notebooks/Quadrat_statistics.ipynb

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    "# Quadrat Based Statistical Method for Planar Point Patterns\n",
    "\n",
    "**Authors: Serge Rey <sjsrey@gmail.com>, Wei Kang <weikang9009@gmail.com> and Hu Shao <shaohutiger@gmail.com>**\n",
    "\n",
    "## Introduction\n",
    "\n",
    "In this notebook, we are going to introduce how to apply quadrat statistics to a point pattern to infer whether it comes from a CSR process.\n",
    "\n",
    "1. In [Quadrat Statistic](#Quadrat-Statistic) we introduce the concept of quadrat based method.\n",
    "2. We illustrate how to use the module **quadrat_statistics.py** through an example dataset **juvenile** in [Juvenile Example](#Juvenile-Example)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Quadrat Statistic\n",
    "\n",
    "In the previous notebooks, we introduced the concept of Complete Spatial Randomness (CSR) process which serves as the benchmark process. Utilizing CSR properties, we can discriminate those that are not from a CSR process. Quadrat statistic is one such method. Since a CSR process has two major characteristics:\n",
    "1. Uniform: each location has equal probability of getting a point (where an event happens).\n",
    "2. Independent: location of event points are independent.\n",
    "\n",
    "We can imagine that for any point pattern, if the underlying process is a CSR process, the expected point counts inside any cell of area $|A|$ should be $\\lambda |A|$ ($\\lambda$ is the intensity which is uniform across the study area for a CSR). Thus, if we impose a $m \\times k$ rectangular tessellation over the study area (window), we can easily calculate the expected number of points inside each cell under the null of CSR. By comparing the observed point counts against the expected counts and calculate a $\\chi^2$ test statistic, we can decide whether to reject the null based on the position of the $\\chi^2$ test statistic in the sampling distribution. \n",
    "\n",
    "$$\\chi^2 = \\sum^m_{i=1} \\sum^k_{j=1} \\frac{[x_{i,j}-E(x_{i,j})]^2}{\\lambda |A_{i,j}|}$$\n",
    "\n",
    "There are two ways to construct the sampling distribution and acquire a p-value:\n",
    "1. Analytical sampling distribution: a $\\chi^2$ distribution of $m \\times k -1$ degree of freedom. We can refer to the $\\chi^2$ distribution table to acquire the p-value. If it is smaller than $0.05$, we will reject the null at the $95\\%$ confidence level.\n",
    "2. Empirical sampling distribution: a distribution constructed from a large number of $\\chi^2$ test statistics for  simulations under the null of CSR. If the $\\chi^2$ test statistic for the observed point pattern is among the largest $5%$ test statistics, we would say that it is very unlikely that it is the outcome of a CSR process at the $95\\%$ confidence level. Then, the null is rejected. A pseudo p-value can be calculated based on which we can use the same rule as p-value to make the decision:\n",
    "$$p(\\chi^2) = \\frac{1+\\sum^{nsim}_{i=1}\\phi_i}{nsim+1}$$\n",
    "where \n",
    "$$ \n",
    "\\phi_i =\n",
    " \\begin{cases}\n",
    "    1       & \\quad \\text{if } \\psi_i^2 \\geq \\chi^2 \\\\\n",
    "    0       & \\quad \\text{otherwise } \\\\\n",
    "  \\end{cases}\n",
    "$$\n",
    "\n",
    "$nsim$ is the number of simulations, $\\psi_i^2$ is the $\\chi^2$ test statistic calculated for each simulated point pattern, $\\chi^2$ is the $\\chi^2$ test statistic calculated for the observed point pattern, $\\phi_i$ is an indicator variable.\n",
    "\n",
    "We are going to introduce how to use the **quadrat_statistics.py** module to perform quadrat based method using either of the above two approaches to constructing the sampling distribution and acquire a p-value.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Juvenile Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/wk0110/My Drive (weikang9009@gmail.com)/python_repos/pysal-refactor/libpysal/libpysal/cg/alpha_shapes.py:42: NumbaDeprecationWarning: \u001b[1mThe 'nopython' keyword argument was not supplied to the 'numba.jit' decorator. The implicit default value for this argument is currently False, but it will be changed to True in Numba 0.59.0. See https://numba.readthedocs.io/en/stable/reference/deprecation.html#deprecation-of-object-mode-fall-back-behaviour-when-using-jit for details.\u001b[0m\n",
      "  def nb_dist(x, y):\n",
      "/Users/wk0110/My Drive (weikang9009@gmail.com)/python_repos/pysal-refactor/libpysal/libpysal/cg/alpha_shapes.py:168: NumbaDeprecationWarning: \u001b[1mThe 'nopython' keyword argument was not supplied to the 'numba.jit' decorator. The implicit default value for this argument is currently False, but it will be changed to True in Numba 0.59.0. See https://numba.readthedocs.io/en/stable/reference/deprecation.html#deprecation-of-object-mode-fall-back-behaviour-when-using-jit for details.\u001b[0m\n",
      "  def get_faces(triangle):\n",
      "/Users/wk0110/My Drive (weikang9009@gmail.com)/python_repos/pysal-refactor/libpysal/libpysal/cg/alpha_shapes.py:202: NumbaDeprecationWarning: \u001b[1mThe 'nopython' keyword argument was not supplied to the 'numba.jit' decorator. The implicit default value for this argument is currently False, but it will be changed to True in Numba 0.59.0. See https://numba.readthedocs.io/en/stable/reference/deprecation.html#deprecation-of-object-mode-fall-back-behaviour-when-using-jit for details.\u001b[0m\n",
      "  def build_faces(faces, triangles_is, num_triangles, num_faces_single):\n",
      "/Users/wk0110/My Drive (weikang9009@gmail.com)/python_repos/pysal-refactor/libpysal/libpysal/cg/alpha_shapes.py:264: NumbaDeprecationWarning: \u001b[1mThe 'nopython' keyword argument was not supplied to the 'numba.jit' decorator. The implicit default value for this argument is currently False, but it will be changed to True in Numba 0.59.0. See https://numba.readthedocs.io/en/stable/reference/deprecation.html#deprecation-of-object-mode-fall-back-behaviour-when-using-jit for details.\u001b[0m\n",
      "  def nb_mask_faces(mask, faces):\n",
      "/Users/wk0110/opt/anaconda3/lib/python3.9/site-packages/geopandas/_compat.py:112: UserWarning: The Shapely GEOS version (3.10.2-CAPI-1.16.0) is incompatible with the GEOS version PyGEOS was compiled with (3.10.4-CAPI-1.16.2). Conversions between both will be slow.\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "import libpysal as ps\n",
    "import numpy as np\n",
    "from pointpats import PointPattern, as_window\n",
    "from pointpats import PoissonPointProcess as csr\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import the quadrat_statistics module to conduct quadrat-based method. \n",
    "\n",
    "Among the three major classes in the module, **RectangleM, HexagonM, QStatistic**, the first two are aimed at imposing a tessellation (rectangular or hexagonal shape) over the minimum bounding rectangle of the point pattern and calculate the number of points falling in each cell; **QStatistic** is the main class with which we can calculate a p-value, as well as a pseudo p-value to help us make the decision of rejecting the null or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pointpats.quadrat_statistics as qs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['HexagonM',\n",
       " 'PointPattern',\n",
       " 'QStatistic',\n",
       " 'RectangleM',\n",
       " '__all__',\n",
       " '__author__',\n",
       " '__builtins__',\n",
       " '__cached__',\n",
       " '__doc__',\n",
       " '__file__',\n",
       " '__loader__',\n",
       " '__name__',\n",
       " '__package__',\n",
       " '__spec__',\n",
       " 'math',\n",
       " 'np',\n",
       " 'plt',\n",
       " 'scipy']"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(qs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Open the point shapefile \"juvenile.shp\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "juv = ps.io.open(ps.examples.get_path(\"juvenile.shp\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "168"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(juv) # 168 point events in total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "juv_points = np.array([event for event in juv]) # get x,y coordinates for all the points\n",
    "juv_points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construct a point pattern from numpy array **juv_points**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pointpats.pointpattern.PointPattern at 0x7fedf185a280>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pp_juv = PointPattern(juv_points)\n",
    "pp_juv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Point Pattern\n",
      "168 points\n",
      "Bounding rectangle [(2.0,6.0), (94.0,95.0)]\n",
      "Area of window: 8188.0\n",
      "Intensity estimate for window: 0.02051783097215437\n",
      "      x     y\n",
      "0  94.0  93.0\n",
      "1  80.0  95.0\n",
      "2  79.0  90.0\n",
      "3  78.0  92.0\n",
      "4  76.0  92.0\n"
     ]
    }
   ],
   "source": [
    "pp_juv.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pp_juv.plot(window= True, title= \"Point pattern\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rectangle quadrats & analytical sampling distribution\n",
    "\n",
    "We can impose rectangle tessellation over mbb of the point pattern by specifying **shape** as \"rectangle\". We can also specify the number of rectangles in each row and column. For the current analysis, we use the $3 \\times 3$ rectangle grids."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "q_r = qs.QStatistic(pp_juv,shape= \"rectangle\",nx = 3, ny = 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the plot method to plot the quadrats as well as the number of points falling in each quadrat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_r.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "909.7777777777778"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_r.mr.rectangle_width * q_r.mr.rectangle_height #calculate the area of each grid cell "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33.107142857142854"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_r.chi2 #chi-squared test statistic for the observed point pattern"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_r.df #degree of freedom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.890978545159614e-05"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_r.chi2_pvalue # analytical pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the p-value based on the analytical $\\chi^2$ distribution (degree of freedom = 8) is 0.0000589, much smaller than 0.05. We might determine that the underlying process is not CSR. We can also turn to empirical sampling distribution to ascertain our decision."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rectangle quadrats & empirical sampling distribution\n",
    "\n",
    "To construct a empirical sampling distribution, we need to simulate CSR within the window of the observed point pattern a lot of times. Here, we generate 999 point patterns under the null of CSR."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "csr_process = csr(pp_juv.window, pp_juv.n, 999, asPP=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We specify parameter **realizations** as the point process instance which contains 999 CSR realizations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "q_r_e = qs.QStatistic(pp_juv,shape= \"rectangle\",nx = 3, ny = 3, realizations = csr_process)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.001"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_r_e.chi2_r_pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pseudo p-value is 0.002, which is smaller than 0.05. Thus, we reject the null at the $95\\%$ confidence level."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hexagon quadrats & analytical sampling distribution\n",
    "\n",
    "We can also impose hexagon tessellation over mbb of the point pattern by specifying **shape** as \"hexagon\". We can also specify the length of the hexagon edge. For the current analysis, we specify it as 15."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "q_h = qs.QStatistic(pp_juv,shape= \"hexagon\",lh = 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_h.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "129.38095238095238"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_h.chi2 #chi-squared test statistic for the observed point pattern"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_h.df #degree of freedom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.909272893094198e-18"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_h.chi2_pvalue  # analytical pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to the inference of rectangle tessellation, since the analytical p-value is much smaller than 0.05, we reject the null of CSR. The point pattern is not random."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hexagon quadrats & empirical sampling distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "q_h_e = qs.QStatistic(pp_juv,shape= \"hexagon\",lh = 15, realizations = csr_process)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.001"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_h_e.chi2_r_pvalue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because 0.001 is smaller than 0.05, we reject the null."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
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