{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab 4-2: Quantile Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Why quantile regression?\n", "What if we think that the rank order of values is basically the same in two datasets, but we don’t know if they’re linearly related. We can use a quantile regression to model a relationship between two variables without needing to assume anything about the function of that relationship (linear, or otherwise).\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example we're again considering [SWE](https://www.nrcs.usda.gov/wps/portal/nrcs/detail/null/?cid=nrcseprd1314833) measurements from two sites in California's Sierra Nevada, and want to evaluate the question:\n", "\n", "**Quantile regression**: Could we use SWE measurements at Slide Canyon to predict SWE at Blue Canyon?" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import scipy.stats as stats\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "# we will aslo need this 1d interpolation function\n", "from scipy.interpolate import interp1d" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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yearsBLC_maxSLI_max
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\n", "
" ], "text/plain": [ " years BLC_max SLI_max\n", "21 2006 761 1692\n", "22 2007 99 597\n", "23 2008 926 899\n", "24 2009 439 935\n", "25 2010 553 1023" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Read in a .csv file\n", "data = pd.read_csv('../data/pillows_example.csv')\n", "data.tail()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot SWE for both sites to take a look at the data" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "\n", "data.plot(x='years', y='SLI_max', c='r', ax=ax, label='Slide Canyon')\n", "data.plot(x='years', y='BLC_max', c='b', ax=ax, label='Blue Canyon')\n", "\n", "ax.set_title('Timeline of Peak Snow Water Equivalent (SWE)')\n", "ax.set_xlabel('Water Year')\n", "ax.set_ylabel('Peak SWE (mm)');\n", "plt.legend(loc=\"best\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Steps to create a quantile regression model:\n", "\n", "**1)** For each of your two datasets, create an empirical CDF\n", "\n", "We can do this with a custom function like the `cunnane_quantile_array()` function below, which gives us quantile values given an array of numbers.\n", "\n", "However, in this case, we want to be able to \"look up\" any quantile value (even those that lie between data points). For this, we can use `scipy.stats.mstats.mquantiles()` instead.\n", "\n", "Review the documentation for [scipy.stats.mstats.mquantiles](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mstats.mquantiles.html), recall that the default options give us the Cunnane plotting position. Note how the function handles quantiles as they approach 0 or 1 at the lowest and highest end of our values. How many (quantile) values should we use in the input to this function to create an empirical CDF?" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# This function should be able to accept any one-dimensional numpy array or list, of numbers\n", "# It returns two numpy arrays, one of the sorted numbers, the other of the plotting position\n", "def cunnane_quantile_array(numbers):\n", " '''This function also computes the Cunnane plotting position given an array or list of numbers (rather than a pandas dataframe).\n", " It has two outputs, first the sorted numbers, second the Cunnane plotting position for each of those numbers.\n", " [Steven Pestana, spestana@uw.edu, Oct. 2020]'''\n", " \n", " # 1) sort the data, using the numpy sort function (np.sort())\n", " sorted_numbers = np.sort(numbers)\n", " \n", " # length of the list of numbers\n", " n = len(sorted_numbers) \n", " \n", " # make an empty array, of the same length. below we will add the plotting position values to this array\n", " cunnane_plotting_position = np.empty(n)\n", " \n", " # 2) compute the Cunnane plotting position for each number, using a for loop and the enumerate function\n", " for rank, number in enumerate(sorted_numbers):\n", " cunnane_plotting_position[rank] = ( (rank+1) - (2/5) ) / ( n + (1/5) )\n", " \n", " return sorted_numbers, cunnane_plotting_position" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can create both types of quantile plots and look at them together. When building the quantile regression model, we'll use both." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "\n", "# Here we use the actual values from the dataset to create the plots\n", "BLC_ordered, BLC_quantile = cunnane_quantile_array(data['BLC_max'])\n", "SLI_ordered, SLI_quantile = cunnane_quantile_array(data['SLI_max'])\n", "plt.plot(BLC_ordered, BLC_quantile, 'o', markeredgecolor='b', markerfacecolor='None', markersize=7, label='Blue Canyon Quantile Plot from observed values')\n", "plt.plot(SLI_ordered, SLI_quantile, 'o', markeredgecolor='r', markerfacecolor='None', markersize=7, label='Slide Canyon Quantile Plot from observed values')\n", "\n", "\n", "# We can also create these by picking arbitrary quantile values, then using the scipy.stats.mstats.mquantiles function\n", "quantiles = np.linspace(0,1,100) # 100 quantile values linearly spaced between 0 and 1\n", "plt.plot(stats.mstats.mquantiles(data['BLC_max'], quantiles), quantiles, \n", " 'b.', label='Blue Canyon Quantile Plot from interpolated probabilities', alpha=0.7)\n", "plt.plot(stats.mstats.mquantiles(data['SLI_max'], quantiles), quantiles, \n", " 'r.', label='Slide Canyon Quantile Plot from interpolated probabilities', alpha=0.7)\n", "\n", "plt.ylabel('Quantile')\n", "plt.xlabel('Peak SWE (mm)')\n", "plt.xlim((0,2500))\n", "plt.ylim((0,1))\n", "plt.title('Quantiles of SWE data')\n", "plt.legend(loc=\"best\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**2)** Use the two empirical CDFs as a way of looking-up (or mapping) values from the predictor to the predictand, by matching which physical value corresponds to the same quantile.\n", "\n", "The example below does this with one data point, where we start with a value of SWE at Slide Canyon, look up its quantile, then find the corresponding SWE value at Blue Canyon." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "In the empirical Slide Canyon CDF, a value of 1058.0 mm SWE (the median) corresponds to a quantile of 0.5\n" ] } ], "source": [ "# This is our empirical cdf of the Slide Canyon data, which also includes values down to 0 and up to 1.\n", "SLI_quantile = np.linspace(0,1,100)\n", "SLI_ordered = stats.mstats.mquantiles(data['SLI_max'], SLI_quantile)\n", "\n", "# When Slide Canyon has SWE equal to it's median, how much snow can we expect at Blue Canyon?\n", "SLI_test = data['SLI_max'].median()\n", "\n", "# Create a linear interpolation object based on these values (this lets us look up any value, x, and get back the y value)\n", "f_SLI = interp1d(SLI_ordered, SLI_quantile)\n", "SLI_test_quantile = f_SLI(SLI_test)\n", "\n", "print('In the empirical Slide Canyon CDF, a value of {} mm SWE (the median) corresponds to a quantile of {}'.format(SLI_test, np.round(SLI_test_quantile,2)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualize this in a plot" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "\n", "# We can also create these by picking arbitrary quantile values, then using the scipy.stats.mstats.mquantiles function\n", "quantiles = np.linspace(0,1,100) # 100 quantile values linearly spaced between 0 and 1\n", "plt.plot(stats.mstats.mquantiles(data['BLC_max'], quantiles), quantiles, \n", " 'b.', label='Blue Canyon Quantile Plot from interpolated probabilities', alpha=0.7)\n", "plt.plot(stats.mstats.mquantiles(data['SLI_max'], quantiles), quantiles, \n", " 'r.', label='Slide Canyon Quantile Plot from interpolated probabilities', alpha=0.7)\n", "\n", "# Plot the test point value\n", "plt.plot(SLI_test,SLI_test_quantile,'D', markerfacecolor='m', markeredgecolor='k',markersize=10, label='SLI_test ({},{})'.format(SLI_test, np.round(SLI_test_quantile,2)))\n", "# Plot a line from the x-axis to the test point\n", "plt.plot([SLI_test, SLI_test], [0, SLI_test_quantile], c='m', linestyle='-')\n", "# Plot a line from the test point to the y-axis\n", "plt.plot([0, SLI_test], [SLI_test_quantile, SLI_test_quantile], c='k', linestyle='-')\n", "\n", "plt.ylabel('Quantile')\n", "plt.xlabel('Peak SWE (mm)')\n", "plt.xlim((0,2500))\n", "plt.ylim((0,1))\n", "plt.title('Quantiles of SWE data')\n", "plt.legend(loc=\"best\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that our test value corresponds to the median value at Slide Canyon, quantile value 0.5. \n", "\n", "(Yes, you would hope so, since I defined it as the median to begin with, but it's always best practice to start coding with a situation where you know the right answer.)\n", "\n", "Now, we need to take this Slide Canyon quantile value (0.5) and find the Blue Canyon SWE value that corresponds to its same quantile value (finding the Blue Canyon median in this case)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first need to create an interpolation object that lets us translate from Blue Canyon quantile values to Blue Canyon SWE values:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "In the empirical Blue Canyon CDF, a quantile of 0.5 corresponds to a SWE value of 289.5 mm SWE (the median)\n" ] } ], "source": [ "# This is our empirical cdf of the Blue Canyon data, which also includes values down to 0 and up to 1.\n", "BLC_quantile = np.linspace(0,1,100)\n", "BLC_ordered = stats.mstats.mquantiles(data['BLC_max'], BLC_quantile)\n", "\n", "# Create a linear interpolation object based on these values (this lets us look up any value, y, and get back the x value) \n", "# *note we've reversed the order of quantiles and SWE compared the the first interpolation object we created\n", "g_BLC = interp1d(BLC_quantile, BLC_ordered)\n", "\n", "# So if we look up a quantile value in our function g_BLC()\n", "BLC_test = g_BLC(SLI_test_quantile)\n", "\n", "print('In the empirical Blue Canyon CDF, a quantile of {} corresponds to a SWE value of {} mm SWE (the median)'.format(np.round(SLI_test_quantile,2), BLC_test))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualize the complete problem:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "\n", "# We can also create these by picking arbitrary quantile values, then using the scipy.stats.mstats.mquantiles function\n", "quantiles = np.linspace(0,1,100) # 100 quantile values linearly spaced between 0 and 1\n", "plt.plot(stats.mstats.mquantiles(data['BLC_max'], quantiles), quantiles, \n", " 'b.', label='Blue Canyon Quantile Plot from interpolated probabilities', alpha=0.7)\n", "plt.plot(stats.mstats.mquantiles(data['SLI_max'], quantiles), quantiles, \n", " 'r.', label='Slide Canyon Quantile Plot from interpolated probabilities', alpha=0.7)\n", "\n", "# Plot the Slide Canyon test point value\n", "plt.plot(SLI_test,SLI_test_quantile,'D', markerfacecolor='m', markeredgecolor='k',markersize=10, label='SLI_test ({},{})'.format(SLI_test, np.round(SLI_test_quantile,2)))\n", "# Plot a line from the x-axis to the test point\n", "plt.plot([SLI_test, SLI_test], [0, SLI_test_quantile], c='m', linestyle='-')\n", "# Plot a line from the test point to the y-axis\n", "plt.plot([0, SLI_test], [SLI_test_quantile, SLI_test_quantile], c='k', linestyle='-')\n", "\n", "# Plot the Blue Canyon test point value\n", "plt.plot(BLC_test,SLI_test_quantile,'D', markerfacecolor='c', markeredgecolor='k',markersize=10, label='BLC_test ({},{})'.format(BLC_test, np.round(SLI_test_quantile,2)))\n", "# Plot a line from the test point to the x-axis\n", "plt.plot([BLC_test, BLC_test], [0, SLI_test_quantile], c='c', linestyle='-')\n", "\n", "plt.ylabel('Quantile')\n", "plt.xlabel('Peak SWE (mm)')\n", "plt.xlim((0,2500))\n", "plt.ylim((0,1))\n", "plt.title('Quantiles of SWE data')\n", "plt.legend(loc=\"best\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "## Aplly to full dataset\n", "\n", "Now that we've walked through a single-point example, we can apply these steps efficiently to the whole dataset, starting from the beginning:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1) Create empirical CDFs for both data sets" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "quantiles = np.linspace(0,1,100)\n", "\n", "# This is our empirical cdf of the Slide Canyon data, which also includes values down to 0 and up to 1.\n", "SLI_ordered = stats.mstats.mquantiles(data['SLI_max'], quantiles)\n", "\n", "# This is our empirical cdf of the Blue Canyon data, which also includes values down to 0 and up to 1.\n", "BLC_ordered = stats.mstats.mquantiles(data['BLC_max'], quantiles)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2) Use the CDFs to \"look up\" SWE from Slide Canyon to predict SWE in Blue Canyon" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# Create our interpolation function for looking up a quantile given a value of SWE at Slide Canyon\n", "f_SLI = interp1d(SLI_ordered, quantiles)\n", "# Create our interpolation function for looking up SWE at Blue Canyon given a quantile\n", "g_BLC = interp1d(quantiles, BLC_ordered)\n", "\n", "# Now, we can create a prediction for every value in the Slide Canyon dataset to come up with a matching prediction for the Blue Canyon dataset\n", "BLC_predicted=g_BLC( f_SLI( data['SLI_max'] ) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the results:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# And we can see how well this did by making a time series plot of our actual and predicted values\n", "# Original data:\n", "plt.figure(figsize=(10,5))\n", "plt.plot(data['years'],data['SLI_max'],'b-', label='Slide Canyon Observed');\n", "plt.plot(data['years'],data['BLC_max'],'r-', label='Blue Canyon Observed');\n", "\n", "# Predicted with linear regression between Slide Canyon and Blue Canyon\n", "plt.plot(data['years'],BLC_predicted,'k--', label='Blue Canyon Predicted from Quantile Regression')\n", "plt.legend()\n", "plt.title('Timeline of Peak Snow Water Equivalent (SWE)')\n", "plt.xlabel('Water Year')\n", "plt.ylabel('Peak SWE (mm)');\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare the results of the quantile regression with the results of the linear regression in the previous lab.\n", "\n", "Which do you think is the best approach here and why?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Why you should not do statistics in the absense of physically-based science (from Professor Jessica Lundquist)\n", "What you see above is that the quantile mapping forces the rank order of the predicted timeseries to match the rank order of the prectictor time series. In this particular case, that isn't always the best idea. Blue Canyon is at a much lower elevation, and in warmer winters, Blue Canyon will get rain at times when Slide Canyon gets snow. In those years, any attempt at correlation falls apart. Thus, we would want to add a predictor variable that had something about temperature or rain vs snow (which hasn't yet been provided in these examples)." ] }, { "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }