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "liks1 = blm_model.liks1[1:]\n",
    "\n",
    "print('Log-likelihoods monotonic (movers):', np.min(np.diff(liks1)) >= 0)\n",
    "\n",
    "x_axis = range(1, len(liks1))\n",
    "plt.plot(x_axis, np.diff(liks1), '.', label='liks1', color='red')\n",
    "plt.plot(x_axis, np.zeros(len(liks1) - 1))\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Change in log-likelihood')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-likelihoods monotonic (stayers): True\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Change in log-likelihood')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "liks0 = blm_model.liks0\n",
    "\n",
    "print('Log-likelihoods monotonic (stayers):', np.min(np.diff(liks0)) >= 0)\n",
    "\n",
    "x_axis = range(1, len(liks0))\n",
    "plt.plot(x_axis, np.diff(liks0), '.', label='liks0', color='red')\n",
    "plt.plot(x_axis, np.zeros(len(liks0) - 1))\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Change in log-likelihood')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now we can investigate the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LP+Zs473le/nzBd1cGLXNcwt2sv7AEb64bRjx4YH8siuHB7/cRHigL1M/WMtVie3IK6lk5rJUbhvVmchgX1eHrNQxnHkDeS2QICIdRcQH24f9nKMPEpHuQBiw0omxnJaYED+Gdgznn99to7SyGoDkrEJeW7Sb64d2YP2BI+zLLeXN6wbSv10oPWJb8cwVfQj282L+toMujr7pu/u8Ljzzww6+SEojq6CMhdsPcfdnG4iPCKSowsK4XjFcOqAN87ce5Mb31jCxfxuWpRx2ddiUVFTz6er9vD5lAJ0ig/DwEM7tHsUD53ejXWt/xnSP4qt16azZm8cTk3oz7dwurg5ZqXo5rUdgjKkWkbuABdimj75njNkmIk8AScaY35LCNcAsY8wZveXTUM9e2ZdHvt7C0H8tIjzIl+KKah66oBvDO0fwwYq9jOgSXmexl4gwqmsUW9LzmdivjQsjb/oS41vz1g2DeH1xCs8v2En71gHcfV4Xnvo+mUBfT65ObIePlwcTesdy7TurmL/lIK38XH9XM7uogtAAH6KOKk/Sv10o76/Yyw3D4rlhWLxrglOqAZz622SMmQfMO6rtsaMe/8OZMTSWVn7ezLh2IIeLKzhSUkmH8MCaWz5twwKYuznrmHOSswpritSpE0uMb80HU4fUPJ63JYuzOoZTabHyyqJdPDCuGx4ewtge0by6aDdPX9bHhdHaxIb4UVheRVpeKe1a/16eY+WeXLpGn7iQoVJNSdOfW9jERAT5khAdXGc18LndIskrreT1n3dTXmWhymLlszUHWJmay6X927ow2uYrxN+bQ4XlPH9lX1al5jHq+cXc8O5qnluwk06RgVzc17Eie87k5+3JzSM7cvvH61i3P4+C0iq+XJfO64tTuH1UZ1eHp5TDXN+/bgG8PD346E9n8eg3W3hzyUI8ROgeG8xHfxpCSEDTmubYXAztFE5heRWLd2Qz+7ahJB8sYsOBfLZnFvKvy/o2mXIN087tQkiAD3/5agsHC8oZ0D6UmX9I1O0zVbMiTfzW/DESExNNUlKSq8M4roKyKqxWQ1gTmNrY3O0+VMQdn6wHINTfm5ScYh67uCeXD4xzcWRKNT8iss4Yk1jfc9ojaGSOlqVWJ5cQHczC+89hU3oBpRXVDGgf1mhrL5RSv9NEoJo0EaG/fcXx0TLyy5i3OYsqq5WxPaJ1gFapU6SDxapZ+mpdum0PhtwScooquO6d1bz80y5Xh6VUs6Q9AtXsHC6u4J/fbeObaSNqyjrfdW4XLn5tOWO6R9MnTgdqlWoI7RGoZufn5GxGdYuqU9s/PMiXyYPimLf12PUcSqkT0x6Ban7EVu3zaMZA05hU6nqF5VV8suoAv+45TGiAD9cMbseILhGuDks1UdojUM3OmO5RLN2VQ0r273tNHy6u4Mt16cdUiHVHReVVXPWflWzLLLBXbW3NX77azPsr9ro6NNVEaY9AAZBfWskXSWkkZxXRITyAawa3P+mGO64SHuTLPyf14oo3VzK+Vwx+3h58vyWLG4fFN5mFXKWV1cxcupcF2w7i5Slc1CeWm0bE4+vl/Omvs9ak0TkyiNev/X0/inMSIrn4teVMHhRXszmSUr/RHoEi/UgpF726nB1ZRYzoEsGRkkoufm0ZWzMKXB3acV02II75951Nt5hg2oT6M+vWYU1mN7Nqi5Ub31vDzkOFPHlpL/46oQe/7sll2ifr672l1dhWpuYysX/dQoftWgfQLTqYLelN9+9UuY72CBQvLdzNFQPbMv18W33/yYPi6NU2hCfnbufz24a5OLrjiw3x548jO7o6jGMs2pFNlcXw+pSBNTvQDeoQxvkvLWXd/iMkxrd26uuHBfiQmV9Wp81qNWQWlOmKd1Uv7REoftmVzdVD6m4BetmAtmxIy6esst5N49QJbErLZ0z3qDrbkHp7ejCqayQb0/Kd/vrXDGnH20tT2ZNTDNh2UXtjSQoRQb50j9FFd+pY2iNQBPh4kV9aSdtQ/5q2ovJqPEXwbIQ9ld1NbIgfa/cdOaY9JbuYxHjnlyUfHN+ae8YkcMWbv9IhPJCcwnJiQvx48/qBTaZYn2paNBEorhgYx/MLdvKfGwbh6+WJ1Wp4bsFOLuobW6fctnLMxH5teWVRCl+tS+fSAW2xGsMnq/az93AJ43pGn5EYpgxpz6T+bdiWWUiovzcJWn5DnYBWH1VUVlt5YPYmVqXmktghjK2ZBbQLC+DN6wdpEb1TtDWjgEe+3kJmfhkWY0iICuLfV/SlU2Tj7ll9xL4f8rLdhwny9WLyoDguH9hWv/mrY5yo+qgmAlUjJbuYHQcLiQ8PbDLTMBubxWr4ZVc2W9ILaRvmz0V9Yp1a0TQzvwxPDyG6VeNPxS0qr+LSGSsYHN+aKxPjyC2u5JVFuxnRJYK/TujRqK+VfqSUl3/azdJdOQT52RLOLWd3wttTe4zNxYkSgVP/FkVkvIjsFJEUEXn4OMdcJSLbRWSbiHzqzHjUiXWJCuLivm1abBIoqajm6rdW8tLC3VRaLPywJYsxLywh1T6o6gxtQv2dkgQAZiel0y0mmGeu6MugDq05v1cMn948lM/XpnGwoLzRXievpJKr/rOSNiF+fHXHcF66qj+/puTy8FdbGu01lGs1eIxARDyAIGNM4UmO8wRmAOOAdGCtiMwxxmyvdUwC8AgwwhhzRESiGhqPUo56c8ke2oT68/LV/Wtm9Ly/Yi9/+99WPr1lqIuja7j1B45wfs+YOm0hAd4M6hDG5vR8YkJijnNmw8xae4DhXSJqphe3ax3AzD8kMvLfP7M/t4QO4YGN8jrKdRzqEYjIpyLSSkQCga3AdhF58CSnDQFSjDGpxphKYBYw6ahjbgFmGGOOABhjshsWvlKOm7c1i1vP6VRnWud1Z3Vgc3oB+aWVLozs1ES38jumN2OMYe/hkkbthWzPLOTshLp1ivx9PBnQPowdB4uOc5ZqThy9NdTT3gO4FPgB6AjccJJz2gJptR6n29tq6wp0FZEVIrJKRMbXdyERuVVEkkQkKScnx8GQG48xhrmbM7nh3dVc8tpy/m9eMoeLKxw+v7zKQmlltRMjVI6ob/jUYOzPNb/B1SlD2vHJ6gOsSs0FoKLawosLd9HK35u+jViKu33rgGNWJFushuSsQtq3Dmi011Gu4+itIW8R8caWCF43xlSJSGOMMnsBCcBoIA5YKiJ9jDH5tQ8yxrwNvA22weJGeN0GeXVRCt9vyeS+sV2JbuXH/zZkcMWbv/K/O0eccKXm4eIK/jFnG4uSszEYBrQL4x8Te9FNF/U4JKugjMU7cvDx8mBcj2hCAk5vBtOEPrH855c9vHrNgJpewcerDtCvXchpX9sVukQF89yVffnz7E0AFFdU0zculJk3DGrUWUPXntWeia+voE9cCBf1iaWovJpnF+ygU2QgPWJbNdrrKNdxNBG8BewDNmH7sO4AnHCMAMgA2tV6HGdvqy0dWG2MqQL2isgubIlhrYNxOd2RkkreXZ7KTw+MIirY1t0e1CGMB77YxKdrDjDt3C71nme1Gqa+v5ahnVqz+tEx+Hl5MntdGte/u5of7ztHl/qfxHvL9/LKot2M6R5FWZWFJ+du5/kr+53WPPzbR3Vm6gdrueT15ZydEMmOg4XsPlTMJzef1YiRn1nndY9mVNco9uWWEOTr5ZSB6biwAN69MZEn527nL19txkOECX1imXHdwJOfrJoHY8wp/QBeJ3seSMV2G8kHWxLpddQx44EP7X+OwHYrKfxE1x00aJA5k5btyjFXv/XrMe0LtmaZqe+vOe55K3bnmAte+sVYrdY67fd/vsHMXLqn0eNsSZKzCkziUwtNxpHSmrZNaUdM338sMPmllad1bYvFahbvOGReW7TLfLM+3ZRVVp9uuG6lqLzKlFfp/7PmCEgyx/lcdahHICL3Au8DRcA7wADgYeDHEySYahG5C1gAeALvGWO2icgT9oDm2J87X0S2AxbgQWNMbgPymNNFt/Jlf24p1RYrXrXmTKceLiG6le9xzzuQV0qftiHHdNH7tg0h9XCJ0+JtCb7blMmVg+JoU6vkRd+4UIZ2as2i5ENcPjDulK/t4SGM7hbF6G7Nf4La2n15fPDrPjLzy+jbNoSbz+5EOyffsw/y1WIELZGjg8V/NLbB4vOBMGwDxc+c7CRjzDxjTFdjTGdjzNP2tsfsSQB7oppujOlpjOljjJl1iu/DaRKig4kPD+Tf83dQXmUrwLb+wBHeWbaXa4d0OO55PWJbsWpvLtUWa5325SmH6R6j91VPpMpi8PM+dpGXn7cnVUf9/zwV2YXlbDhwhMLyqtO+lqvM25LFtE/WM6xTOH+d0INAXy8uf/NX9uqXDHUKHE3vv32tnQB8ZP9m3/ymWZyi168dwENfbmbo/y0ixN+bymorT07qdcJN0vvGhZAQFcy0T9dz75iuBPp68tHK/aTmlPDqlDbHPU/BuJ7RPPDFJm4aEU8r+yYqaXmlLN6RzaOnsWK2vMrCI19v4ecd2bRvHcD+3BJuGtGR+8cmnNGSDAWllTw9L5l1+/OJDPbhwQu6M6iD48XoLFbDv+Yl88Z1A2tKWg+Ob42ftydvLE7huSv7OSt01UI5mgjWiciP2O73PyIiwcDpfzVrJsKDfHn3psFkF5ZTWF5FfHhgndtE9RER3rhuIG8sTuH2j9dRUW1hTI9oZt02lAAf7V6fSGKHMM7rHsVFry7j8gFxlFdZ+Gp9On++oBtRpzEY+tT326mstvLrw+cR6OtFdmE5f/xwLW1C/LjmqDLczpKRX8qYF37Bz9uTkV0i2JNTzOQ3f+WvF3XnlrM7O3SNQ4XlVFRbj9nXYEKfGG7+UMuvqIZz9BPpT0B/INUYUyoi4cBUp0XVREW18mvQB5GftyfTz+9WsyJTOUZEePySnlzcN5aFyYfw9fLgs1uGnlYFzfIqC99uyGTxg6MJtN/njmrlxyMX9uCZH3acsUQw/fNNRAT5svTB0Xh42L5MvPzTLv79w06mDuuIlwPVXlv5e1NeaeFISWWd2Wf7DpcSGXz8cSuljsfRMQID9ATusT8OBJrmhraqRRAREuNb88iFPZh+frfTLqNcWmkBgfCjpu22bx3QoMWBp2tzeoF9dfPvv3r3nNcFY2DFnsMOXSPI14uL+sby2JxtlFTYFiqm5ZXy7/k7uH7o8cetlDoeRxPBG8AwYIr9cRG2OkJKNQthAd7EtPJj2e66H7ZzN2cxpKNzt46szctTyD0q8ZRXW7EaQ2gDFrU9fkkvvDyE4c/8zPiXl3Lxa8u5fGAcE/vp+JNqOEdvDZ1ljBkoIhsAjK1AnK6IUs2GiPDIhO5M/2Ijd4zuQs/YVizdncPspHQ+v+3MFZwb2yOad5bt5YZhHYgIsnWq7/xkPUF+XvRr5/iAsb+PJy9d3Z+cogoOFZbTMSKw5paXUg3l6L+cKns1UQMgIpG40WBxU5GWV8qP2w/hITC+dwyxIf4nP0nVOK97NO/dNJgPft3Hgq0H6dmmFd/cOdzpc+9re+6KvmxOz2fw04toG+pPbnEl1VbrKa9ujgz21XEBddoc2phGRK4DrgYGAh8Ck4G/GWNmOze8Y7nrxjTvLd/Laz/vZnzvWCxWKwu2HeLRCT24anC7k5+smpwlO7NZsPUgHcID+ePIjrolqHK6E21M41CPwBjziYisA8ZgW1NwqTEmuRFjVCewJ6eYGYtT+P6es2tW294xuoRLZ6zgnK6RxITouH1z01JWN6uWoSFfQ3YD3wBzgBIROTPz7Zq5nQeL+GjVfn7YkkVFteWUrvHDliwm9W9bp+RCx4hAxvWMZsG2g40VqlLKTTlaa+hu4HHgELaaQIJtvKCv80Jr3qxWw1+/sa1iPa97FAfySnly7nbenzqkwWWorQY86ln46imCI7f2lFLqRBwdLL4X6NbUCsI1ZV9vyCD5YBFLHhxds5L4i6Q07p21gR/uPbtBJQ0u6BXDde+s5tZRnWpKYafllbJg+0HuGZvglPiVUu7D0USQBhSc9ChVY86mTG4/p1OdchKTB8bxyk+7SckubtACqW4xwUwdEc+EV5YxqX9bqi1W5mzKZPq4rrQN1ZlDSqnT42giSAWWiMj3QM1qGGPMi06JqgWotljx9a47BOPhIfh6e1B5ChU0p53bhfPtYwIeHsI3d44gPkI3DVdKnT5HE8EB+4+P/UedxNge0Xy0cj+jukbhab/Bv2x3DpXV1lMuQ50QHXzapRaUUupojk4f/aezA2lprj2rPT8lH+LyN3/lwt4xHMgrZf7Wg7w+ZUBNYlBKqabghIlARL7Dvpq4PsaYiY0eUQvh5+3Jf/84hEU7slmzN492YQH8cO/ZTtlTVinlBipLMd7+FFYWEuJ7/L1QTsXJegTP2/97ORADfGx/PAXbVFJ1Al6eHlzQK4YLesW4OhS3N+GVpWzPKgLA21P420XduXF4JxdHpRpd5gbYMQ/Oe9TVkTSaSkslH254g5u/f4LLuvZiT2U+W27c0qivccIFZcaYX4wxvwAjjDFXG2O+s/9cC5x9souLyHgR2SkiKSLycD3P3yQiOSKy0f5z86m/FaXqN/DJH9meVUS/uBCmDu+Ar6cHj89JZnbSAVeHpk5XZQlYay3UXPg4LH8RDm13XUyN7MNtH/LqtnfpG9+WPZX5TnkNR1cWB4pIzdcnEemIbU+C47IXqZsBXIhtL4MpItKznkM/N8b0t/+842A8Sjlke2YBeSVVPDWpF9/eNZLHJ/Zm6xPj8fPy4LFvt7k6PLdQWlnN20v3cNVbK/nDe2v4en06VmsjLIQ0Bv57KSz+l+3x/l/hyD4Y/Qj88u/Tv34TcXPHSce09fmwD30+7ENBRePM6nd01tD92KaPpmJbVdwBuO0k5wwBUowxqQAiMguYBLScVK2avA9/3QfA9cPi67Sf0zWSH7fr3U1nq6y28od319A60Ie7zu1CSUU1byzZw7Ldh2nl58X6A/lEBftyw7AODa+9tGcRFB+EpHdh2DRY8gyc8yD0vhxe6WfrFUTX992z+TDGcNnXF9b7XJfQLrTyObUZiEdzqEdgjJkPJGBbYXwPtlXGC05yWltsC9F+k25vO9oVIrJZRL4UkXpLaYrIrSKSJCJJOTk5joSsFABn2Ted2Xe4uE77lowCPM/ghvXu6oetWXh4CG/dMIhzukZyYZ9YXriyL//bmEGlxcoTk3pxUd9Y/va/rXy2pgG36oyxffCPeRx6ToL5D9t6A/2uAZ9AGH53i+gVFB5JZQ+V9T739cSvG1Sh4EQcSgQiEgA8CNxljNkEtBeRixvh9b8D4o0xfYGF2EpcH8MY87YxJtEYkxgZGdkIL6vcxeWD2uEhMPbFpazfnwfAA19sJKugnAl9dBDf2dbuy+PC3jF1PrA+Xn2AhKggBrQPY0D7MC4fGMe7Nw7mhR93OV6Ycc8iKC+EXpfByOmw9SsYegd42nd5G3wz7F/R7McKQn54hC0Hi9ly/ifHPPfO5pmN9jqO3hp6H1iHbbtKgAxgNjD3BOdkALW/4cfZ22ocVbvoHeBZB+NRymFz7hrBpBm/cvmbK2vaesQG89q1A10YlXuICPLlQF5pnbZ1+48gInU21OkWE0wrPy8O5JaefNHkb72BUQ+BhydUlYG1Gpa9CFu+/P04azWseQsueaUx39KZlZ0M5fnw9iiIj6NLZRVfZx7inZBgbowb22gv42gi6GyMuVpEpgAYY0rl5H2StUCCfWA5A7gGuLb2ASISa4zJsj+cCOgeB6rR9W4byp5/TWD1nly2ZhZw9eD2BPnpto5nwuRBcUx8fQXjekQzvEsEFquhymIlt7iSs7tE1BxXXFHN4eIKWgc6ULhgzyLIPwARXeHQNrBa4fynbIPGox8Bv1pz7EObebX8+3+fJrq8ooBWPq0QEW5p5Jdx9LehUkT8+X2rys7UqjlUH2NMtYjcBSwAPIH3jDHbROQJIMkYMwe4R0QmAtVAHnDTqb0NpU7urM7hnNU53NVhuJW4sABevro/D365GV9vD0orLPj5eODlKew9XEJCdDDFFdU8/u02zu0eRXiQA9tuHtkHAeHwzVHzVcI6QkAYtB3klPfiao29iKw2R7eqPB94FNs00B+BEcBUY8xip0V2HO66VaVSzZnFath5sAg/bw86RQbxyer9vPjjLkICvDlcVMHoblH86/I+BPlqT81ZTrRVpUOJwH6RcGAotumjq4wxhxsvRMdpIlCqZaiotrA/t5TwQB/HegLqtJz2nsUissgYMwb4vp42pZqlovIqZq09gJeHB1MGt8PPR7+Nnkm+Xp501Wq6TcLJis75AQFAhIiEYesNALSi/jUBSjULLy3cyas/p+Dv7YnVGJ6cu51/TOzFH45aeKaUOzjZV6DbgPuANtimj/6WCAqB150XllLOszk9n1cXpfDUZb257qwOALyyaBePf7uNC3rFaIVY5XZOVnTuFWNMR+DPxphOxpiO9p9+xhhNBKpZevmnXXSKDKxJAgD3julKZLAvLy/c5cLIlHINR2+KWkUk1BiTD2C/TTTFGPOG0yJTAKzbn8ecjZlUWgzjekYxumsUHrqxzWkpKKsiop7BydAAb3JL6l/O765Wpeby8ar9ZBdVMLB9GH8cGU9UsPaYWhpHq4/e8lsSADDGHIFGX9OgjjJjcQr3fLaR6BA/EqKC+PcPO3noq804OtNL1W9kQgTr9ueRX/r7h35Wfhkp2cVMHhTnwsialq/WpXP/5xsZ2imc+8YkUFZZzWUzfuVgQbmrQ1ONzNEegaeIiLF/AtlLTOvexU6UllfKzGWp/Hj/OTXfwKYMac9Fry1jZWouwztHnOQK6mi5xRX85avNrNmbhzHCgCcWMrxLONHBfszdkkXX6GDOd6NNhL7fnMn0LzZRUW1FsBXom3WbrYpMZbWVZ+bv4MOpQ+jZxlbhcniXCDw9tvPOslT+dnHzruqp6nK0RzAf+FxExojIGOAze5tykmW7D3Ne96g63XB/H08uH9CWxTuyXRhZ8zXt0/XEhwey5tGxJD85nvN7RbNyTy7LUw7zpxEdmXfPSFeHeMZ8tzGDaZ9uoLLaSreYIIL8vFi1N49BTy4EYF9uCcG+XjVJ4DcX94tl9d48V4SsnMjRHsFfsM0gusP+eCG2InHKSQJ8PCksqz6mvaCsCn+d795guw4VcSC3lE9uHoqnfYzlrRsSmbE4hcz8Mv5yYXcXR3hmTZ+9CQH2PnNRTdtDszfxxbp0UrILCQ3wIbekkrJKC/4+njXHpOWVEhGkNwNaGkf3I7ACHwCPGmMmG2PeMsY4WC9WnYoxPaJYtz+PVam/F2jdk1PMV+szuLR/GxdG1jwdLCgnPiKwJgn8pnNkEIcK3e+ed5XF0L9d3do1z17ZD4DnF+wmKtiPYZ3CeXredsqrbL/qB3JLeWnhrjqzrVTL4OjK4onAc9jGBTqKSH/gCWPMRCfG5taC/bx5/dqBTPtkPd1jg/Hz8mTtvjweu6QXnSKDXB1es9OrTSu2ZhRwuLiizoyhhdsPMaB9mAsjc520vLI6jzPs5aK7x9p2of33FX15YPYmhj/zM21C/UjLK+OeMQmM7Rl9xmNVzuVo0bl1wHnAEmPMAHvbFmNMHyfHdwx3qzVUXmVh6a4cqiyGkV0iCAnwdnVIzdYLP+5k4fZD3De2KzEhfnyzPp0lu3L4dtoIQgPc63bH+Jd/YcfBYu45rzPTz+/O4aJShv7fYqqtsK/W7SKAjPwycooqSIgKIlCLwjVbp110TkRWGWOGisiGWolgs31nsTPK3RKBajzGGOZsymTWmjQKyqoYmRDBLWd3qrNBijvp9dh8Sirr3uF9/sq+TB5U746xqpk77aJzwDYRuRbbNNIEbPsW/9pYASp1OnYdKuK2j5LYe9h2a6NjRAAzb0iky1EFzUSESf3bMqm/lskC2PbEeNbsPcyLP+6mZ2wrHpvYy9UhKRdxtEcQgG0/gvOx1RtaADxpjDnjo2zaI1C1lVZW0/+JhSREBfHclX3BwIOzN5OSU8yGx8YRoDOslAJO3CNwdNZQqTHmUWPMYPsm8o+6IgkodbSXFu7C18uD7+4aQc/YEHq2CeG7u0fg7enBKz9p3SClHOHorKGuwJ+B+NrnGGPOc05YSjlmW2YhXaOD8PD4/TuNh4cHXaOD2JpR2ODrpeYUsyk9n+hgP4Z2Cte6TsotONpvng38B9siMofXD4jIeOAVbHsWv2OMeeY4x10BfAkMNsY0+/s+xhgqqq34enkgoh8kztQ9Jpgv16Uf0747u5irBzs+6GmxGv72vy0s3H6IYZ0j2JNdjMVqeG/qYNqG+jdmyEo1OY4mgmpjzJsNubC9HtEMYByQDqwVkTnGmO1HHRcM3Ausbsj1myKr1TBzWSrvLN9LQWkVca39mT6uKxf31QVgzjJ9XDc+WrWfSTOW8+o1A7BaDfd9vpGKKiv3jenq8HVmrT3ArkPFLH3oXAJ8vDDG8MaSPTz05SY+uXmoE9+BUq7naK2h70TkThGJFZHWv/2c5JwhQIoxJtUYUwnMAibVc9yTwL+BZj/m8OYve5i39SCf3nwWO58az78u68PT3ydrbSAnCvLz4ttpI8gtrmTUc0s494VfyCup5H93DSfIz/GB4m/WZ3D3eV1qBpdFhFvO7sS2zEKy3XDlsXIvjv6m3Gj/74O12gzQ6QTntAXSaj1OB86qfYCIDATaGWO+F5Ha1+ao424FbgVo3769gyGfWVUWK+8t38uXdwynY4RtZebQTuE8dnFP3lq6h3O7R7k4wparZ5sQlv/lPKxWK0Cd8QJHlVVZCParu1jP21Pw8/KkrEqrqaiWzdFZQx3r+TlREjgpEfEAXgQecOD137bPVkqMjIw8nZd1msKyKizG1CSB3/RtF8o++/x25VweHh6nlAQAzu0WxaerD9TZ62HxzmwCfD1p3zqgsUJUqklyuO8sIsM5dtbQf09wSgZQe7Quzt72m2CgN7DEPqAaA8wRkYnNccA4NMAHPy9PtmcW1indu3JPLt1igk9wpmoKbjmnE9e8vYqpH6xlbI9oUrKLmbMpk5eu6kdmQTnRwb54eZ5aklGqqXN0QdlHQGdgI7/PGjLGmHtOcI4XsAsYgy0BrAWuNcZsO87xS7DtjXzCJNCUF5R9tGo/7y/fy5OX9qZnbCuW7s7hybnbeeO6QQzpeLIhFeVqZZUW5mzKYMOBfCKDfckuLOeHrQdryjDfN7YrU4Y0zVuTSp1MY5SYSAR6Gkeyhp0xplpE7sK2CtkTeM8Ys01EngCSjDFzHL1Wc3HD0A4E+Xry9PfJpB8ppVebEF6bMlCTQDPh7+PJ1YPbkxjfmhd/3EleaRU/PTCKqGA/tmcWcvvH6wgL8GF8b9suZvmllfxrXjLr9ucTGezDgxd0Z1AH96xkqpo3R3sEs4F7jDFZzg/pxJpyj8AVjDG6VqGR5JVUcs9nG9h1qIjc4goCfL24fVRn7hzdGRFh/taDvL9iL5/fNoyM/FLGvPALft6ejOwSwZ6cYnZkFfG3i3rwp7NPa/hMKadojB5BBLBdRNYAFb816n4ErjN3cyavLUph56EiOkYEcseozlzVgAVU7q6gtJLnFuxkW1YhCVFBPDy+Bw99tYmu0cH8e3IfJr2+grl3n831766mY0QgE/rE0j0mmIx8Ww3/6Z9vIiLIl6UPjq4ZoH5p4U6emb+DqSPiT3nQWilXcDQR/MOZQaiGmb81i/+bt4PnJvdlaKdwNqTl8+CXm7AYo/ewHbA9q4BJr68g0NeL3m1asSg5m6/WZ+Dn5cHr1w7E29MDb08PcooquG9sAp+tOcCEPrH8vCObfnGhAGxOL+CRCd3rfODfOyaB139OYcWeXM5OaJqz25Sqj6PTR38BdmCb6RMMJNvblAu8sWQPT13Wm+FdIvDwEAZ1COPFq/rzxpIUGjCM47bu+Hg9nSODuG9MAuN7xzL/vnPo3aYV5VUW/Lw98fQQHji/G7d/vI69OSUcKizn3eV7eX1xCtPO7QKAl4eQV1JZ57rl1VasBlo1YCGbUk2BQ4lARK4C1gBXAlcBq0VksjMDUzYHckuZv/Ug2zN/L6C2J7v4mEHJfnEhZOaXU2Vx70SwOT2f2z5KYsQzP3PN2yv5afuhY47Zn1tKZn4ZOw4WsW7/Eca++AuXD2yLxUDS/jwAJg+K44lJvfh0zQEOFpSzMS2fT24+q2Zq8Jge0cxclsrh4t9XHd/x8XqC/bzo104HjFXz4uhXl0exFYTLBhCRSOAnbIXilBNUW6w88vUWFu3IZmD7MJKzComPCOCN6wbRJTqYtXvzGNPj971j1x/IJy7MHx8v9703vSktn6kfrOX+cV15dEJPtmUW8PicbRSUVXHFoDiAmoT6wlX9GWffe3fHwUImv7kSgNv+m8Qdo7vQKTKQBdsO4uUpNTOHant2cl/Gv5zP4KcX0TbUn9ziSqqtVj67ResSqebH0UTg8VsSsMvF8TpF6hS8s3wvmQVlrPjLefj7eGKxGv7+7Vb++d02po3uzN/+txVPD2Fop3A2puXz8Febuct+28Jdvb44henjunL90A4AtA8PIDbUn2mfrOeyAW3x8BDmbcmidYA3z/ywgzHdI20lq6OC8BBoHeDNuzcN4ZNV+1m6+zCD2ofx7bQetA48dj9jHy8Pfv7zaJbszGbB1oN0CA/kjyM7unUiVs2Xo4lgvogsAD6zP74amOeckBTAl+vSeW5y35rFTJ4ewl8u6M6wZxbxr8v68PglvXj+x53sPFhEp4gg7h2bwGUD4lwctWttSS/g8Ut61mnr3y6Ukspq8koriQjyxWIMl/Rrw+x16fR8fAGdI4LYm1tCeZWFe8ck0L9dKP3bhTr8mqO7RTG6m9aRUs3bCROBiHQBoo0xD4rI5cBI+1MrgU+cHZw7Ky6vJjyw7qbqv1XTrLRYGd87pmZhk7KJC/NnR1YRcWG/1wZKP2Kr89TKXlDugl4x3PnxOpb+eTSzktLYmJZPYnwY32zIYMpZOuNKuaeT9WNfBgoBjDFfG2OmG2OmA9/Yn1NOcnZCBF8kpdVpm7s5k67RwTUfaqquP43syBNzt7MtswCAzPwyHpy9mevP6lBzy6Z/u1AuHdCWi19fQXGFhbiwAL7bnMXDF/Y4ZhxAKXdxsltD0caYLUc3GmO2iEi8c0JSAPeN68pV/1lJVkE553SNYGtGAV+vz2DmjfUuDFTAhX1iySmq4LqZq6m2GjwErh/agfvGJtQ57qHx3ZnQJ5aF2w8R7OfF13cMJ/6oqrFKuZOTJYLQEzyn+/c5UdtQf+bePZJZa9P4KTmbdmH+/G/aCNppSeTjWrwjm5d+2kWvNq2wGtieZasEW1/V0N5tQ+jdNoTSymru/nQDK/YcxmI19IxtxatTBtAhXBODch8nSwRJInKLMWZm7UYRuRlY57ywFEBYoA93jO7s6jCahSMlldz3+UbenzqYge1t8/iTswqZMnMVA9uH0eY4+w6PfXEppRXV/GV8d1oH+vDKT7s5/6WlrP7rGEIDjp0tpFRLdLJEcB/wjYhcx+8f/ImAD3CZE+NSqkF+2HqQc7pG1iQBgB6xrZjQJ5bvNmVy26hjE+q8zVkcLCgjMT6MJ+ZuxxjwFPD28uDpeck8N7nfmXwLSrnMCROBMeYQMFxEzsW2iQzA98aYn50emVINUFpZTYj/sf+cQ/29Kamsf6vJRTsO4ekhrNl7hMmD4ri0fxte+HEXG9Ly+TlZ95lW7sPRWkOLjTGv2X80CagmZ3S3SOZvPciRWvV/iiuqmbMpk/OOs1902zB/qiyGJyf14vkr+zEyIZJvpo3Ax1PIK62s9xylWiKtjqVahC5RwVyV2I5JM1Zw3Vnt8fL04NPV+xndLZJ+cSHHHF9RbcHHXjl03paDTOzXhkAfL56cl0ylm9drUu5HE4FqMR4a352zEyL5fksmFis8dkkvzkmIOGbjnm83ZvDk3O01pSNW782l3xMLEcDX24OEqED2Hi51wTtQyjWcmghEZDzwCratKt8xxjxz1PO3A9Ow7YNcDNxqjNnuzJhUyzasczjDOodjtRqyiyooq7IQ4PP7P/OtGQU89X0yH/5xCL3ahDDk6YXkFFUSHezL29cPYPb6DD5encbkQe5drkO5F4e2qjylC4t4Ytu8fhyQjm3z+im1P+hFpJUxptD+54nAncaY8Se6rm5VqU7m+81ZPDM/mbJKCxVVVi7u14bHLu6Jv48nf//fVmJC/Gr2FSirtHDeC4vJKqjZeI/zukfx3k2DXRW+Uk7RGFtVnoohQIoxJtUexCxgElCTCH5LAnaBgFvfnK22WCmrshDk66X7EJ+iNXvz+Od323jjuoEkxrcmr6SSv3+7lb/9bysvXNWPvJLKOns5+Pt4svKRsVw3cxXn94rm+rPa4+np6cJ3oNSZ58yauW2B2sVy0u1tdYjINBHZAzwL3FPfhUTkVhFJEpGknJwcpwTrSlUWK8/8sINBT/3EWf9axLiXlrKwng1V1Ml9+Os+7h2bQGJ8awBaB/rwzOV9WLj9ILnFFZzVqTVzN2fV2cktu7CcLRkFXNy3jSYB5ZZcPlhsjJkBzBCRa4G/ATfWc8zbwNtguzV0ZiN0vqe/Tyb1cAnz7j2bNiF+rEjJ5f4vNhLi782Qjq1dHV6zkn6klO4xHeu0Bft5Exviz8HCciYPiuPztWnc9dkGJg+M43BxBW8u2cOt53QiPMj3OFdVqmVzZo8gA2hX63Gcve14ZgGXOjGeJqmwvIqv1qfz0lX9aBvqj4gwMiGC6eO68u7yVFeH1+z0jQtlyc66i8HS8ko5VFROx4hAAny8+Py2YfRpG8I7y1NZlJzNoxf14K7zEo5zRaVaPmf2CNYCCSLSEVsCuAa4tvYBIpJgjNltf3gRsBs3k11YTkSQ7zHfRvu0DeG/K/e7KKrm65azO3H5m7/i5+3J+N4x7DtcwjM/7OD2UZ1rZg8F+Xpx+6jO3F5P2Qml3JHTEoExplpE7gIWYJs++p4xZpuIPAEkGWPmAHeJyFigCjhCPbeFWrq2oQEcKa0kLa+0TmXRFSmH6REb7MLImqf24QF8cdtQXl+cwtT31xIV7Mtd53VhYr82rg5NqSbLadNHnaUlTh99Y0kKczZm8tjFPekcFcSP2w7y0k+7+eyWoXSL0WSglDp9rpo+qhx0x6jORAT68tT3yWQXldO/XRj//eMQTQJKqTNCE0ETICJcNbgdVw1ud/KDlVKqkTlz1pBSSqlmQBOBUkq5OU0ESinl5nSMQLkFq9WwZl8eOUUVDGgfSlxYwMlPUspNaCJQLV5aXik3f5iECHSMCOTv327lioFx/O2iHlrcTyk0ESg3MP2LjVw2sC23ndMJEaGgrIprZ67i242ZXDrgmDqISrkdHSNQLVpaXil7D5dy88iONd/+Q/y9uevcLny1Pt3F0SnVNGgiUC1aSWU1wX5eeHnW/aceEuBNaaXFRVEp1bRoIlAtWkJUMJXVVlal5ta0GWP4fG0ao7tGujAypZoOHSNQLZqnh/DUpb2585P1XJXYjvjwAOZvO0hOUQVPXdrb1eEp1SRoj0C1eOd2j+KrO4YDsHbfES7oFcOXtw8n2M/bxZEp1TRoj0C5hY4RgTx8YXdXh6FUk6Q9AqWUcnOaCJRSys1pIlBKKTeniUAppdycUxOBiIwXkZ0ikiIiD9fz/HQR2S4im0VkkYh0cGY8SimljuW0RCAinsAM4EKgJzBFRHoeddgGINEY0xf4EnjWWfEopZSqnzN7BEOAFGNMqjGmEpgFTKp9gDFmsTGm1P5wFRDnxHiUUkrVw5mJoC2QVutxur3teP4E/FDfEyJyq4gkiUhSTk5OI4aolFKqSQwWi8j1QCLwXH3PG2PeNsYkGmMSIyO1PoxSSjUmZ64szgDa1XocZ2+rQ0TGAo8Co4wxFU6MRymlVD2c2SNYCySISEcR8QGuAebUPkBEBgBvARONMdlOjEUppdRxOC0RGGOqgbuABUAy8IUxZpuIPCEiE+2HPQcEAbNFZKOIzDnO5ZRSSjmJU4vOGWPmAfOOanus1p/HOvP1lVJKnVyTGCxWSinlOpoIlFLKzWkiUEopN6eJQCml3JwmAqWUcnOaCJRSys1pIlBKKTeniUAppdycJgKllHJzmgiUUsrNaSJQSik3p4lAKaXcnCYCpZRyc5oIlFLKzWkiUEopN6eJQCml3JxTN6ZRqjFkF5bz1foMDhWWM7BDGON7xeDjpd9hlGos+tukmrS1+/IY/8oyDuSVEhfmz8er9nP12yspqah2dWhKtRhOTQQiMl5EdopIiog8XM/z54jIehGpFpHJzoxFNT/GGB7+ajP/vqIv/3d5H24+uxOf3zqUNqH+vLd8r6vDU6rFcFoiEBFPYAZwIdATmCIiPY867ABwE/Cps+JQzde+3FJKKy2M7RFV0yYi/GFoB35KPuTCyJRqWZw5RjAESDHGpAKIyCxgErD9twOMMfvsz1mdGIdqpny8PKistmKxGrw8paa9tMqiYwRKNSJn/ja1BdJqPU63tzWYiNwqIkkikpSTk9Mowammr22oPx0jAvnvyv01beVVFt5cvIeJ/U/pn5JSqh7NYtaQMeZt4G2AxMRE4+Jw1Bn0/JX9uPH9NczbkkWnyECW7jrM8M7hXDukvatDU6rFcGYiyADa1XocZ29TymHxEYH8NH0US3flcKiwgqkjOtIjtpWrw1KqRXFmIlgLJIhIR2wJ4BrgWie+nmqhvD09GNMj2tVhKNViOW2MwBhTDdwFLACSgS+MMdtE5AkRmQggIoNFJB24EnhLRLY5Kx6llFL1c+oYgTFmHjDvqLbHav15LbZbRkoppVxE5+AppZSb00SglFJuThOBUkq5OTGmeU3LF5EcYH89T0UAh89wOM7QUt4HtJz3ou+j6Wkp7+VMvo8OxpjI+p5odongeEQkyRiT6Oo4TldLeR/Qct6Lvo+mp6W8l6byPvTWkFJKuTlNBEop5eZaUiJ429UBNJKW8j6g5bwXfR9NT0t5L03ifbSYMQKllFKnpiX1CJRSSp0CTQRKKeXmWlQiEJErRWSbiFhFxOVTshrqZHs8Nxci8p6IZIvIVlfHcjpEpJ2ILBaR7fZ/V/e6OqZTISJ+IrJGRDbZ38c/XR3T6RARTxHZICJzXR3L6RCRfSKyRUQ2ikiSK2NpUYkA2ApcDix1dSAN5eAez83FB8B4VwfRCKqBB4wxPYGhwLRm+ndSAZxnjOkH9AfGi8hQ14Z0Wu7FVtG4JTjXGNPf1WsJWlQiMMYkG2N2ujqOU1Szx7MxphL4bY/nZscYsxTIc3Ucp8sYk2WMWW//cxG2D59mt0emsSm2P/S2/zTLWSIiEgdcBLzj6lhakhaVCJq5RtvjWTU+EYkHBgCrXRzKKbHfTtkIZAMLjTHN8n0ALwMPAVYXx9EYDPCjiKwTkVtdGUiz2LO4NhH5CYip56lHjTHfnul4VMsnIkHAV8B9xphCV8dzKowxFqC/iIQC34hIb2NMsxrDEZGLgWxjzDoRGe3icBrDSGNMhohEAQtFZIe9N33GNbtEYIwZ6+oYnET3eG6CRMQbWxL4xBjztavjOV3GmHwRWYxtDKdZJQJgBDBRRCYAfkArEfnYGHO9i+M6JcaYDPt/s0XkG2y3h12SCPTWUNNRs8eziPhg2+N5jotjcmsiIsC7QLIx5kVXx3OqRCTS3hNARPyBccAOlwZ1Cowxjxhj4owx8dh+P35urklARAJFJPi3PwPn48LE3KISgYhcZt8DeRjwvYgscHVMjjreHs+ujerUiMhnwEqgm4iki8ifXB3TKRoB3ACcZ5/it9H+bbS5iQUWi8hmbF84FhpjmvXUyxYgGlguIpuANcD3xpj5rgpGS0wopZSba1E9AqWUUg2niUAppdycJgKllHJzmgiUUsrNaSJQSik3p4lAuQ0RKa6n7XYR+YP9z0scrVorIvG/VVcVkUQRedX+53+IyJ8bM25nXlcpaIYri5VqTMaY/zTCNZIAl5YRVup0aI9AubX6vmmLiIeIfCAiT9mLtT0nImtFZLOI3FbPNUYfVRu/p713kSoi99Q6brqIbLX/3OdA+6MisktElgPdGvN9K1Wb9giUqssL+ATYaox52l4VssAYM1hEfIEVIvIjJy7j3B04FwgGdorIm0BfYCpwFiDAahH5BduXseO1X4Nt/wAvYD2wrrHfrFKgiUCpo72FrbzH0/bH5wN9RWSy/XEIkADsOsE1vjfGVAAVIpKNrZzASOAbY0wJgIh8DZyN7cO/vnYPe3upvV3rTimn0VtDStX1K3CuiPjZHwtwt30Xqf7GmI7GmB9Pco2KWn+2oF+4VBOniUCput4F5gFfiIgXtiKAd9jLUSMiXe3VIhtqGXCpiATYz7/M3na89qX2dn97lcpLTvudKXUc+k1FuZMAe3Xa39RbWtoY86KIhAAfAdcB8cB6e1nqHODShr6wMWa9iHyArdIkwDvGmA0AJ2j/HNiEbVextQ19TaUcpdVHlVLKzemtIaWUcnOaCJRSys1pIlBKKTeniUAppdycJgKllHJzmgiUUsrNaSJQSik39/8KVwuSqAYRCwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot likelihood vs. connectedness\n",
    "blm_fit.plot_liks_connectedness()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "blm_fit.plot_log_earnings()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "blm_fit.plot_type_proportions()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finally, we can compare estimates to the truth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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igKQrgW2ULo/dEBE7JV0H3B8RW+p9TjMzO3wzPeHudyLibkm/N9XnEfH3R3LyiNgKbK3ad+00x+aP5FxmZjY7M/UozqV0tdNU6zoFcERBYWZmrS81KCLiE+W310XETys/K88tmJlZh6v1hruvTrHv9noWYmZmrWmmOYp/CZwMLKmap1gMLGxkYWZm1hpmmqN4A3ABsJSXzlPsAz7QoJrMzKyFzDRHcQdwh6RcRHj1OjOzOajWOYqLJS2WNF/SsKRfSHpfQyszM7OWUGtQ/JuIeI7SMNQe4LeAaRfpMzOzzlFrUMwvv74L+Ep5eQ0zM2uiwkiBdfesozDS3JmAWtd6+rqkHwH/DPyhpFfSKc+HMDNrA4WRAud96bxDT7HbvmZ73R95Op2aehQRcTXw20B/RLxI6Wl3Uz1kyMzMGmDjgxsZL44TBOPFcTY+uLFp504NCkl/WrE5EBFFgIh4HvhQIwszM7PWMFOPYnXF+2uqPltV51rMzGwag6cN0t3VjRDdXd0MnjbYtHPPNEehad5PtW1mZg2SW54jWZOQ7EnI9+WbNj8BMwdFTPN+qm0zM2ug3PJcUwNi0kxBcZqk5yj1Hv5F+T3lba/1ZGY2B8y0hEdXswoxM7PWVOsNd2ZmNkc5KMzMLJWDwszMUjkozMwslYPCzMxSOSjMzCxVpkEhaZWkRyTtlnT1FJ9fJelhSQ+VH5j0m1nUaWY2l2UWFJK6gBuBdwAnAZdKOqnqsH+itGLtqcDtwH9rbpVmZs2X1XMnplPr8yga4Wxgd0Q8BiBpM6Wlyx+ePCAitlcc/13Aj181s45WGCkwsHHg0HMnhgeHM1m2o1KWQXE8MFKxPQqck3L8FcCdU30gaS2wFqCnp4ckSepUYuOMjY21RZ2N5DZwG4DbYNJkO2z62SbGD4xzkIOMHxhnw/YNjL9uPNPasgyKmkl6H9APnDvV5xGxHlgP0N/fH/l8vjmFFQqQJJDPQ+7wEj9JEppWZ4tyG7gNwG0wabIdFowsYNPIpkM9isvPu3xO9yieAJZXbPeW972EpPOBjwPnRkS2sVqpUICBAZiYgO5uGB4+7LAwM6uWW55jeHA4k+XEp5NlUNwHrJS0glJArAbeW3mApDOAm4BVEfFU80tMkSSlkCgWS69J4qAws7rIajnx6WR21VNEHACuBLYBu4DbImKnpOskXVg+7AbgWOArknZI2pJRuS+Xz5d6El1dpVd3nc2sQ2U6RxERW4GtVfuurXh/ftOLqlUuVxpumuUchZlZu2iLyeyWlcs5IMys43kJDzMzS+WgMDOzVA4KMzNL5aAwM7NUDgozM0vlq57MzDJSGCkcugO7lTkozMwyUL1K7A2n3ECefNZlTclDT2ZmGUj2JEwUJyhGkYniBDue3ZF1SdNyUJiZZSDfl6e7q5suddHd1c3pS07PuqRpeejJzCwD1avEjj/aOotjV3NQmJllpHKV2OTRJNtiUnjoyczMUjkozMwslYPCzMxSOSjMzJqkMFJg3T3rKIwUsi7lsHgy28ysCQojBc770nmHbrDbvmZ7Sz3uNI17FFMpFGDdutKrmVkdbHxwI+PFcYJgvDjOxgc3Zl1SzdyjqFYowMAATEyUnoU9POyn2JnZnOYeRbUkKYVEsVh6TZKsKzKzDjB42iDdXd0I0d3VzeBpg1mXVDP3KKrl86WexGSPIp/PuiIz6wC55TmSNcmhO7HbZX4CHBQvl8uVhpuSpBQSHnYyszqpvBO7nTgoppLLOSDMzMoynaOQtErSI5J2S7p6is8XSLq1/Pn3JPVlUKaZ2ZyWWVBI6gJuBN4BnARcKumkqsOuAH4VEb8F/HfgMw0typfFmlkdtesNdtWyHHo6G9gdEY8BSNoMXAQ8XHHMRcAny+9vBz4vSRERda/Gl8WaWR0VRgrkv5TnxeKLzO+aT7Imacv5Ccg2KI4HRiq2R4FzpjsmIg5IehZYBvyy8iBJa4G1AD09PSSzuKT1dZs2sWJ8HB08yMHxcfZs2MDPxhu3PvzY2Nis6uwkbgO3AXRuG3zux59jojgBwERxgnV3ruOqE6+a9vhWboeOmMyOiPXAeoD+/v7Iz+aS1gULYNMmmJjgqO5uTrj8ck5oYI8iSRJmVWcHcRu4DaBz2+DWsVvhyV9vH//a41P/nq3cDllOZj8BLK/Y7i3vm/IYSfOAJcDehlQzeVns9dd72MnMjtjgaYMs6FqAEAu6FrTVDXbVsuxR3AeslLSCUiCsBt5bdcwWYA1QAN4N3N2Q+YlJvizWzOoktzzH9jXb2/IGu2qZBUV5zuFKYBvQBWyIiJ2SrgPuj4gtwBeAWyTtBp6mFCZmZi2rMFJ4STi0c0BMynSOIiK2Alur9l1b8X4/8J5m12VmNhuFkQIDGwcOLSU+PDjcEUHhRQHNzOok2ZMwUZygGEUmihMke5KsS6oLB4WZWZ3k+/J0d3XTpS66u7rJ9+WzLqkuOuLyWDOzVpBbnmN4cLgjJrArOSjMzOqoUyawK3noyczMUjkozMwslYPCzMxSOSjMzCyVg8LMzFI5KMzMLJWDwszMUjkozMwslYPCzMxSOSjMzCyVg8LMzFI5KMzMLJWDwsxsFgojBdbds47CSCHrUhrOq8eamR2mTn2S3XTcozAzO0yd+iS76TgozMwOU6c+yW46HnoyMztMnfoku+k4KMzMZqETn2Q3HQ89mZlZqkyCQtIrJH1T0k/Kr78xxTGnSypI2inpIUn/Lotazczmuqx6FFcDwxGxEhgub1d7ARiMiJOBVcBfSFravBLNzAyyC4qLgC+V338J+LfVB0TEjyPiJ+X3PweeAl7ZrALNzCrNpRvsqikimn9S6ZmIWFp+L+BXk9vTHH82pUA5OSIOTvH5WmAtQE9Pzxs3b97ciLLramxsjGOPPTbrMjLlNnAbQHu0wc5nd/KRhz7CiwdfZP5R8/nsqZ/l5CUn1/UcWbfDeeed90BE9E/1WcOuepL0LeDVU3z08cqNiAhJ06aVpNcAtwBrpgqJ8nesB9YD9Pf3Rz6fn23ZTZMkCe1QZyO5DdwG0B5tULinwIE4wEEOciAO8NwrniP/1nxdz9HK7dCwoIiI86f7TNL/k/SaiHiyHARPTXPcYuAbwMcj4rsNKtXMLNXkDXaTS3Z0+g121bK6j2ILsAb4dPn1juoDJHUD/wBsjIjbm1uemdmvzbUb7KplFRSfBm6TdAXwOPD7AJL6gf8YEX9Q3vc2YJmk95d/7v0RsaP55ZrZXDeXbrCrlklQRMReYGCK/fcDf1B+/2Xgy00uzczMqvjObDMzS+WgMDOzVA4KMzNL5aAwM7NUDgozM0uVyRIejSTpF5QuuW11xwG/zLqIjLkN3AbgNpiUdTv8ZkRMuZ5exwVFu5B0/3TrqswVbgO3AbgNJrVyO3joyczMUjkozMwslYMiO+uzLqAFuA3cBuA2mNSy7eA5CjMzS+UehZmZpXJQmJlZKgdFhiTdIOlHkh6S9A+SlmZdU7NJeo+knZIOlpeZnzMkrZL0iKTdkq7Oup5mk7RB0lOSfph1LVmRtFzSdkkPl/87+OOsa5qKgyJb3wROiYhTgR8D12RcTxZ+CPwe8O2sC2kmSV3AjcA7gJOASyWdlG1VTXczsCrrIjJ2APhIRJwEvAn4o1b898BBkaGI+MeIOFDe/C7Qm2U9WYiIXRHxSNZ1ZOBsYHdEPBYRE8Bm4KKMa2qqiPg28HTWdWQpIp6MiP9Tfr8P2AUcn21VL+egaB2XA3dmXYQ1zfHASMX2KC34C8KaR1IfcAbwvYxLeZmsHoU6Z0j6FvDqKT76eETcUT7m45S6oJuaWVuz1NIGZnOZpGOBrwIfjojnsq6nmoOiwSLi/LTPy88DvwAYiA69qWWmNpijngCWV2z3lvfZHCNpPqWQ2BQRf591PVPx0FOGJK0C/hS4MCJeyLoea6r7gJWSVkjqBlYDWzKuyZpMkoAvALsi4nNZ1zMdB0W2Pg8sAr4paYekv8m6oGaTdLGkUSAHfEPStqxraobyRQxXAtsoTWDeFhE7s62quSQNAQXgDZJGJV2RdU0ZeDNwGfA75d8BOyS9M+uiqnkJDzMzS+UehZmZpXJQmJlZKgeFmZmlclCYmVkqB4WZmaVyUJjNkqRlFZc0/l9JT1Rsd8/ws0slfbBiOy/pfza+arPD5zuzzWYpIvYCpwNI+iQwFhF/Pvm5pHkViz5WWwp8EPirxlZpduQcFGZ1JOlmYD+lxd3ulfQcFQFSfvbCBcCngddL2kFpuflvAMdKuh04BXgAeF+nLuti7cVBYVZ/vcBvR0Sx3NOYytWUnkVyOpSGniiFy8nAz4F7Kd21+50G12o2I89RmNXfVyKiOIuf+35EjEbEQWAH0FfXqsxmyUFhVn/PV7w/wEv/O1uY8nPjFe+LuMdvLcJBYdZYe4AzASSdCawo799HaUFIs5bnoDBrrK8Cr5C0k9JqsT+GQ1dM3Svph5JuyLJAs5l49VgzM0vlHoWZmaVyUJiZWSoHhZmZpXJQmJlZKgeFmZmlclCYmVkqB4WZmaX6/+G5lMv0me+PAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(sim_params['A1'].flatten(), blm_model.A1.flatten(), '.', label='A1', color='red')\n",
    "plt.plot(sim_params['A2'].flatten(), blm_model.A2.flatten(), '.', label='A2', color='green')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(sim_params['S1'].flatten(), blm_model.S1.flatten(), '.', label='S1', color='red')\n",
    "plt.plot(sim_params['S2'].flatten(), blm_model.S2.flatten(), '.', label='S2', color='green')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(sim_params['A1_cat']['cat_control'].flatten(), blm_model.A1_cat['cat_control'].flatten(), '.', label='A1_cat', color='red')\n",
    "plt.plot(sim_params['A2_cat']['cat_control'].flatten(), blm_model.A2_cat['cat_control'].flatten(), '.', label='A2_cat', color='green')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(sim_params['S1_cat']['cat_control'].flatten(), blm_model.S1_cat['cat_control'].flatten(), '.', label='S1_cat', color='red')\n",
    "plt.plot(sim_params['S2_cat']['cat_control'].flatten(), blm_model.S2_cat['cat_control'].flatten(), '.', label='S2_cat', color='green')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(sim_params['A1_cts']['cts_control'].flatten(), blm_model.A1_cts['cts_control'].flatten(), '.', label='A1_cts', color='red')\n",
    "plt.plot(sim_params['A2_cts']['cts_control'].flatten(), blm_model.A2_cts['cts_control'].flatten(), '.', label='A2_cts', color='green')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(sim_params['S1_cts']['cts_control'].flatten(), blm_model.S1_cts['cts_control'].flatten(), '.', label='S1_cts', color='red')\n",
    "plt.plot(sim_params['S2_cts']['cts_control'].flatten(), blm_model.S2_cts['cts_control'].flatten(), '.', label='S2_cts', color='green')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(sim_params['pk1'].flatten(), blm_model.pk1.flatten(), '.', label='pk1', color='red')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(sim_params['pk0'].flatten(), blm_model.pk0.flatten(), '.', label='pk0', color='red')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "\n",
    "Warning\n",
    "\n",
    "The parameters are identified only up to a constant intercept.\n",
    "\n",
    "Because of this, to maintain consistency between estimations, PyTwoWay automatically normalizes worker-firm types to have effect 0, depending on the control variables used (normalization only occurs with categorical control variables - for a stationary control variable, only the first period is normalized (if it is non-stationary, both periods are normalized); for a control variable that does not interact with worker types, only the lowest worker type is normalized (if it does interact with worker types, all worker types are normalized)).\n",
    "\n",
    "If we take the sum over the estimators we see the model performs well.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## First period ##\n",
    "plt.plot(\n",
    "    (sim_params['A1'] + sim_params['A1_cat']['cat_control'][0]).flatten(),\n",
    "    (blm_model.A1 + blm_model.A1_cat['cat_control'][0]).flatten(),\n",
    "    '.', label='A1 + A1_cat[0]', color='red'\n",
    ")\n",
    "plt.plot(\n",
    "    (sim_params['A1'] + sim_params['A1_cat']['cat_control'][1]).flatten(),\n",
    "    (blm_model.A1 + blm_model.A1_cat['cat_control'][1]).flatten(),\n",
    "    '.', label='A1 + A1_cat[1]', color='green'\n",
    ")\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(\n",
    "    np.sqrt((sim_params['S1'] ** 2 + sim_params['S1_cat']['cat_control'][0] ** 2).flatten()),\n",
    "    np.sqrt((blm_model.S1 ** 2 + blm_model.S1_cat['cat_control'][0] ** 2).flatten()),\n",
    "    '.', label='sqrt(S1^2 + S1_cat[0]^2)', color='red'\n",
    ")\n",
    "plt.plot(\n",
    "    np.sqrt((sim_params['S1'] ** 2 + sim_params['S1_cat']['cat_control'][1] ** 2).flatten()),\n",
    "    np.sqrt((blm_model.S1 ** 2 + blm_model.S1_cat['cat_control'][1] ** 2).flatten()),\n",
    "    '.', label='sqrt(S1^2 + S1_cat[1]^2)', color='green'\n",
    ")\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "## Second period ##\n",
    "plt.plot(\n",
    "    (sim_params['A2'] + sim_params['A2_cat']['cat_control'][0]).flatten(),\n",
    "    (blm_model.A2 + blm_model.A2_cat['cat_control'][0]).flatten(),\n",
    "    '.', label='A2 + A2_cat[0]', color='red'\n",
    ")\n",
    "plt.plot(\n",
    "    (sim_params['A2'] + sim_params['A2_cat']['cat_control'][1]).flatten(),\n",
    "    (blm_model.A2 + blm_model.A2_cat['cat_control'][1]).flatten(),\n",
    "    '.', label='A2 + A2_cat[1]', color='green'\n",
    ")\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.plot(\n",
    "    np.sqrt((sim_params['S2'] ** 2 + sim_params['S2_cat']['cat_control'][0] ** 2).flatten()),\n",
    "    np.sqrt((blm_model.S2 ** 2 + blm_model.S2_cat['cat_control'][0] ** 2).flatten()),\n",
    "    '.', label='sqrt(S2^2 + S2_cat[0]^2)', color='red'\n",
    ")\n",
    "plt.plot(\n",
    "    np.sqrt((sim_params['S2'] ** 2 + sim_params['S2_cat']['cat_control'][1] ** 2).flatten()),\n",
    "    np.sqrt((blm_model.S2 ** 2 + blm_model.S2_cat['cat_control'][1] ** 2).flatten()),\n",
    "    '.', label='sqrt(S2^2 + S2_cat[1]^2)', color='green'\n",
    ")\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Estimate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variance decomposition\n",
    "\n",
    "The package contains the class `BLMVarianceDecomposition`, which allows for the estimation of the decomposition of the variance components of the BLM estimator.\n",
    "\n",
    "In this example, we use the same simulated data and estimation parameters as in the previous example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize BLM variance decomposition estimator\n",
    "blm_fit = tw.BLMVarianceDecomposition(blm_params)\n",
    "# Fit BLM estimator\n",
    "blm_fit.fit(\n",
    "    jdata=jdata, sdata=sdata,\n",
    "    blm_model=blm_model,\n",
    "    n_samples=20,\n",
    "    Q_var=[\n",
    "        tw.Q.VarCovariate('psi'),\n",
    "        tw.Q.VarCovariate('cat_control'),\n",
    "        tw.Q.VarCovariate('cts_control')\n",
    "    ],\n",
    "    ncore=1\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Investigate the results\n",
    "\n",
    "Results correspond to:\n",
    "\n",
    "- `y`: income (outcome) column\n",
    "- `eps`: residual\n",
    "- `psi`: firm effects\n",
    "- `alpha`: worker effects\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Note\n",
    "\n",
    "Results from all estimations are stored in the class attribute dictionary `.res`. We take the mean, but storing all results gives the option to estimate different sample statistics.\n",
    "\n",
    "</div>\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "\n",
    "Note\n",
    "\n",
    "The particular variance that is estimated is controlled through the parameter `'Q_var'` and the covariance that is estimated is controlled through the parameter `'Q_cov'`.\n",
    "\n",
    "By default, the variance is `var(psi)` and the covariance is `cov(psi, alpha)`. The default estimates don't include `var(alpha)`, but if you don't include controls, `var(alpha)` can be computed as the residual from `var(y) = var(psi) + var(alpha) + 2 * cov(psi, alpha) + var(eps)`.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'var(y)': 4.1784778224072054\n",
      "'var(eps)': 3.862767039874967\n",
      "'var(cat_control)': 0.17504851379038694\n",
      "'var(cts_control)': 0.03529768004099764\n",
      "'var(psi)': 0.052474105201016495\n",
      "'cov(psi, alpha)': -0.0014679055738114212\n"
     ]
    }
   ],
   "source": [
    "for k, v in blm_fit.res.items():\n",
    "    print(f'{k!r}: {v.mean()}')"
   ]
  }
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