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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Permutation Variances\n", | |
"\n", | |
"#### Good nulls, bad nulls, and ugly empirical approximations\n", | |
"\n", | |
"*Levi John Wolf*\n", | |
"\n", | |
"`levi.john.wolf[at]bristol.ac.uk`" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The forms of the estimators implemented here are due to interpretations from Bivand and Wong (2018) and Sokal et al. (1998)'s work on top of Anselin (1995)'s original paper defining the expectation and variance of the Local Moran's $I_i$ statistic. As Sokal et al. (1998) argues, there are actually *two* nulls that one might consider. \n", | |
"\n", | |
"This notebook looks at these, and explores their realizations for both the expectation, variance, and z-scored values of Moran's $I$. \n", | |
"\n", | |
"## Total Randomization Null\n", | |
"\n", | |
"The total randomization null is similar to the one used in the global $I$. In this case, all realizations of maps are equally likely, so the data does not directly enter into the expected value, and only higher moments enter into the variance. \n", | |
"\n", | |
"$$ E[I_i] = - \\frac{w_i}{n-1}$$\n", | |
"\n", | |
"where $w_i = \\sum_j^n w_{ij}$. In the row-standardized case, this collapses to the expectation for $I$ itself under the same null, and thus the expected value for $I_i$ at each site is also $E[I]$. The variance (in the Sokal (1998) form) requires some auxiliary definitions. First, let's define $m_k$ as the $k$th moment, $m_k = \\frac{1}{n} \\sum_i^n z_i^k$. And, let's define $b_2 = m_4/m_2^2$ and the sum of squared weights as $w_{i(2)} = \\sum_j^n w_{ij}^2$. Then, the variance of $I_i$ under the total randomization hypothesis is (from Bivand and Wong (2018), eq. 24):\n", | |
"\n", | |
"$$ Var[I_i] = \\frac{w_{i(2)}(n-b_2)}{n-1} + \\frac{(w_i^2 - w_{i(2)})(2b_2 - n)}{(n-1)(n-2)} - \\left(-\\frac{w_i}{n-1}\\right)^2 $$\n", | |
"\n", | |
"## Conditional Randomization Null (Empirical)\n", | |
"\n", | |
"But, we've adopted a \"better\" method that focuses on generating an empirical distribution of the sampled maps, and then gets the moments of the conditional distribution from there. That is, \n", | |
"1. we've implemented the actual conditional randomization procedure, \n", | |
"2. we get a reference distribution of $I_i$ values under that randomization\n", | |
"3. we compute the average and the variance of that distribution. \n", | |
"\n", | |
"These values, the empirical conditional randomization null, I'll denote $E_e$ and $Var_e$. They have no closed form solution, but tend to be different for each site. \n", | |
"\n", | |
"\n", | |
"## Conditional Randomization Null (Analytical)\n", | |
"\n", | |
"Ineed, since we simulate the *conditional randomization* null, we may pay attention to the analytical treatment given by Sokal et al. (1998). in equations (A7) and (A8). They find \n", | |
"\n", | |
"> The oucomes of these tests are not different enough in our study to make the correctness of the assumptions a major concern. \n", | |
"\n", | |
"But... \n", | |
"\n", | |
"> We find that both skewness and kurtosis are more pronounced in the total randomization replicates than in those randomized conditionally. Significance tests based on conditional randomization assumptions might thus be more reliable than those based on total randomization assumptions. \n", | |
"\n", | |
"So, let's at least understand what their theoretical values are, so that we can see how well the simulator recovers them. \n", | |
"\n", | |
"In this case, we fix the value of $z_i$, so the expectation and variance both include $z_i$ directly. We'll use the same notation, using $E_c$ and $Var_c$ to denote the moments under the *conditional* hypothesis. For this, we get an expectation that depends on $z_i$ and the second moment:\n", | |
"\n", | |
"$$ E_c[I_i] = -\\frac{z_i^2w_i}{m_2(n-1)}$$\n", | |
"\n", | |
"And a variance that depends on both as well:\n", | |
"\n", | |
"$$ Var_c[I_i] = \\left(\\frac{z_i}{m_2}\\right)^2 \n", | |
"\\left(\\frac{n}{n-2}\\right) \\left(w_{i(2)} - \\frac{w_i^2}{n-1}\\right) \\left(m_2 - \\frac{z_i^2}{n-1}\\right)$$\n", | |
"\n", | |
"These are slightly more complicated. In the least, we get expected values that are different for each site, since $z_i$ is involved in both expressions. \n", | |
"\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Two examples" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For a small dataset (`desmith`) we can see the following:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import libpysal, esda, pandas, seaborn\n", | |
"import matplotlib.pyplot as plt\n", | |
"\n", | |
"w = libpysal.io.open(libpysal.examples.get_path('desmith.gal')).read()\n", | |
"y = libpysal.io.open(libpysal.examples.get_path('desmith.txt')).by_col['z']" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"lmo = esda.Moran_Local(y, w=w, transformation='r', permutations=9999)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Expected value of local $I_i$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The total randomization version is all equal to the null for $I$:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([-0.11111111, -0.11111111, -0.11111111, -0.11111111, -0.11111111,\n", | |
" -0.11111111, -0.11111111, -0.11111111, -0.11111111, -0.11111111])" | |
] | |
}, | |
"execution_count": 3, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"lmo.EI" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"-0.1111111111111111" | |
] | |
}, | |
"execution_count": 4, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"-1/(w.n-1)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The *analytical conditional* randomization version varies by site, but is still negative:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([-0.00838113, -0.0243949 , -0.07031778, -0.21520869, -0.16547163,\n", | |
" -0.00178435, -0.11531888, -0.36138555, -0.05471258, -0.09413562])" | |
] | |
}, | |
"execution_count": 5, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"lmo.EIc" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The *empirical conditional* randomization version is close, but not identical, to the theoretical version:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([-0.00699568, -0.02124244, -0.06232136, -0.19373966, -0.14913933,\n", | |
" -0.00214232, -0.09606102, -0.32051384, -0.05039731, -0.09400307])" | |
] | |
}, | |
"execution_count": 6, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"lmo.EI_sim" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 1.0, 'Expectation under conditional permutation')" | |
] | |
}, | |
"execution_count": 7, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.plot((-.5, .1),(-.5, .1), color='grey', linestyle=':')\n", | |
"plt.scatter(lmo.EIc, lmo.EI_sim)\n", | |
"plt.xlabel('Analytical')\n", | |
"plt.ylabel('Empirical')\n", | |
"plt.title('Expectation under conditional permutation')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Variance of local $I_i$" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The total randomization variance will depend mainly on the row sum of squared weights for a row-standardized variable, since the square of the row-sums will always be 1. \n", | |
"\n", | |
"For a row-standardized estimator, this will generally be higher for observations with many neighbors and lower for observations with few neighbors:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([0.47374172, 0.47356458, 0.47209663, 0.15866023, 0.15972526,\n", | |
" 0.47376436, 0.46927721, 0.24584217, 0.26498308, 0.47077467])" | |
] | |
}, | |
"execution_count": 8, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"lmo.VI" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": [ | |
"<div>\n", | |
"<style scoped>\n", | |
" .dataframe tbody tr th:only-of-type {\n", | |
" vertical-align: middle;\n", | |
" }\n", | |
"\n", | |
" .dataframe tbody tr th {\n", | |
" vertical-align: top;\n", | |
" }\n", | |
"\n", | |
" .dataframe thead th {\n", | |
" text-align: right;\n", | |
" }\n", | |
"</style>\n", | |
"<table border=\"1\" class=\"dataframe\">\n", | |
" <thead>\n", | |
" <tr style=\"text-align: right;\">\n", | |
" <th></th>\n", | |
" <th>0</th>\n", | |
" <th>1</th>\n", | |
" <th>2</th>\n", | |
" <th>5</th>\n", | |
" <th>6</th>\n", | |
" <th>9</th>\n", | |
" <th>7</th>\n", | |
" <th>8</th>\n", | |
" <th>3</th>\n", | |
" <th>4</th>\n", | |
" </tr>\n", | |
" </thead>\n", | |
" <tbody>\n", | |
" <tr>\n", | |
" <th>cardinalities</th>\n", | |
" <td>2.000</td>\n", | |
" <td>2.000</td>\n", | |
" <td>2.000</td>\n", | |
" <td>2.000</td>\n", | |
" <td>2.000</td>\n", | |
" <td>2.000</td>\n", | |
" <td>3.000</td>\n", | |
" <td>3.000</td>\n", | |
" <td>4.000</td>\n", | |
" <td>4.00</td>\n", | |
" </tr>\n", | |
" <tr>\n", | |
" <th>variance</th>\n", | |
" <td>0.474</td>\n", | |
" <td>0.474</td>\n", | |
" <td>0.472</td>\n", | |
" <td>0.474</td>\n", | |
" <td>0.469</td>\n", | |
" <td>0.471</td>\n", | |
" <td>0.246</td>\n", | |
" <td>0.265</td>\n", | |
" <td>0.159</td>\n", | |
" <td>0.16</td>\n", | |
" </tr>\n", | |
" </tbody>\n", | |
"</table>\n", | |
"</div>" | |
], | |
"text/plain": [ | |
" 0 1 2 5 6 9 7 8 3 \\\n", | |
"cardinalities 2.000 2.000 2.000 2.000 2.000 2.000 3.000 3.000 4.000 \n", | |
"variance 0.474 0.474 0.472 0.474 0.469 0.471 0.246 0.265 0.159 \n", | |
"\n", | |
" 4 \n", | |
"cardinalities 4.00 \n", | |
"variance 0.16 " | |
] | |
}, | |
"execution_count": 9, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"pandas.DataFrame(dict(cardinalities=lmo.w.cardinalities.values(), \n", | |
" variance=lmo.VI)).sort_values('cardinalities').T.round(3)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In the analytical conditional randomization version, we get seriously different variances:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([0.03636013, 0.10412408, 0.28600769, 0.26389674, 0.21576683,\n", | |
" 0.00779261, 0.44633942, 0.57696508, 0.12929777, 0.3730742 ])" | |
] | |
}, | |
"execution_count": 10, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"lmo.VIc" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 1.0, 'Analytical Variance under randomization')" | |
] | |
}, | |
"execution_count": 11, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.plot((0,.5), (0,.5), color='grey', linestyle=':')\n", | |
"plt.scatter(lmo.VIc, lmo.VI)\n", | |
"plt.xlabel('Conditional')\n", | |
"plt.ylabel('Total')\n", | |
"plt.title('Analytical Variance under randomization')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In the empirical conditional version, we get values closer to the analytical version, but the empirical variance is strictly smaller than the analytical one! " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([0.0293014 , 0.08396485, 0.23039025, 0.21297018, 0.17399721,\n", | |
" 0.00627484, 0.35908056, 0.46446072, 0.10479239, 0.2992273 ])" | |
] | |
}, | |
"execution_count": 12, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"lmo.VI_sim" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 1.0, 'Variance under conditional randomization')" | |
] | |
}, | |
"execution_count": 13, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.plot((0,.5), (0,.5), color='grey', linestyle=':')\n", | |
"plt.scatter(lmo.VIc, lmo.VI_sim)\n", | |
"plt.xlabel('Analytical')\n", | |
"plt.ylabel('Empirical')\n", | |
"plt.title('Variance under conditional randomization')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Z(I_i) scores" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"This makes the z scores very similar, although large $Z(I_i)$ get understated:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 14, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 1.0, 'Z(I_i) under Conditional Permutation')" | |
] | |
}, | |
"execution_count": 14, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"z_cond = (lmo.Is - lmo.EIc)/lmo.VIc**.5\n", | |
"plt.scatter(lmo.z_sim, z_cond)\n", | |
"plt.plot((-.5, 2), (-.5, 2), color='k', linestyle=':')\n", | |
"plt.xlabel('Empirical')\n", | |
"plt.ylabel('Analytical')\n", | |
"plt.title('Z(I_i) under Conditional Permutation')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 15, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 1.0, 'Analytical Z(I_i) under randomization ')" | |
] | |
}, | |
"execution_count": 15, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"z_tr = (lmo.Is - lmo.EI)/lmo.VI**.5\n", | |
"plt.scatter(z_cond, z_tr)\n", | |
"plt.plot((-.5, 2), (-.5, 2), color='k', linestyle=':')\n", | |
"plt.xlabel('Conditional')\n", | |
"plt.ylabel('Total')\n", | |
"plt.title('Analytical Z(I_i) under randomization ')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# In a bigger example, things get weird, but still are fine" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We'll use the 1989 Gini score from our `NAT.shp` examples:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 16, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import geopandas, numpy\n", | |
"\n", | |
"df = geopandas.read_file(libpysal.examples.get_path('NAT.shp'))\n", | |
"w = libpysal.weights.Queen.from_dataframe(df)\n", | |
"big_lmo = esda.Moran_Local(df.GI89, w=w, transformation='r', \n", | |
" permutations=9999)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Expected Value" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For the analytical expectation, there's one expectation (within floating point error):" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 17, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([-0.00032425, -0.00032425])" | |
] | |
}, | |
"execution_count": 17, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"numpy.unique(big_lmo.EI)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 18, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"-0.00032425421530479895" | |
] | |
}, | |
"execution_count": 18, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"-1/(w.n - 1)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For the analytical conditional expectation, we get a variety of values, all negative:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 19, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(big_lmo.EIc, bins=100, label='Conditional')\n", | |
"plt.axvline(-1/(w.n-1), color='red', label='Total')\n", | |
"plt.title(\"Analytical Expected value of local I\")\n", | |
"plt.legend()\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"This arises because of the $-z_i^2$ term. " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"And, for the empirical versions, well...we get something normal:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 20, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(big_lmo.EI_sim, bins=100, label='Conditional')\n", | |
"plt.axvline(-1/(w.n-1), color='red', label='Total')\n", | |
"plt.title(\"Analytical Expected value of local I\")\n", | |
"plt.legend()\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Predictably, the two are very different:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 21, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x7f49cfac26a0>]" | |
] | |
}, | |
"execution_count": 21, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x432 with 3 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"parab = numpy.polyfit(y=big_lmo.EIc, x=big_lmo.EI_sim, deg=2)\n", | |
"predict = numpy.poly1d(parab)\n", | |
"\n", | |
"jp = seaborn.jointplot(y=big_lmo.EIc, x=big_lmo.EI_sim, color='k')\n", | |
"\n", | |
"fit_x = numpy.linspace(-.02, .02)\n", | |
"fit_y = predict(fit_x)\n", | |
"\n", | |
"jp.ax_joint.plot(fit_x, fit_y, color='orangered', \n", | |
" linestyle=':', linewidth=4)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"From the broad shape, though, it seems large expected values under the analytic expression generally result in large empirical expectations, but they may be either negative or positive. " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Variance" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For the variance, things are also complicated, but generally reflect the same pattern we saw before: large cardinalities mean lower variance:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 22, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0, 0.5, 'Analytical Variance of Local I')" | |
] | |
}, | |
"execution_count": 22, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"card = numpy.asarray(list(big_lmo.w.cardinalities.values()))\n", | |
"plt.scatter(card, big_lmo.VI) \n", | |
"plt.xlabel('Cardinality')\n", | |
"plt.ylabel('Analytical Variance of Local I')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"But, for the analytical variance assuming conditional permutation, we get a wide range of variances for each analytical value. While the largest analytical variance is 1, the largest conditional variance gets out to 5:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 23, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"Text(0.5, 1.0, 'Analytical Variance under randomization')" | |
] | |
}, | |
"execution_count": 23, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.plot((0,1), (0,1), color='grey', linestyle=':')\n", | |
"plt.scatter(big_lmo.VIc, big_lmo.VI)\n", | |
"plt.xlabel('Conditional')\n", | |
"plt.ylabel('Total')\n", | |
"plt.title('Analytical Variance under randomization')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Interestingly, though, the variances are very similar, and there does not appear to be a bias in terms of the direction of difference:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 24, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"[<matplotlib.lines.Line2D at 0x7f49b1cf8790>]" | |
] | |
}, | |
"execution_count": 24, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x432 with 3 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"jp = seaborn.jointplot(y=big_lmo.VIc, x=big_lmo.VI_sim, color='k')\n", | |
"\n", | |
"jp.ax_joint.plot((0,5),(0,5), color='orangered', \n", | |
" linestyle=':', linewidth=3)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 25, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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hL0kd+X90TQaKmTjd8wAAAABJRU5ErkJggg==\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(big_lmo.VIc - big_lmo.VI_sim, bins=100)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Z-scores" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"But, this puts is in pretty good shape for the $Z(I_i)$:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 26, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x432 with 3 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"big_z_cond = (big_lmo.Is - big_lmo.EIc)/big_lmo.VIc**.5\n", | |
"jg = seaborn.jointplot(x=big_lmo.z_sim, y=big_z_cond)\n", | |
"jg.ax_joint.set_xlabel('Empirical')\n", | |
"jg.ax_joint.set_ylabel('Analytical')\n", | |
"jg.fig.suptitle('Z(I_i) under Conditional Permutation', \n", | |
" y=1.1)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"What about the ones that use total randomization nulls:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 27, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x432 with 3 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"big_z_tr= (big_lmo.Is - big_lmo.EI)/big_lmo.VI**.5\n", | |
"jg = seaborn.jointplot(x=big_z_cond, y=big_z_tr)\n", | |
"jg.ax_joint.set_xlabel('Conditional')\n", | |
"jg.ax_joint.set_ylabel('Total')\n", | |
"jg.fig.suptitle('Z(I_i) under Permutation', \n", | |
" y=1.1)\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Ouch! " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 28, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(-5.0, 10.0)" | |
] | |
}, | |
"execution_count": 28, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 576x144 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.subplots(1,1,figsize=(8,2))\n", | |
"seaborn.kdeplot(big_z_cond)\n", | |
"seaborn.kdeplot(big_z_tr)\n", | |
"plt.xlim(-5, 10)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Could something like this give rise to Bivand & Wong's result? We still need to find out exactly how their analytical $Z(I_i)$ values are constructed. " | |
] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python [conda env:analysis]", | |
"language": "python", | |
"name": "conda-env-analysis-py" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.8.6" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 4 | |
} |
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