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@TaylorOshan
Created July 2, 2016 02:19
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"import os\n",
"os.chdir('../')\n",
"from vec_SA import VecMoran\n",
"import numpy as np\n",
"from pysal.weights.Distance import DistanceBand\n",
"import matplotlib.pyplot as plt\n",
"%pylab inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Demonstrating the vector-based Moran's I statistic for spatial autocorrelation and the associated proposed randomization techniques for generating psuedo p-values\n",
"\n",
"##### - Technique A: Randomly select one vector among the N observed vectors and assign its origin (destination) to the origin (destination) point of another observed vector. This is equivlanet to geometrically translating both the original origin and the original destination by the coordinates of the new origin (destination) point, which preserves the direction and magnitude of the original vector. Using this technique it is possible to generate new vectors that are outside the bounding box of the original set of vectors, thererby violating any potential study area boundaries.\n",
"##### - Technique B: For each vector among the N observed vectors, reassign its origin (destination) point to the destination (origin) from another randomly selected vector from the N observed vectors. This does does not preserve distance or magnitude, though it does ensure that all new vectors remain within the bounding box of the of the original vectors"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Generate 1000 random datasets of 50 vectors, then calculate the vector Moran's I from the destination perspective (VMD) and a psuedo p value (based on 99 permutations) using randomization technique A and randomization technique B for each of the 1000 datasets. "
]
},
{
"cell_type": "code",
"execution_count": 237,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [],
"source": [
"dest_A_rand_I = []\n",
"dest_B_rand_I = []\n",
"dest_A_rand_p = []\n",
"dest_B_rand_p = []\n",
"for i in range(1000):\n",
" phi = np.random.uniform(0,np.pi*2, 50).reshape((-1,1))\n",
" num = np.arange(0,50).reshape((-1,1))\n",
" OX = np.random.randint(0,500, 50).reshape((-1,1))\n",
" OY = np.random.randint(0,500, 50).reshape((-1,1))\n",
" DX = np.cos(phi)*(np.random.randint(0,500, 50)).reshape((-1,1))\n",
" DY = np.sin(phi)*np.random.randint(0,500, 50).reshape((-1,1))\n",
"\n",
" vecs = np.hstack([num, OX, OY, DX, DY])\n",
" dests = vecs[:, 3:5]\n",
" wd = DistanceBand(dests, threshold=9999, alpha=-1.5, binary=False)\n",
"\n",
" vmd = VecMoran(vecs, wd, focus='destination', rand='A', permutations=999)\n",
" dest_A_rand_I.append(vmd.I)\n",
" dest_A_rand_p.append(vmd.p_z_sim)\n",
" vmd = VecMoran(vecs, wd, focus='destination', rand='B', permutations=999)\n",
" dest_B_rand_I.append(vmd.I)\n",
" dest_B_rand_p.append(vmd.p_z_sim)\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 238,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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OHaKiRYvSokWLiIjoueeeMzzrtWvXfG5z+vTpIX8+BFnQ9wIwH8Aqx/exAPo6PvcD8IXj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\npu8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10d6dd490>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X,Y,U,V = zip(*vecs[:,1:])\n",
"plt.subplot(111)\n",
"for x in range(0,len(vecs[:,1])):\n",
" plt.arrow(X[x], #x1\n",
" Y[x], # y1\n",
" U[x]-X[x], # x2 - x1\n",
" V[x]-Y[x], # y2 - y1\n",
" fc=\"k\", ec=\"k\", head_width=0.05, head_length=0.1)\n",
"plt.xlim([-510,550])\n",
"plt.ylim([-510,550])\n",
"plt.title('Example of 50 random vectors')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Generate 1000 random datasets of 50 vectors with constrained origins (to induce positive spatial autocorrrlation), then calculate the vector Moran's I from the destination perspective (VMD) and a psuedo p value (based on 99 permutations) using randomization technique A and randomization technique B for each of the 1000 datasets. "
]
},
{
"cell_type": "code",
"execution_count": 239,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"\n",
"dest_A_cons_I = []\n",
"dest_B_cons_I = []\n",
"dest_A_cons_p = []\n",
"dest_B_cons_p = []\n",
"for i in range(1000):\n",
" phi = np.random.uniform(0,np.pi*2, 50).reshape((-1,1))\n",
" num = np.arange(0,50).reshape((-1,1))\n",
" OX = np.random.randint(450,500, 50).reshape((-1,1))\n",
" OY = np.random.randint(450,500, 50).reshape((-1,1))\n",
" DX = np.cos(phi)*(np.random.randint(450,500, 50)).reshape((-1,1))\n",
" DY = np.sin(phi)*np.random.randint(450,500, 50).reshape((-1,1))\n",
"\n",
" vecs = np.hstack([num, OX, OY, DX, DY])\n",
" dests = vecs[:, 3:5]\n",
" wd = DistanceBand(dests, threshold=9999, alpha=-1.5, binary=False)\n",
"\n",
" vmd = VecMoran(vecs, wd, focus='destination', rand='A', permutations=999)\n",
" dest_A_cons_I.append(vmd.I)\n",
" dest_A_cons_p.append(vmd.p_z_sim)\n",
" vmd = VecMoran(vecs, wd, focus='destination', rand='B', permutations=999)\n",
" dest_B_cons_I.append(vmd.I)\n",
" dest_B_cons_p.append(vmd.p_z_sim)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 240,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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WamoqChYsiMjISADA77//jtu3bwNgbBbOom7ZsmXGG2YDBo/ewGOF9evXo2fPnlldDeTK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"text/plain": [
"<matplotlib.figure.Figure at 0x10c01d590>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X,Y,U,V = zip(*vecs[:,1:])\n",
"plt.subplot(111)\n",
"for x in range(0,len(vecs[:,1])):\n",
" plt.arrow(X[x], #x1\n",
" Y[x], # y1\n",
" U[x]-X[x], # x2 - x1\n",
" V[x]-Y[x], # y2 - y1\n",
" fc=\"k\", ec=\"k\", head_width=0.05, head_length=0.1)\n",
"plt.xlim([-510,550])\n",
"plt.ylim([-510,550])\n",
"plt.title('Example of 50 random vectors with constrained origins')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 247,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x11311fd90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x111894450>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Method A random\n",
"plt.hist(dest_A_rand_I, bins = 25)\n",
"plt.title('Distribution of VMD I values from random vectors - Method A')\n",
"plt.show()\n",
"plt.hist(dest_A_rand_p, bins = 25)\n",
"plt.title('Distribution of p values from random vectors - Method A')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 248,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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kSZIkSZIkSZIkSZIkSZIkbbb/D5D84cSWEDc3AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1107ec450>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x10dab2bd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Method A constricted\n",
"plt.hist(dest_A_cons_I, bins=25)\n",
"plt.title('Distribution of VMD I values from constrained vectors - Method A')\n",
"plt.show()\n",
"plt.hist(dest_A_cons_p, bins=25)\n",
"plt.title('Distribution of p values from constrained vectors - Method A')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 249,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x1147fb650>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x1135d5e50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Method B random\n",
"plt.hist(dest_B_rand_I, bins=25)\n",
"plt.title('Distribution of VMD I values from random vectors - Method B')\n",
"plt.show()\n",
"plt.hist(dest_B_rand_p, bins=25)\n",
"plt.title('Distribution of p values from random vectors - Method B')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 250,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x10b837690>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x10d5c07d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Method B constricted\n",
"plt.hist(dest_B_cons_I, bins=25)\n",
"plt.title('Distribution of VMD I values from constrained vectors - Method B')\n",
"plt.show()\n",
"plt.hist(dest_B_cons_p, bins=25)\n",
"plt.title('Distribution of p values from constrained vectors - Method B')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 245,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a\n"
]
}
],
"source": [
"print 'a'"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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