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Last active August 29, 2015 13:58
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Interactive spatial autocorrelation
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"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pysal as ps\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.linalg import inv"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Interactive spatial autocorrelation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook illustrates the concept of spatial autocorrelation using the new interactivity in IPython. The data generating process (DGP) considered here is the following:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. $u = \\lambda Wu + \\epsilon$\n",
"\n",
"1. $u - \\lambda Wu = \\epsilon$\n",
"\n",
"1. $u (I - \\lambda W) = \\epsilon$\n",
"\n",
"1. $u = (I - \\lambda W)^{-1} \\epsilon$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Where `u` is a vector spatially autocorrelated, `W` is a spatial weights matrix as you could created with `PySAL`, and $\\epsilon$ is an i.i.d. random vector."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To implement the previous DGP, the simple method `draw_map` (actual code pasted at the bottom of the notebook, so make sure to run that cell beforehand) creates a random vector with degree of spatial autocorrelation $\\lambda$ and allocates it to a lattice geography, where every pixel is assumed to be an area with a value. Right next to it, the function also displays the Moran's scatter plot. Both map and plot depend on the $\\lambda$ parameter that controls the degree of spatial autocorrelation.\n",
"\n",
"Here's a static version of the function:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"draw_map(0.95)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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9lEy//56cEYAiE+++S+2VBw2iexdGdB3wGYJKSuwQMAzDMDmSkUGL9tGjtLjP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\nAABRCAAAgCgEAABAFAIAACAKAQAAkPQfmlcSgtqbGMkAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x107fa2050>"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, we can make the $\\lambda$ value change in an interactive way:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.html.widgets import interact\n",
"interact(draw_map, lamb=(-0.9, 0.9))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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GHkaNQqOfd99FIynp/efKBfd0kqLp6IoVMFqsERODEEnfvjgWLUVVEhdn+ViL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\niUkCERERafp/9xfpqV0VbKkAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x10b580190>"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 8,
"text": [
"<function __main__.draw_map>"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Actual plotting function"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def draw_map(lamb):\n",
" s = 20\n",
" n = s**2\n",
" w = ps.lat2W(s, s, rook=False)\n",
" w.transform = 'R'\n",
" e = np.random.random((n, 1))\n",
" u = inv(np.eye(n) - lamb * w.full()[0])\n",
" u = np.dot(u, e)\n",
" ul = ps.lag_spatial(w, u)\n",
" u = (u - u.mean()) / np.std(u)\n",
" ul = (ul - ul.mean()) / np.std(ul)\n",
" gu = u.reshape((s, s))\n",
" # Figure\n",
" f = plt.figure(figsize=(9, 4))\n",
" ax1 = f.add_subplot(121)\n",
" ax1.matshow(gu, cmap=plt.cm.YlGn)\n",
" ax1.set_frame_on(False)\n",
" ax1.axes.get_xaxis().set_visible(False)\n",
" ax1.axes.get_yaxis().set_visible(False)\n",
" #---\n",
" ax2 = f.add_subplot(122)\n",
" sc = ax2.scatter(u, ul, linewidth=0)\n",
" ols = ps.spreg.OLS(ul, u)\n",
" tag = \"b = %.3f\"%ols.betas[1][0]\n",
" ax2.plot(u, ols.predy, c='red', label=tag)\n",
" ax2.axvline(0, c='0.5')\n",
" ax2.axhline(0, c='0.5')\n",
" ax2.legend()\n",
" plt.xlabel('u')\n",
" plt.ylabel('Wu')\n",
" plt.suptitle(\"$\\lambda$ = %.2f\"%lamb)\n",
" plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
}
],
"metadata": {}
}
]
}
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