{ "cells": [ { "cell_type": "markdown", "id": "559b7845", "metadata": {}, "source": [ "# Logistic Regression, LDA, QDA, and KNN\n", "\n", "\n", "\"Open\n", "\n", "\n", "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/intro-stat-learning/ISLP_labs/v2.2?labpath=Ch04-classification-lab.ipynb)" ] }, { "cell_type": "markdown", "id": "73b275ae", "metadata": {}, "source": [ "## The Stock Market Data\n", "\n", "In this lab we will examine the `Smarket` \n", "data, which is part of the `ISLP`\n", "library. This data set consists of percentage returns for the S&P 500\n", "stock index over 1,250 days, from the beginning of 2001 until the end\n", "of 2005. For each date, we have recorded the percentage returns for\n", "each of the five previous trading days, `Lag1` through\n", " `Lag5`. We have also recorded `Volume` (the number of\n", "shares traded on the previous day, in billions), `Today` (the\n", "percentage return on the date in question) and `Direction`\n", "(whether the market was `Up` or `Down` on this date).\n", "\n", "We start by importing our libraries at this top level; these are all imports we have seen in previous labs." ] }, { "cell_type": "code", "execution_count": 1, "id": "28bd64cb", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:09.508409Z", "iopub.status.busy": "2024-06-04T23:19:09.508152Z", "iopub.status.idle": "2024-06-04T23:19:10.300967Z", "shell.execute_reply": "2024-06-04T23:19:10.300663Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from matplotlib.pyplot import subplots\n", "import statsmodels.api as sm\n", "from ISLP import load_data\n", "from ISLP.models import (ModelSpec as MS,\n", " summarize)" ] }, { "cell_type": "markdown", "id": "63093cb3", "metadata": {}, "source": [ "We also collect together the new imports needed for this lab." ] }, { "cell_type": "code", "execution_count": 2, "id": "f0a0173d", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.302676Z", "iopub.status.busy": "2024-06-04T23:19:10.302557Z", "iopub.status.idle": "2024-06-04T23:19:10.318173Z", "shell.execute_reply": "2024-06-04T23:19:10.317991Z" } }, "outputs": [], "source": [ "from ISLP import confusion_table\n", "from ISLP.models import contrast\n", "from sklearn.discriminant_analysis import \\\n", " (LinearDiscriminantAnalysis as LDA,\n", " QuadraticDiscriminantAnalysis as QDA)\n", "from sklearn.naive_bayes import GaussianNB\n", "from sklearn.neighbors import KNeighborsClassifier\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.linear_model import LogisticRegression" ] }, { "cell_type": "markdown", "id": "1398b276", "metadata": {}, "source": [ "Now we are ready to load the `Smarket` data." ] }, { "cell_type": "code", "execution_count": 3, "id": "3640fda5", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.319434Z", "iopub.status.busy": "2024-06-04T23:19:10.319329Z", "iopub.status.idle": "2024-06-04T23:19:10.328090Z", "shell.execute_reply": "2024-06-04T23:19:10.327895Z" } }, "outputs": [ { "data": { "text/html": [ "
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YearLag1Lag2Lag3Lag4Lag5VolumeTodayDirection
020010.381-0.192-2.624-1.0555.0101.191300.959Up
120010.9590.381-0.192-2.624-1.0551.296501.032Up
220011.0320.9590.381-0.192-2.6241.41120-0.623Down
32001-0.6231.0320.9590.381-0.1921.276000.614Up
420010.614-0.6231.0320.9590.3811.205700.213Up
..............................
124520050.4220.252-0.024-0.584-0.2851.888500.043Up
124620050.0430.4220.252-0.024-0.5841.28581-0.955Down
12472005-0.9550.0430.4220.252-0.0241.540470.130Up
124820050.130-0.9550.0430.4220.2521.42236-0.298Down
12492005-0.2980.130-0.9550.0430.4221.38254-0.489Down
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1250 rows × 9 columns

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" ], "text/plain": [ " Year Lag1 Lag2 Lag3 Lag4 Lag5 Volume Today Direction\n", "0 2001 0.381 -0.192 -2.624 -1.055 5.010 1.19130 0.959 Up\n", "1 2001 0.959 0.381 -0.192 -2.624 -1.055 1.29650 1.032 Up\n", "2 2001 1.032 0.959 0.381 -0.192 -2.624 1.41120 -0.623 Down\n", "3 2001 -0.623 1.032 0.959 0.381 -0.192 1.27600 0.614 Up\n", "4 2001 0.614 -0.623 1.032 0.959 0.381 1.20570 0.213 Up\n", "... ... ... ... ... ... ... ... ... ...\n", "1245 2005 0.422 0.252 -0.024 -0.584 -0.285 1.88850 0.043 Up\n", "1246 2005 0.043 0.422 0.252 -0.024 -0.584 1.28581 -0.955 Down\n", "1247 2005 -0.955 0.043 0.422 0.252 -0.024 1.54047 0.130 Up\n", "1248 2005 0.130 -0.955 0.043 0.422 0.252 1.42236 -0.298 Down\n", "1249 2005 -0.298 0.130 -0.955 0.043 0.422 1.38254 -0.489 Down\n", "\n", "[1250 rows x 9 columns]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Smarket = load_data('Smarket')\n", "Smarket" ] }, { "cell_type": "markdown", "id": "f40d5bbb", "metadata": {}, "source": [ "This gives a truncated listing of the data.\n", "We can see what the variable names are." ] }, { "cell_type": "code", "execution_count": 4, "id": "ff825fa5", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.329300Z", "iopub.status.busy": "2024-06-04T23:19:10.329214Z", "iopub.status.idle": "2024-06-04T23:19:10.331118Z", "shell.execute_reply": "2024-06-04T23:19:10.330931Z" } }, "outputs": [ { "data": { "text/plain": [ "Index(['Year', 'Lag1', 'Lag2', 'Lag3', 'Lag4', 'Lag5', 'Volume', 'Today',\n", " 'Direction'],\n", " dtype='object')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Smarket.columns" ] }, { "cell_type": "markdown", "id": "1c87b92f", "metadata": {}, "source": [ "We compute the correlation matrix using the `corr()` method\n", "for data frames, which produces a matrix that contains all of\n", "the pairwise correlations among the variables.\n", " \n", "By instructing `pandas` to use only numeric variables, the `corr()` method does not report a correlation for the `Direction` variable because it is\n", " qualitative." ] }, { "cell_type": "code", "execution_count": 5, "id": "6e10c8fa", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.332318Z", "iopub.status.busy": "2024-06-04T23:19:10.332231Z", "iopub.status.idle": "2024-06-04T23:19:10.336148Z", "shell.execute_reply": "2024-06-04T23:19:10.335919Z" } }, "outputs": [ { "data": { "text/html": [ "
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YearLag1Lag2Lag3Lag4Lag5VolumeToday
Year1.0000000.0297000.0305960.0331950.0356890.0297880.5390060.030095
Lag10.0297001.000000-0.026294-0.010803-0.002986-0.0056750.040910-0.026155
Lag20.030596-0.0262941.000000-0.025897-0.010854-0.003558-0.043383-0.010250
Lag30.033195-0.010803-0.0258971.000000-0.024051-0.018808-0.041824-0.002448
Lag40.035689-0.002986-0.010854-0.0240511.000000-0.027084-0.048414-0.006900
Lag50.029788-0.005675-0.003558-0.018808-0.0270841.000000-0.022002-0.034860
Volume0.5390060.040910-0.043383-0.041824-0.048414-0.0220021.0000000.014592
Today0.030095-0.026155-0.010250-0.002448-0.006900-0.0348600.0145921.000000
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" ], "text/plain": [ " Year Lag1 Lag2 Lag3 Lag4 Lag5 Volume \\\n", "Year 1.000000 0.029700 0.030596 0.033195 0.035689 0.029788 0.539006 \n", "Lag1 0.029700 1.000000 -0.026294 -0.010803 -0.002986 -0.005675 0.040910 \n", "Lag2 0.030596 -0.026294 1.000000 -0.025897 -0.010854 -0.003558 -0.043383 \n", "Lag3 0.033195 -0.010803 -0.025897 1.000000 -0.024051 -0.018808 -0.041824 \n", "Lag4 0.035689 -0.002986 -0.010854 -0.024051 1.000000 -0.027084 -0.048414 \n", "Lag5 0.029788 -0.005675 -0.003558 -0.018808 -0.027084 1.000000 -0.022002 \n", "Volume 0.539006 0.040910 -0.043383 -0.041824 -0.048414 -0.022002 1.000000 \n", "Today 0.030095 -0.026155 -0.010250 -0.002448 -0.006900 -0.034860 0.014592 \n", "\n", " Today \n", "Year 0.030095 \n", "Lag1 -0.026155 \n", "Lag2 -0.010250 \n", "Lag3 -0.002448 \n", "Lag4 -0.006900 \n", "Lag5 -0.034860 \n", "Volume 0.014592 \n", "Today 1.000000 " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Smarket.corr(numeric_only=True)" ] }, { "cell_type": "markdown", "id": "b6659038", "metadata": {}, "source": [ "As one would expect, the correlations between the lagged return variables and\n", "today’s return are close to zero. The only substantial correlation is between `Year` and\n", " `Volume`. By plotting the data we see that `Volume`\n", "is increasing over time. In other words, the average number of shares traded\n", "daily increased from 2001 to 2005." ] }, { "cell_type": "code", "execution_count": 6, "id": "c30034ac", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.337474Z", "iopub.status.busy": "2024-06-04T23:19:10.337394Z", "iopub.status.idle": "2024-06-04T23:19:10.430280Z", "shell.execute_reply": "2024-06-04T23:19:10.429786Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Smarket.plot(y='Volume');" ] }, { "cell_type": "markdown", "id": "79919219", "metadata": {}, "source": [ "## Logistic Regression\n", "Next, we will fit a logistic regression model in order to predict\n", " `Direction` using `Lag1` through `Lag5` and\n", " `Volume`. The `sm.GLM()` function fits *generalized linear models*, a class of\n", "models that includes logistic regression. Alternatively,\n", "the function `sm.Logit()` fits a logistic regression\n", "model directly. The syntax of\n", "`sm.GLM()` is similar to that of `sm.OLS()`, except\n", "that we must pass in the argument `family=sm.families.Binomial()`\n", "in order to tell `statsmodels` to run a logistic regression rather than some other\n", "type of generalized linear model." ] }, { "cell_type": "code", "execution_count": 7, "id": "61a82664", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.434291Z", "iopub.status.busy": "2024-06-04T23:19:10.433853Z", "iopub.status.idle": "2024-06-04T23:19:10.501135Z", "shell.execute_reply": "2024-06-04T23:19:10.483890Z" } }, "outputs": [ { "data": { "text/html": [ "
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coefstd errzP>|z|
intercept-0.12600.241-0.5230.601
Lag1-0.07310.050-1.4570.145
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Lag40.00940.0500.1870.851
Lag50.01030.0500.2080.835
Volume0.13540.1580.8550.392
\n", "
" ], "text/plain": [ " coef std err z P>|z|\n", "intercept -0.1260 0.241 -0.523 0.601\n", "Lag1 -0.0731 0.050 -1.457 0.145\n", "Lag2 -0.0423 0.050 -0.845 0.398\n", "Lag3 0.0111 0.050 0.222 0.824\n", "Lag4 0.0094 0.050 0.187 0.851\n", "Lag5 0.0103 0.050 0.208 0.835\n", "Volume 0.1354 0.158 0.855 0.392" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "allvars = Smarket.columns.drop(['Today', 'Direction', 'Year'])\n", "design = MS(allvars)\n", "X = design.fit_transform(Smarket)\n", "y = Smarket.Direction == 'Up'\n", "glm = sm.GLM(y,\n", " X,\n", " family=sm.families.Binomial())\n", "results = glm.fit()\n", "summarize(results)" ] }, { "cell_type": "markdown", "id": "ee972938", "metadata": {}, "source": [ "The smallest *p*-value here is associated with `Lag1`. The\n", "negative coefficient for this predictor suggests that if the market\n", "had a positive return yesterday, then it is less likely to go up\n", "today. However, at a value of 0.15, the *p*-value is still\n", "relatively large, and so there is no clear evidence of a real\n", "association between `Lag1` and `Direction`.\n", "\n", "We use the `params` attribute of `results`\n", "in order to access just the\n", "coefficients for this fitted model." ] }, { "cell_type": "code", "execution_count": 8, "id": "d09a55d9", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.504964Z", "iopub.status.busy": "2024-06-04T23:19:10.504628Z", "iopub.status.idle": "2024-06-04T23:19:10.523026Z", "shell.execute_reply": "2024-06-04T23:19:10.521952Z" } }, "outputs": [ { "data": { "text/plain": [ "intercept -0.126000\n", "Lag1 -0.073074\n", "Lag2 -0.042301\n", "Lag3 0.011085\n", "Lag4 0.009359\n", "Lag5 0.010313\n", "Volume 0.135441\n", "dtype: float64" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.params" ] }, { "cell_type": "markdown", "id": "4c886505", "metadata": {}, "source": [ "Likewise we can use the\n", "`pvalues` attribute to access the *p*-values for the coefficients." ] }, { "cell_type": "code", "execution_count": 9, "id": "a14e688f", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.532342Z", "iopub.status.busy": "2024-06-04T23:19:10.530799Z", "iopub.status.idle": "2024-06-04T23:19:10.538953Z", "shell.execute_reply": "2024-06-04T23:19:10.538379Z" } }, "outputs": [ { "data": { "text/plain": [ "intercept 0.600700\n", "Lag1 0.145232\n", "Lag2 0.398352\n", "Lag3 0.824334\n", "Lag4 0.851445\n", "Lag5 0.834998\n", "Volume 0.392404\n", "dtype: float64" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.pvalues" ] }, { "cell_type": "markdown", "id": "cd01f173", "metadata": {}, "source": [ "The `predict()` method of `results` can be used to predict the\n", "probability that the market will go up, given values of the\n", "predictors. This method returns predictions\n", "on the probability scale. If no data set is supplied to the `predict()`\n", "function, then the probabilities are computed for the training data\n", "that was used to fit the logistic regression model.\n", "As with linear regression, one can pass an optional `exog` argument consistent\n", "with a design matrix if desired. Here we have\n", "printed only the first ten probabilities." ] }, { "cell_type": "code", "execution_count": 10, "id": "2d1d337a", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.545854Z", "iopub.status.busy": "2024-06-04T23:19:10.545607Z", "iopub.status.idle": "2024-06-04T23:19:10.550331Z", "shell.execute_reply": "2024-06-04T23:19:10.549806Z" } }, "outputs": [ { "data": { "text/plain": [ "array([0.50708413, 0.48146788, 0.48113883, 0.51522236, 0.51078116,\n", " 0.50695646, 0.49265087, 0.50922916, 0.51761353, 0.48883778])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs = results.predict()\n", "probs[:10]" ] }, { "cell_type": "markdown", "id": "c464dc7d", "metadata": {}, "source": [ "In order to make a prediction as to whether the market will go up or\n", "down on a particular day, we must convert these predicted\n", "probabilities into class labels, `Up` or `Down`. The\n", "following two commands create a vector of class predictions based on\n", "whether the predicted probability of a market increase is greater than\n", "or less than 0.5." ] }, { "cell_type": "code", "execution_count": 11, "id": "db97e20c", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.553209Z", "iopub.status.busy": "2024-06-04T23:19:10.553027Z", "iopub.status.idle": "2024-06-04T23:19:10.555510Z", "shell.execute_reply": "2024-06-04T23:19:10.555019Z" } }, "outputs": [], "source": [ "labels = np.array(['Down']*1250)\n", "labels[probs>0.5] = \"Up\"" ] }, { "cell_type": "markdown", "id": "2079aa26", "metadata": {}, "source": [ "The `confusion_table()`\n", "function from the `ISLP` package summarizes these predictions, showing how\n", "many observations were correctly or incorrectly classified. Our function, which is adapted from a similar function\n", "in the module `sklearn.metrics`, transposes the resulting\n", "matrix and includes row and column labels.\n", "The `confusion_table()` function takes as first argument the\n", "predicted labels, and second argument the true labels." ] }, { "cell_type": "code", "execution_count": 12, "id": "5173815c", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.558137Z", "iopub.status.busy": "2024-06-04T23:19:10.557755Z", "iopub.status.idle": "2024-06-04T23:19:10.568812Z", "shell.execute_reply": "2024-06-04T23:19:10.568379Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "Truth Down Up\n", "Predicted \n", "Down 145 141\n", "Up 457 507" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "confusion_table(labels, Smarket.Direction)" ] }, { "cell_type": "markdown", "id": "e02ffcf4", "metadata": {}, "source": [ "The diagonal elements of the confusion matrix indicate correct\n", "predictions, while the off-diagonals represent incorrect\n", "predictions. Hence our model correctly predicted that the market would\n", "go up on 507 days and that it would go down on 145 days, for a\n", "total of 507 + 145 = 652 correct predictions. The `np.mean()`\n", "function can be used to compute the fraction of days for which the\n", "prediction was correct. In this case, logistic regression correctly\n", "predicted the movement of the market 52.2% of the time." ] }, { "cell_type": "code", "execution_count": 13, "id": "b49ce3a2", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.571227Z", "iopub.status.busy": "2024-06-04T23:19:10.571020Z", "iopub.status.idle": "2024-06-04T23:19:10.575331Z", "shell.execute_reply": "2024-06-04T23:19:10.574762Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.5216, 0.5216)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(507+145)/1250, np.mean(labels == Smarket.Direction)" ] }, { "cell_type": "markdown", "id": "ad43edf5", "metadata": {}, "source": [ "At first glance, it appears that the logistic regression model is\n", "working a little better than random guessing. However, this result is\n", "misleading because we trained and tested the model on the same set of\n", "1,250 observations. In other words, $100-52.2=47.8%$ is the\n", "*training* error rate. As we have seen\n", "previously, the training error rate is often overly optimistic --- it\n", "tends to underestimate the test error rate. In\n", "order to better assess the accuracy of the logistic regression model\n", "in this setting, we can fit the model using part of the data, and\n", "then examine how well it predicts the *held out* data. This\n", "will yield a more realistic error rate, in the sense that in practice\n", "we will be interested in our model’s performance not on the data that\n", "we used to fit the model, but rather on days in the future for which\n", "the market’s movements are unknown.\n", "\n", "To implement this strategy, we first create a Boolean vector\n", "corresponding to the observations from 2001 through 2004. We then\n", "use this vector to create a held out data set of observations from\n", "2005." ] }, { "cell_type": "code", "execution_count": 14, "id": "773ab528", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.578285Z", "iopub.status.busy": "2024-06-04T23:19:10.578069Z", "iopub.status.idle": "2024-06-04T23:19:10.582814Z", "shell.execute_reply": "2024-06-04T23:19:10.582379Z" } }, "outputs": [ { "data": { "text/plain": [ "(252, 9)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "train = (Smarket.Year < 2005)\n", "Smarket_train = Smarket.loc[train]\n", "Smarket_test = Smarket.loc[~train]\n", "Smarket_test.shape" ] }, { "cell_type": "markdown", "id": "8a416bea", "metadata": {}, "source": [ "The object `train` is a vector of 1,250 elements, corresponding\n", "to the observations in our data set. The elements of the vector that\n", "correspond to observations that occurred before 2005 are set to\n", "`True`, whereas those that correspond to observations in 2005 are\n", "set to `False`. Hence `train` is a\n", "*boolean* array, since its\n", "elements are `True` and `False`. Boolean arrays can be used\n", "to obtain a subset of the rows or columns of a data frame\n", "using the `loc` method. For instance,\n", "the command `Smarket.loc[train]` would pick out a submatrix of the\n", "stock market data set, corresponding only to the dates before 2005,\n", "since those are the ones for which the elements of `train` are\n", "`True`. The `~` symbol can be used to negate all of the\n", "elements of a Boolean vector. That is, `~train` is a vector\n", "similar to `train`, except that the elements that are `True`\n", "in `train` get swapped to `False` in `~train`, and vice versa.\n", "Therefore, `Smarket.loc[~train]` yields a\n", "subset of the rows of the data frame\n", "of the stock market data containing only the observations for which\n", "`train` is `False`.\n", "The output above indicates that there are 252 such\n", "observations.\n", "\n", "We now fit a logistic regression model using only the subset of the\n", "observations that correspond to dates before 2005. We then obtain predicted probabilities of the\n", "stock market going up for each of the days in our test set --- that is,\n", "for the days in 2005." ] }, { "cell_type": "code", "execution_count": 15, "id": "e8b1b1e8", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.585518Z", "iopub.status.busy": "2024-06-04T23:19:10.585316Z", "iopub.status.idle": "2024-06-04T23:19:10.592938Z", "shell.execute_reply": "2024-06-04T23:19:10.592438Z" } }, "outputs": [], "source": [ "X_train, X_test = X.loc[train], X.loc[~train]\n", "y_train, y_test = y.loc[train], y.loc[~train]\n", "glm_train = sm.GLM(y_train,\n", " X_train,\n", " family=sm.families.Binomial())\n", "results = glm_train.fit()\n", "probs = results.predict(exog=X_test)" ] }, { "cell_type": "markdown", "id": "230e2b8e", "metadata": {}, "source": [ "Notice that we have trained and tested our model on two completely\n", "separate data sets: training was performed using only the dates before\n", "2005, and testing was performed using only the dates in 2005.\n", "\n", "Finally, we compare the predictions for 2005 to the\n", "actual movements of the market over that time period.\n", "We will first store the test and training labels (recall `y_test` is binary)." ] }, { "cell_type": "code", "execution_count": 16, "id": "c1993ea5", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.595809Z", "iopub.status.busy": "2024-06-04T23:19:10.595620Z", "iopub.status.idle": "2024-06-04T23:19:10.599118Z", "shell.execute_reply": "2024-06-04T23:19:10.598574Z" } }, "outputs": [], "source": [ "D = Smarket.Direction\n", "L_train, L_test = D.loc[train], D.loc[~train]" ] }, { "cell_type": "markdown", "id": "dbc2679d", "metadata": {}, "source": [ "Now we threshold the\n", "fitted probability at 50% to form\n", "our predicted labels." ] }, { "cell_type": "code", "execution_count": 17, "id": "8f909de4", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.601671Z", "iopub.status.busy": "2024-06-04T23:19:10.601471Z", "iopub.status.idle": "2024-06-04T23:19:10.609107Z", "shell.execute_reply": "2024-06-04T23:19:10.608569Z" } }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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" ], "text/plain": [ "Truth Down Up\n", "Predicted \n", "Down 77 97\n", "Up 34 44" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "labels = np.array(['Down']*252)\n", "labels[probs>0.5] = 'Up'\n", "confusion_table(labels, L_test)" ] }, { "cell_type": "markdown", "id": "8145ecec", "metadata": {}, "source": [ "The test accuracy is about 48% while the error rate is about 52%" ] }, { "cell_type": "code", "execution_count": 18, "id": "3c479105", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.611827Z", "iopub.status.busy": "2024-06-04T23:19:10.611594Z", "iopub.status.idle": "2024-06-04T23:19:10.615795Z", "shell.execute_reply": "2024-06-04T23:19:10.615260Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.4801587301587302, 0.5198412698412699)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(labels == L_test), np.mean(labels != L_test)" ] }, { "cell_type": "markdown", "id": "4b1609dd", "metadata": {}, "source": [ "The `!=` notation means *not equal to*, and so the last command\n", "computes the test set error rate. The results are rather\n", "disappointing: the test error rate is 52%, which is worse than\n", "random guessing! Of course this result is not all that surprising,\n", "given that one would not generally expect to be able to use previous\n", "days’ returns to predict future market performance. (After all, if it\n", "were possible to do so, then the authors of this book would be out\n", "striking it rich rather than writing a statistics textbook.)\n", "\n", "We recall that the logistic regression model had very underwhelming\n", "*p*-values associated with all of the predictors, and that the\n", "smallest *p*-value, though not very small, corresponded to\n", " `Lag1`. Perhaps by removing the variables that appear not to be\n", "helpful in predicting `Direction`, we can obtain a more\n", "effective model. After all, using predictors that have no relationship\n", "with the response tends to cause a deterioration in the test error\n", "rate (since such predictors cause an increase in variance without a\n", "corresponding decrease in bias), and so removing such predictors may\n", "in turn yield an improvement. Below we refit the logistic\n", "regression using just `Lag1` and `Lag2`, which seemed to\n", "have the highest predictive power in the original logistic regression\n", "model." ] }, { "cell_type": "code", "execution_count": 19, "id": "3f473ec0", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.618328Z", "iopub.status.busy": "2024-06-04T23:19:10.618134Z", "iopub.status.idle": "2024-06-04T23:19:10.657121Z", "shell.execute_reply": "2024-06-04T23:19:10.656851Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "Truth Down Up\n", "Predicted \n", "Down 35 35\n", "Up 76 106" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = MS(['Lag1', 'Lag2']).fit(Smarket)\n", "X = model.transform(Smarket)\n", "X_train, X_test = X.loc[train], X.loc[~train]\n", "glm_train = sm.GLM(y_train,\n", " X_train,\n", " family=sm.families.Binomial())\n", "results = glm_train.fit()\n", "probs = results.predict(exog=X_test)\n", "labels = np.array(['Down']*252)\n", "labels[probs>0.5] = 'Up'\n", "confusion_table(labels, L_test)" ] }, { "cell_type": "markdown", "id": "46cf03c1", "metadata": {}, "source": [ "Let’s evaluate the overall accuracy as well as the accuracy within the days when\n", "logistic regression predicts an increase." ] }, { "cell_type": "code", "execution_count": 20, "id": "b3cd8b84", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.658566Z", "iopub.status.busy": "2024-06-04T23:19:10.658490Z", "iopub.status.idle": "2024-06-04T23:19:10.660432Z", "shell.execute_reply": "2024-06-04T23:19:10.660219Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.5595238095238095, 0.5824175824175825)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(35+106)/252,106/(106+76)" ] }, { "cell_type": "markdown", "id": "4641aad1", "metadata": {}, "source": [ "Now the results appear to be a little better: 56% of the daily\n", "movements have been correctly predicted. It is worth noting that in\n", "this case, a much simpler strategy of predicting that the market will\n", "increase every day will also be correct 56% of the time! Hence, in\n", "terms of overall error rate, the logistic regression method is no\n", "better than the naive approach. However, the confusion matrix\n", "shows that on days when logistic regression predicts an increase in\n", "the market, it has a 58% accuracy rate. This suggests a possible\n", "trading strategy of buying on days when the model predicts an\n", "increasing market, and avoiding trades on days when a decrease is\n", "predicted. Of course one would need to investigate more carefully\n", "whether this small improvement was real or just due to random chance.\n", "\n", "Suppose that we want to predict the returns associated with particular\n", "values of `Lag1` and `Lag2`. In particular, we want to\n", "predict `Direction` on a day when `Lag1` and\n", " `Lag2` equal $1.2$ and $1.1$, respectively, and on a day when they\n", "equal $1.5$ and $-0.8$. We do this using the `predict()`\n", "function." ] }, { "cell_type": "code", "execution_count": 21, "id": "d15e7495", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.661646Z", "iopub.status.busy": "2024-06-04T23:19:10.661582Z", "iopub.status.idle": "2024-06-04T23:19:10.664591Z", "shell.execute_reply": "2024-06-04T23:19:10.664373Z" } }, "outputs": [ { "data": { "text/plain": [ "0 0.479146\n", "1 0.496094\n", "dtype: float64" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "newdata = pd.DataFrame({'Lag1':[1.2, 1.5],\n", " 'Lag2':[1.1, -0.8]});\n", "newX = model.transform(newdata)\n", "results.predict(newX)" ] }, { "cell_type": "markdown", "id": "595d2fa9", "metadata": {}, "source": [ "## Linear Discriminant Analysis" ] }, { "cell_type": "markdown", "id": "0d31037d", "metadata": {}, "source": [ "We begin by performing LDA on the `Smarket` data, using the function\n", "`LinearDiscriminantAnalysis()`, which we have abbreviated `LDA()`. We \n", "fit the model using only the observations before 2005." ] }, { "cell_type": "code", "execution_count": 22, "id": "586b8bc1", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.665995Z", "iopub.status.busy": "2024-06-04T23:19:10.665887Z", "iopub.status.idle": "2024-06-04T23:19:10.667484Z", "shell.execute_reply": "2024-06-04T23:19:10.667242Z" } }, "outputs": [], "source": [ "lda = LDA(store_covariance=True)" ] }, { "cell_type": "markdown", "id": "43672635", "metadata": {}, "source": [ "Since the `LDA` estimator automatically \n", "adds an intercept, we should remove the column corresponding to the\n", "intercept in both `X_train` and `X_test`. We can also directly\n", "use the labels rather than the Boolean vectors `y_train`." ] }, { "cell_type": "code", "execution_count": 23, "id": "18fa8ae5", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.668696Z", "iopub.status.busy": "2024-06-04T23:19:10.668623Z", "iopub.status.idle": "2024-06-04T23:19:10.673662Z", "shell.execute_reply": "2024-06-04T23:19:10.673442Z" } }, "outputs": [ { "data": { "text/html": [ "
LinearDiscriminantAnalysis(store_covariance=True)
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" ], "text/plain": [ "LinearDiscriminantAnalysis(store_covariance=True)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_train, X_test = [M.drop(columns=['intercept'])\n", " for M in [X_train, X_test]]\n", "lda.fit(X_train, L_train)" ] }, { "cell_type": "markdown", "id": "a8254b5d", "metadata": {}, "source": [ "Here we have used the list comprehensions introduced\n", "in Section~\\ref{Ch3-linreg-lab:multivariate-goodness-of-fit}. Looking at our first line above, we see that the right-hand side is a list\n", "of length two. This is because the code `for M in [X_train, X_test]` iterates over a list\n", "of length two. While here we loop over a list,\n", "the list comprehension method works when looping over any iterable object.\n", "We then apply the `drop()` method to each element in the iteration, collecting\n", "the result in a list. The left-hand side tells `Python` to unpack this list\n", "of length two, assigning its elements to the variables `X_train` and `X_test`. Of course,\n", "this overwrites the previous values of `X_train` and `X_test`.\n", "\n", "Having fit the model, we can extract the means in the two classes with the `means_` attribute. These are the average of each predictor within each class, and\n", "are used by LDA as estimates of $\\mu_k$. These suggest that there is\n", "a tendency for the previous 2 days’ returns to be negative on days\n", "when the market increases, and a tendency for the previous days’\n", "returns to be positive on days when the market declines." ] }, { "cell_type": "code", "execution_count": 24, "id": "4c9a8391", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.674879Z", "iopub.status.busy": "2024-06-04T23:19:10.674804Z", "iopub.status.idle": "2024-06-04T23:19:10.676917Z", "shell.execute_reply": "2024-06-04T23:19:10.676691Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.04279022, 0.03389409],\n", " [-0.03954635, -0.03132544]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lda.means_" ] }, { "cell_type": "markdown", "id": "2d21cb4e", "metadata": {}, "source": [ "The estimated prior probabilities are stored in the `priors_` attribute.\n", "The package `sklearn` typically uses this trailing `_` to denote\n", "a quantity estimated when using the `fit()` method. We can be sure of which\n", "entry corresponds to which label by looking at the `classes_` attribute." ] }, { "cell_type": "code", "execution_count": 25, "id": "0b774571", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.678089Z", "iopub.status.busy": "2024-06-04T23:19:10.678014Z", "iopub.status.idle": "2024-06-04T23:19:10.679873Z", "shell.execute_reply": "2024-06-04T23:19:10.679660Z" } }, "outputs": [ { "data": { "text/plain": [ "array(['Down', 'Up'], dtype='\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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\n", "" ], "text/plain": [ "Truth Down Up\n", "Predicted \n", "Down 35 35\n", "Up 76 106" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "confusion_table(lda_pred, L_test)" ] }, { "cell_type": "markdown", "id": "2261b398", "metadata": {}, "source": [ "We can also estimate the\n", "probability of each class for\n", "each point in a training set. Applying a 50% threshold to the posterior probabilities of\n", "being in class one allows us to\n", "recreate the predictions contained in `lda_pred`." ] }, { "cell_type": "code", "execution_count": 30, "id": "496f213c", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.694765Z", "iopub.status.busy": "2024-06-04T23:19:10.694696Z", "iopub.status.idle": "2024-06-04T23:19:10.697074Z", "shell.execute_reply": "2024-06-04T23:19:10.696863Z" } }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lda_prob = lda.predict_proba(X_test)\n", "np.all(\n", " np.where(lda_prob[:,1] >= 0.5, 'Up','Down') == lda_pred\n", " )" ] }, { "cell_type": "markdown", "id": "56d0ad8f", "metadata": {}, "source": [ "Above, we used the `np.where()` function that\n", "creates an array with value `'Up'` for indices where\n", "the second column of `lda_prob` (the estimated\n", "posterior probability of `'Up'`) is greater than 0.5.\n", "For problems with more than two classes the labels are chosen as the class whose posterior probability is highest:" ] }, { "cell_type": "code", "execution_count": 31, "id": "7a306b42", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.698382Z", "iopub.status.busy": "2024-06-04T23:19:10.698315Z", "iopub.status.idle": "2024-06-04T23:19:10.700428Z", "shell.execute_reply": "2024-06-04T23:19:10.700221Z" } }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.all(\n", " [lda.classes_[i] for i in np.argmax(lda_prob, 1)] == lda_pred\n", " )" ] }, { "cell_type": "markdown", "id": "01fe47ab", "metadata": {}, "source": [ "If we wanted to use a posterior probability threshold other than\n", "50% in order to make predictions, then we could easily do so. For\n", "instance, suppose that we wish to predict a market decrease only if we\n", "are very certain that the market will indeed decrease on that\n", "day --- say, if the posterior probability is at least 90%.\n", "We know that the first column of `lda_prob` corresponds to the\n", "label `Down` after having checked the `classes_` attribute, hence we use\n", "the column index 0 rather than 1 as we did above." ] }, { "cell_type": "code", "execution_count": 32, "id": "f2d7878b", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.701614Z", "iopub.status.busy": "2024-06-04T23:19:10.701548Z", "iopub.status.idle": "2024-06-04T23:19:10.703307Z", "shell.execute_reply": "2024-06-04T23:19:10.703099Z" } }, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(lda_prob[:,0] > 0.9)" ] }, { "cell_type": "markdown", "id": "d5c3e881", "metadata": {}, "source": [ "No days in 2005 meet that threshold! In fact, the greatest posterior\n", "probability of decrease in all of 2005 was 52.02%.\n", "\n", "The LDA classifier above is the first classifier from the\n", "`sklearn` library. We will use several other objects\n", "from this library. The objects\n", "follow a common structure that simplifies tasks such as cross-validation,\n", "which we will see in Chapter~\\ref{Ch5:resample}. Specifically,\n", "the methods first create a generic classifier without\n", "referring to any data. This classifier is then fit\n", "to data with the `fit()` method and predictions are\n", "always produced with the `predict()` method. This pattern\n", "of first instantiating the classifier, followed by fitting it, and\n", "then producing predictions is an explicit design choice of `sklearn`. This uniformity\n", "makes it possible to cleanly copy the classifier so that it can be fit\n", "on different data; e.g. different training sets arising in cross-validation.\n", "This standard pattern also allows for a predictable formation of workflows." ] }, { "cell_type": "markdown", "id": "dbeab8f9", "metadata": {}, "source": [ "## Quadratic Discriminant Analysis\n", "We will now fit a QDA model to the `Smarket` data. QDA is\n", "implemented via\n", "`QuadraticDiscriminantAnalysis()`\n", "in the `sklearn` package, which we abbreviate to `QDA()`.\n", "The syntax is very similar to `LDA()`." ] }, { "cell_type": "code", "execution_count": 33, "id": "6fc87c48", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.704453Z", "iopub.status.busy": "2024-06-04T23:19:10.704385Z", "iopub.status.idle": "2024-06-04T23:19:10.707626Z", "shell.execute_reply": "2024-06-04T23:19:10.707394Z" } }, "outputs": [ { "data": { "text/html": [ "
QuadraticDiscriminantAnalysis(store_covariance=True)
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" ], "text/plain": [ "QuadraticDiscriminantAnalysis(store_covariance=True)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qda = QDA(store_covariance=True)\n", "qda.fit(X_train, L_train)" ] }, { "cell_type": "markdown", "id": "7a0ca885", "metadata": {}, "source": [ "The `QDA()` function will again compute `means_` and `priors_`." ] }, { "cell_type": "code", "execution_count": 34, "id": "92f4f928", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.708905Z", "iopub.status.busy": "2024-06-04T23:19:10.708836Z", "iopub.status.idle": "2024-06-04T23:19:10.710715Z", "shell.execute_reply": "2024-06-04T23:19:10.710514Z" } }, "outputs": [ { "data": { "text/plain": [ "(array([[ 0.04279022, 0.03389409],\n", " [-0.03954635, -0.03132544]]),\n", " array([0.49198397, 0.50801603]))" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qda.means_, qda.priors_" ] }, { "cell_type": "markdown", "id": "c431c86f", "metadata": {}, "source": [ "The `QDA()` classifier will estimate one covariance per class. Here is the\n", "estimated covariance in the first class:" ] }, { "cell_type": "code", "execution_count": 35, "id": "d016f22c", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.711933Z", "iopub.status.busy": "2024-06-04T23:19:10.711857Z", "iopub.status.idle": "2024-06-04T23:19:10.713787Z", "shell.execute_reply": "2024-06-04T23:19:10.713572Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[ 1.50662277, -0.03924806],\n", " [-0.03924806, 1.53559498]])" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qda.covariance_[0]" ] }, { "cell_type": "markdown", "id": "9255f459", "metadata": {}, "source": [ "The output contains the group means. But it does not contain the\n", "coefficients of the linear discriminants, because the QDA classifier\n", "involves a quadratic, rather than a linear, function of the\n", "predictors. The `predict()` function works in exactly the\n", "same fashion as for LDA." ] }, { "cell_type": "code", "execution_count": 36, "id": "0c8fa11a", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.714998Z", "iopub.status.busy": "2024-06-04T23:19:10.714933Z", "iopub.status.idle": "2024-06-04T23:19:10.718857Z", "shell.execute_reply": "2024-06-04T23:19:10.718646Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "Truth Down Up\n", "Predicted \n", "Down 30 20\n", "Up 81 121" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qda_pred = qda.predict(X_test)\n", "confusion_table(qda_pred, L_test)" ] }, { "cell_type": "markdown", "id": "9d80294b", "metadata": {}, "source": [ "Interestingly, the QDA predictions are accurate almost 60% of the\n", "time, even though the 2005 data was not used to fit the model." ] }, { "cell_type": "code", "execution_count": 37, "id": "b010de50", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.720069Z", "iopub.status.busy": "2024-06-04T23:19:10.720000Z", "iopub.status.idle": "2024-06-04T23:19:10.721978Z", "shell.execute_reply": "2024-06-04T23:19:10.721773Z" } }, "outputs": [ { "data": { "text/plain": [ "0.5992063492063492" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(qda_pred == L_test)" ] }, { "cell_type": "markdown", "id": "b57525d1", "metadata": {}, "source": [ "This level of accuracy is quite impressive for stock market data, which is\n", "known to be quite hard to model accurately. This suggests that the\n", "quadratic form assumed by QDA may capture the true relationship more\n", "accurately than the linear forms assumed by LDA and logistic\n", "regression. However, we recommend evaluating this method’s\n", "performance on a larger test set before betting that this approach\n", "will consistently beat the market!" ] }, { "cell_type": "markdown", "id": "152e9b52", "metadata": {}, "source": [ "## Naive Bayes\n", "Next, we fit a naive Bayes model to the `Smarket` data. The syntax is\n", "similar to that of `LDA()` and `QDA()`. By\n", "default, this implementation `GaussianNB()` of the naive Bayes classifier models each\n", "quantitative feature using a Gaussian distribution. However, a kernel\n", "density method can also be used to estimate the distributions." ] }, { "cell_type": "code", "execution_count": 38, "id": "78cac089", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.723135Z", "iopub.status.busy": "2024-06-04T23:19:10.723068Z", "iopub.status.idle": "2024-06-04T23:19:10.726306Z", "shell.execute_reply": "2024-06-04T23:19:10.726108Z" } }, "outputs": [ { "data": { "text/html": [ "
GaussianNB()
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" ], "text/plain": [ "GaussianNB()" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "NB = GaussianNB()\n", "NB.fit(X_train, L_train)" ] }, { "cell_type": "markdown", "id": "0da48d75", "metadata": {}, "source": [ "The classes are stored as `classes_`." ] }, { "cell_type": "code", "execution_count": 39, "id": "acce3488", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.727548Z", "iopub.status.busy": "2024-06-04T23:19:10.727484Z", "iopub.status.idle": "2024-06-04T23:19:10.729522Z", "shell.execute_reply": "2024-06-04T23:19:10.729308Z" } }, "outputs": [ { "data": { "text/plain": [ "array(['Down', 'Up'], dtype='\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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\n", "" ], "text/plain": [ "Truth Down Up\n", "Predicted \n", "Down 29 20\n", "Up 82 121" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nb_labels = NB.predict(X_test)\n", "confusion_table(nb_labels, L_test)" ] }, { "cell_type": "markdown", "id": "a16e034c", "metadata": {}, "source": [ "Naive Bayes performs well on these data, with accurate predictions over 59% of the time. This is slightly worse than QDA, but much better than LDA.\n", "\n", "As for `LDA`, the `predict_proba()` method estimates the probability that each observation belongs to a particular class." ] }, { "cell_type": "code", "execution_count": 46, "id": "1efe1d6a", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.751934Z", "iopub.status.busy": "2024-06-04T23:19:10.751870Z", "iopub.status.idle": "2024-06-04T23:19:10.754306Z", "shell.execute_reply": "2024-06-04T23:19:10.754090Z" } }, "outputs": [ { "data": { "text/plain": [ "array([[0.4873288 , 0.5126712 ],\n", " [0.47623584, 0.52376416],\n", " [0.46529531, 0.53470469],\n", " [0.47484469, 0.52515531],\n", " [0.49020587, 0.50979413]])" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "NB.predict_proba(X_test)[:5]" ] }, { "cell_type": "markdown", "id": "ed4f37e8", "metadata": {}, "source": [ "## K-Nearest Neighbors\n", "We will now perform KNN using the `KNeighborsClassifier()` function. This function works similarly\n", "to the other model-fitting functions that we have\n", "encountered thus far.\n", "\n", "As is the\n", "case for LDA and QDA, we fit the classifier\n", "using the `fit` method. New\n", "predictions are formed using the `predict` method\n", "of the object returned by `fit()`." ] }, { "cell_type": "code", "execution_count": 47, "id": "b0b8ae27", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.755478Z", "iopub.status.busy": "2024-06-04T23:19:10.755409Z", "iopub.status.idle": "2024-06-04T23:19:10.763883Z", "shell.execute_reply": "2024-06-04T23:19:10.763665Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "Truth Down Up\n", "Predicted \n", "Down 43 58\n", "Up 68 83" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "knn1 = KNeighborsClassifier(n_neighbors=1)\n", "X_train, X_test = [np.asarray(X) for X in [X_train, X_test]]\n", "knn1.fit(X_train, L_train)\n", "knn1_pred = knn1.predict(X_test)\n", "confusion_table(knn1_pred, L_test)" ] }, { "cell_type": "markdown", "id": "84c89555", "metadata": {}, "source": [ "The results using $K=1$ are not very good, since only $50%$ of the\n", "observations are correctly predicted. Of course, it may be that $K=1$\n", "results in an overly-flexible fit to the data." ] }, { "cell_type": "code", "execution_count": 48, "id": "7c9bdd8e", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.765113Z", "iopub.status.busy": "2024-06-04T23:19:10.765038Z", "iopub.status.idle": "2024-06-04T23:19:10.767093Z", "shell.execute_reply": "2024-06-04T23:19:10.766831Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.5, 0.5)" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(83+43)/252, np.mean(knn1_pred == L_test)" ] }, { "cell_type": "markdown", "id": "96e335c6", "metadata": {}, "source": [ "We repeat the\n", "analysis below using $K=3$." ] }, { "cell_type": "code", "execution_count": 49, "id": "a1750e64", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.768344Z", "iopub.status.busy": "2024-06-04T23:19:10.768258Z", "iopub.status.idle": "2024-06-04T23:19:10.774690Z", "shell.execute_reply": "2024-06-04T23:19:10.774467Z" } }, "outputs": [ { "data": { "text/plain": [ "0.5317460317460317" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "knn3 = KNeighborsClassifier(n_neighbors=3)\n", "knn3_pred = knn3.fit(X_train, L_train).predict(X_test)\n", "np.mean(knn3_pred == L_test)" ] }, { "cell_type": "markdown", "id": "ecbad54a", "metadata": {}, "source": [ "The results have improved slightly. But increasing *K* further\n", "provides no further improvements. It appears that for these data, and this train/test split,\n", "QDA gives the best results of the methods that we have examined so\n", "far." ] }, { "cell_type": "markdown", "id": "d3fe0e0d", "metadata": {}, "source": [ "KNN does not perform well on the `Smarket` data, but it often does provide impressive results. As an example we will apply the KNN approach to the `Caravan` data set, which is part of the `ISLP` library. This data set includes 85\n", "predictors that measure demographic characteristics for 5,822\n", "individuals. The response variable is `Purchase`, which\n", "indicates whether or not a given individual purchases a caravan\n", "insurance policy. In this data set, only 6% of people purchased\n", "caravan insurance." ] }, { "cell_type": "code", "execution_count": 50, "id": "2b179be8", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.776042Z", "iopub.status.busy": "2024-06-04T23:19:10.775972Z", "iopub.status.idle": "2024-06-04T23:19:10.790666Z", "shell.execute_reply": "2024-06-04T23:19:10.790430Z" } }, "outputs": [ { "data": { "text/plain": [ "Purchase\n", "No 5474\n", "Yes 348\n", "Name: count, dtype: int64" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Caravan = load_data('Caravan')\n", "Purchase = Caravan.Purchase\n", "Purchase.value_counts()" ] }, { "cell_type": "markdown", "id": "99805400", "metadata": {}, "source": [ "The method `value_counts()` takes a `pd.Series` or `pd.DataFrame` and returns\n", "a `pd.Series` with the corresponding counts\n", "for each unique element. In this case `Purchase` has only `Yes` and `No` values\n", "and the method returns how many values of each there are." ] }, { "cell_type": "code", "execution_count": 51, "id": "e9de7237", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.791954Z", "iopub.status.busy": "2024-06-04T23:19:10.791856Z", "iopub.status.idle": "2024-06-04T23:19:10.793719Z", "shell.execute_reply": "2024-06-04T23:19:10.793502Z" } }, "outputs": [ { "data": { "text/plain": [ "0.05977327378907592" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "348 / 5822" ] }, { "cell_type": "markdown", "id": "e3fdbe45", "metadata": {}, "source": [ "Our features will include all columns except `Purchase`." ] }, { "cell_type": "code", "execution_count": 52, "id": "f81dcb72", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.794971Z", "iopub.status.busy": "2024-06-04T23:19:10.794900Z", "iopub.status.idle": "2024-06-04T23:19:10.796754Z", "shell.execute_reply": "2024-06-04T23:19:10.796532Z" } }, "outputs": [], "source": [ "feature_df = Caravan.drop(columns=['Purchase'])" ] }, { "cell_type": "markdown", "id": "1f92eadb", "metadata": {}, "source": [ "Because the KNN classifier predicts the class of a given test\n", "observation by identifying the observations that are nearest to it,\n", "the scale of the variables matters. Any variables that are on a large\n", "scale will have a much larger effect on the *distance* between\n", "the observations, and hence on the KNN classifier, than variables that\n", "are on a small scale. For instance, imagine a data set that contains\n", "two variables, `salary` and `age` (measured in dollars\n", "and years, respectively). As far as KNN is concerned, a difference of\n", "1,000 USD in salary is enormous compared to a difference of 50 years in\n", "age. Consequently, `salary` will drive the KNN classification\n", "results, and `age` will have almost no effect. This is contrary\n", "to our intuition that a salary difference of 1,000 USD is quite small\n", "compared to an age difference of 50 years. Furthermore, the\n", "importance of scale to the KNN classifier leads to another issue: if\n", "we measured `salary` in Japanese yen, or if we measured\n", " `age` in minutes, then we’d get quite different classification\n", "results from what we get if these two variables are measured in\n", "dollars and years.\n", "\n", "A good way to handle this problem is to *standardize* the data so that all variables are\n", "given a mean of zero and a standard deviation of one. Then all\n", "variables will be on a comparable scale. This is accomplished\n", "using\n", "the `StandardScaler()`\n", "transformation." ] }, { "cell_type": "code", "execution_count": 53, "id": "a7102e7d", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.797953Z", "iopub.status.busy": "2024-06-04T23:19:10.797884Z", "iopub.status.idle": "2024-06-04T23:19:10.799335Z", "shell.execute_reply": "2024-06-04T23:19:10.799104Z" } }, "outputs": [], "source": [ "scaler = StandardScaler(with_mean=True,\n", " with_std=True,\n", " copy=True)" ] }, { "cell_type": "markdown", "id": "eaf2eb3d", "metadata": {}, "source": [ "The argument `with_mean` indicates whether or not\n", "we should subtract the mean, while `with_std` indicates\n", "whether or not we should scale the columns to have standard\n", "deviation of 1 or not. Finally, the argument `copy=True`\n", "indicates that we will always copy data, rather than\n", "trying to do calculations in place where possible.\n", "\n", "This transformation can be fit\n", "and then applied to arbitrary data. In the first line\n", "below, the parameters for the scaling are computed and\n", "stored in `scaler`, while the second line actually\n", "constructs the standardized set of features." ] }, { "cell_type": "code", "execution_count": 54, "id": "c2b6c3fa", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.800622Z", "iopub.status.busy": "2024-06-04T23:19:10.800548Z", "iopub.status.idle": "2024-06-04T23:19:10.805188Z", "shell.execute_reply": "2024-06-04T23:19:10.804964Z" } }, "outputs": [], "source": [ "scaler.fit(feature_df)\n", "X_std = scaler.transform(feature_df)" ] }, { "cell_type": "markdown", "id": "d5d9c875", "metadata": {}, "source": [ "Now every column of `feature_std` below has a standard deviation of\n", "one and a mean of zero." ] }, { "cell_type": "code", "execution_count": 55, "id": "d1e40190", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.806480Z", "iopub.status.busy": "2024-06-04T23:19:10.806406Z", "iopub.status.idle": "2024-06-04T23:19:10.810671Z", "shell.execute_reply": "2024-06-04T23:19:10.810474Z" } }, "outputs": [ { "data": { "text/plain": [ "MOSTYPE 1.000086\n", "MAANTHUI 1.000086\n", "MGEMOMV 1.000086\n", "MGEMLEEF 1.000086\n", "MOSHOOFD 1.000086\n", " ... \n", "AZEILPL 1.000086\n", "APLEZIER 1.000086\n", "AFIETS 1.000086\n", "AINBOED 1.000086\n", "ABYSTAND 1.000086\n", "Length: 85, dtype: float64" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "feature_std = pd.DataFrame(\n", " X_std,\n", " columns=feature_df.columns);\n", "feature_std.std()" ] }, { "cell_type": "markdown", "id": "c225f2b2", "metadata": {}, "source": [ "Notice that the standard deviations are not quite $1$ here; this is again due to some procedures using the $1/n$ convention for variances (in this case `scaler()`), while others use $1/(n-1)$ (the `std()` method). See the footnote on page~\\pageref{Ch4-varformula}.\n", "In this case it does not matter, as long as the variables are all on the same scale.\n", "\n", "Using the function `train_test_split()` we now split the observations into a test set,\n", "containing 1000 observations, and a training set containing the remaining\n", "observations. The argument `random_state=0` ensures that we get\n", "the same split each time we rerun the code." ] }, { "cell_type": "code", "execution_count": 56, "id": "44ff90d4", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.811997Z", "iopub.status.busy": "2024-06-04T23:19:10.811926Z", "iopub.status.idle": "2024-06-04T23:19:10.814896Z", "shell.execute_reply": "2024-06-04T23:19:10.814681Z" } }, "outputs": [], "source": [ "(X_train,\n", " X_test,\n", " y_train,\n", " y_test) = train_test_split(np.asarray(feature_std),\n", " Purchase,\n", " test_size=1000,\n", " random_state=0)" ] }, { "cell_type": "markdown", "id": "293eaa56", "metadata": {}, "source": [ "`?train_test_split` reveals that the non-keyword arguments can be `lists`, `arrays`, `pandas dataframes` etc that all have the same length (`shape[0]`) and hence are *indexable*. In this case they are the dataframe `feature_std` and the response variable `Purchase`.\n", " {Note that we have converted `feature_std` to an `ndarray` to address a bug in `sklearn`.}\n", "We fit a KNN model on the training data using $K=1$,\n", "and evaluate its performance on the test data." ] }, { "cell_type": "code", "execution_count": 57, "id": "f88990de", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.816100Z", "iopub.status.busy": "2024-06-04T23:19:10.816032Z", "iopub.status.idle": "2024-06-04T23:19:10.977519Z", "shell.execute_reply": "2024-06-04T23:19:10.973692Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.111, 0.067)" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "knn1 = KNeighborsClassifier(n_neighbors=1)\n", "knn1_pred = knn1.fit(X_train, y_train).predict(X_test)\n", "np.mean(y_test != knn1_pred), np.mean(y_test != \"No\")" ] }, { "cell_type": "markdown", "id": "57a4a331", "metadata": {}, "source": [ "The KNN error rate on the 1,000 test observations is about $11%$.\n", "At first glance, this may appear to be fairly good. However, since\n", "just over 6% of customers purchased insurance, we could get the error\n", "rate down to almost 6% by always predicting `No` regardless of the\n", "values of the predictors! This is known as the *null rate*.}\n", "\n", "Suppose that there is some non-trivial cost to trying to sell\n", "insurance to a given individual. For instance, perhaps a salesperson\n", "must visit each potential customer. If the company tries to sell\n", "insurance to a random selection of customers, then the success rate\n", "will be only 6%, which may be far too low given the costs\n", "involved. Instead, the company would like to try to sell insurance\n", "only to customers who are likely to buy it. So the overall error rate\n", "is not of interest. Instead, the fraction of individuals that are\n", "correctly predicted to buy insurance is of interest." ] }, { "cell_type": "code", "execution_count": 58, "id": "733b69fb", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:10.986636Z", "iopub.status.busy": "2024-06-04T23:19:10.986365Z", "iopub.status.idle": "2024-06-04T23:19:11.006708Z", "shell.execute_reply": "2024-06-04T23:19:11.001541Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "Truth No Yes\n", "Predicted \n", "No 880 58\n", "Yes 53 9" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "confusion_table(knn1_pred, y_test)" ] }, { "cell_type": "markdown", "id": "d7a1359d", "metadata": {}, "source": [ "It turns out that KNN with $K=1$ does far better than random guessing\n", "among the customers that are predicted to buy insurance. Among 62\n", "such customers, 9, or 14.5%, actually do purchase insurance.\n", "This is double the rate that one would obtain from random guessing." ] }, { "cell_type": "code", "execution_count": 59, "id": "269d3d95", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.019124Z", "iopub.status.busy": "2024-06-04T23:19:11.016874Z", "iopub.status.idle": "2024-06-04T23:19:11.026784Z", "shell.execute_reply": "2024-06-04T23:19:11.025439Z" } }, "outputs": [ { "data": { "text/plain": [ "0.14516129032258066" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "9/(53+9)" ] }, { "cell_type": "markdown", "id": "12bcb480", "metadata": {}, "source": [ "### Tuning Parameters\n", "\n", "The number of neighbors in KNN is referred to as a *tuning parameter*, also referred to as a *hyperparameter*.\n", "We do not know *a priori* what value to use. It is therefore of interest\n", "to see how the classifier performs on test data as we vary these\n", "parameters. This can be achieved with a `for` loop, described in Section~\\ref{Ch2-statlearn-lab:for-loops}.\n", "Here we use a for loop to look at the accuracy of our classifier in the group predicted to purchase\n", "insurance as we vary the number of neighbors from 1 to 5:" ] }, { "cell_type": "code", "execution_count": 60, "id": "db9963d8", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.029587Z", "iopub.status.busy": "2024-06-04T23:19:11.029376Z", "iopub.status.idle": "2024-06-04T23:19:11.164487Z", "shell.execute_reply": "2024-06-04T23:19:11.164119Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "K=1: # predicted to rent: 62, # who did rent 9, accuracy 14.5%\n", "K=2: # predicted to rent: 6, # who did rent 1, accuracy 16.7%\n", "K=3: # predicted to rent: 20, # who did rent 3, accuracy 15.0%\n", "K=4: # predicted to rent: 4, # who did rent 0, accuracy 0.0%\n", "K=5: # predicted to rent: 7, # who did rent 1, accuracy 14.3%\n" ] } ], "source": [ "for K in range(1,6):\n", " knn = KNeighborsClassifier(n_neighbors=K)\n", " knn_pred = knn.fit(X_train, y_train).predict(X_test)\n", " C = confusion_table(knn_pred, y_test)\n", " templ = ('K={0:d}: # predicted to rent: {1:>2},' +\n", " ' # who did rent {2:d}, accuracy {3:.1%}')\n", " pred = C.loc['Yes'].sum()\n", " did_rent = C.loc['Yes','Yes']\n", " print(templ.format(\n", " K,\n", " pred,\n", " did_rent,\n", " did_rent / pred))" ] }, { "cell_type": "markdown", "id": "2d3a4b95", "metadata": {}, "source": [ "We see some variability --- the numbers for `K=4` are very different from the rest.\n", "\n", "### Comparison to Logistic Regression\n", "As a comparison, we can also fit a logistic regression model to the\n", "data. This can also be done\n", "with `sklearn`, though by default it fits\n", "something like the *ridge regression* version\n", "of logistic regression, which we introduce in Chapter~\\ref{Ch6:varselect}. This can\n", "be modified by appropriately setting the argument `C` below. Its default\n", "value is 1 but by setting it to a very large number, the algorithm converges to the same solution as the usual (unregularized)\n", "logistic regression estimator discussed above.\n", "\n", "Unlike the\n", "`statsmodels` package, `sklearn` focuses less on\n", "inference and more on classification. Hence,\n", "the `summary` methods seen in `statsmodels`\n", "and our simplified version seen with `summarize` are not\n", "generally available for the classifiers in `sklearn`." ] }, { "cell_type": "code", "execution_count": 61, "id": "77f8eb90", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.166394Z", "iopub.status.busy": "2024-06-04T23:19:11.166286Z", "iopub.status.idle": "2024-06-04T23:19:11.612761Z", "shell.execute_reply": "2024-06-04T23:19:11.611650Z" } }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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" ], "text/plain": [ "Truth No Yes\n", "Predicted \n", "No 931 67\n", "Yes 2 0" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logit = LogisticRegression(C=1e10, solver='liblinear')\n", "logit.fit(X_train, y_train)\n", "logit_pred = logit.predict_proba(X_test)\n", "logit_labels = np.where(logit_pred[:,1] > .5, 'Yes', 'No')\n", "confusion_table(logit_labels, y_test)" ] }, { "cell_type": "markdown", "id": "fbf84545", "metadata": {}, "source": [ "We used the argument `solver='liblinear'` above to\n", "avoid a warning with the default solver which would indicate that\n", "the algorithm does not converge.\n", "\n", "If we use $0.5$ as the predicted probability cut-off for the\n", "classifier, then we have a problem: only two of the test observations\n", "are predicted to purchase insurance. However, we are not required to use a\n", "cut-off of $0.5$. If we instead predict a purchase any time the\n", "predicted probability of purchase exceeds $0.25$, we get much better\n", "results: we predict that 29 people will purchase insurance, and we are\n", "correct for about 31% of these people. This is almost five times\n", "better than random guessing!" ] }, { "cell_type": "code", "execution_count": 62, "id": "907e3299", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.615999Z", "iopub.status.busy": "2024-06-04T23:19:11.615768Z", "iopub.status.idle": "2024-06-04T23:19:11.628399Z", "shell.execute_reply": "2024-06-04T23:19:11.627025Z" } }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
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" ], "text/plain": [ "Truth No Yes\n", "Predicted \n", "No 913 58\n", "Yes 20 9" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "logit_labels = np.where(logit_pred[:,1]>0.25, 'Yes', 'No')\n", "confusion_table(logit_labels, y_test)" ] }, { "cell_type": "code", "execution_count": 63, "id": "cb3f2b0e", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.631843Z", "iopub.status.busy": "2024-06-04T23:19:11.631560Z", "iopub.status.idle": "2024-06-04T23:19:11.636898Z", "shell.execute_reply": "2024-06-04T23:19:11.636444Z" } }, "outputs": [ { "data": { "text/plain": [ "0.3103448275862069" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "9/(20+9)" ] }, { "cell_type": "markdown", "id": "8d3b5503", "metadata": {}, "source": [ "## Linear and Poisson Regression on the Bikeshare Data\n", "Here we fit linear and Poisson regression models to the `Bikeshare` data, as described in Section~\\ref{Ch4:sec:pois}.\n", "The response `bikers` measures the number of bike rentals per hour\n", "in Washington, DC in the period 2010--2012." ] }, { "cell_type": "code", "execution_count": 64, "id": "23ce05b5", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.639885Z", "iopub.status.busy": "2024-06-04T23:19:11.639635Z", "iopub.status.idle": "2024-06-04T23:19:11.652008Z", "shell.execute_reply": "2024-06-04T23:19:11.651483Z" } }, "outputs": [], "source": [ "Bike = load_data('Bikeshare')" ] }, { "cell_type": "markdown", "id": "fdb0a62a", "metadata": {}, "source": [ "Let's have a peek at the dimensions and names of the variables in this dataframe." ] }, { "cell_type": "code", "execution_count": 65, "id": "027a24c4", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.655682Z", "iopub.status.busy": "2024-06-04T23:19:11.655146Z", "iopub.status.idle": "2024-06-04T23:19:11.661660Z", "shell.execute_reply": "2024-06-04T23:19:11.658906Z" } }, "outputs": [ { "data": { "text/plain": [ "((8645, 15),\n", " Index(['season', 'mnth', 'day', 'hr', 'holiday', 'weekday', 'workingday',\n", " 'weathersit', 'temp', 'atemp', 'hum', 'windspeed', 'casual',\n", " 'registered', 'bikers'],\n", " dtype='object'))" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Bike.shape, Bike.columns" ] }, { "cell_type": "markdown", "id": "ce51b618", "metadata": {}, "source": [ "### Linear Regression\n", "\n", "We begin by fitting a linear regression model to the data." ] }, { "cell_type": "code", "execution_count": 66, "id": "5896ce19", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.664908Z", "iopub.status.busy": "2024-06-04T23:19:11.664631Z", "iopub.status.idle": "2024-06-04T23:19:11.731259Z", "shell.execute_reply": "2024-06-04T23:19:11.730708Z" } }, "outputs": [ { "data": { "text/html": [ "
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coefstd errtP>|t|
intercept-68.63175.307-12.9320.000
mnth[Feb]6.84524.2871.5970.110
mnth[March]16.55144.3013.8480.000
mnth[April]41.42494.9728.3310.000
mnth[May]72.55715.64112.8620.000
mnth[June]67.81876.54410.3640.000
mnth[July]45.32457.0816.4010.000
mnth[Aug]53.24306.6408.0190.000
mnth[Sept]66.67835.92511.2540.000
mnth[Oct]75.83434.95015.3190.000
mnth[Nov]60.31004.61013.0830.000
mnth[Dec]46.45774.27110.8780.000
hr[1]-14.57935.699-2.5580.011
hr[2]-21.57915.733-3.7640.000
hr[3]-31.14085.778-5.3890.000
hr[4]-36.90755.802-6.3610.000
hr[5]-24.13555.737-4.2070.000
hr[6]20.59975.7043.6120.000
hr[7]120.09315.69321.0950.000
hr[8]223.66195.69039.3100.000
hr[9]120.58195.69321.1820.000
hr[10]83.80135.70514.6890.000
hr[11]105.42345.72218.4240.000
hr[12]137.28375.74023.9160.000
hr[13]136.03595.76023.6170.000
hr[14]126.63615.77621.9230.000
hr[15]132.08655.78022.8520.000
hr[16]178.52065.77230.9270.000
hr[17]296.26705.74951.5370.000
hr[18]269.44095.73646.9760.000
hr[19]186.25585.71432.5960.000
hr[20]125.54925.70422.0120.000
hr[21]87.55375.69315.3780.000
hr[22]59.12265.68910.3920.000
hr[23]26.83765.6884.7190.000
workingday1.26961.7840.7110.477
temp157.209410.26115.3210.000
weathersit[cloudy/misty]-12.89031.964-6.5620.000
weathersit[heavy rain/snow]-109.744676.667-1.4310.152
weathersit[light rain/snow]-66.49442.965-22.4250.000
\n", "
" ], "text/plain": [ " coef std err t P>|t|\n", "intercept -68.6317 5.307 -12.932 0.000\n", "mnth[Feb] 6.8452 4.287 1.597 0.110\n", "mnth[March] 16.5514 4.301 3.848 0.000\n", "mnth[April] 41.4249 4.972 8.331 0.000\n", "mnth[May] 72.5571 5.641 12.862 0.000\n", "mnth[June] 67.8187 6.544 10.364 0.000\n", "mnth[July] 45.3245 7.081 6.401 0.000\n", "mnth[Aug] 53.2430 6.640 8.019 0.000\n", "mnth[Sept] 66.6783 5.925 11.254 0.000\n", "mnth[Oct] 75.8343 4.950 15.319 0.000\n", "mnth[Nov] 60.3100 4.610 13.083 0.000\n", "mnth[Dec] 46.4577 4.271 10.878 0.000\n", "hr[1] -14.5793 5.699 -2.558 0.011\n", "hr[2] -21.5791 5.733 -3.764 0.000\n", "hr[3] -31.1408 5.778 -5.389 0.000\n", "hr[4] -36.9075 5.802 -6.361 0.000\n", "hr[5] -24.1355 5.737 -4.207 0.000\n", "hr[6] 20.5997 5.704 3.612 0.000\n", "hr[7] 120.0931 5.693 21.095 0.000\n", "hr[8] 223.6619 5.690 39.310 0.000\n", "hr[9] 120.5819 5.693 21.182 0.000\n", "hr[10] 83.8013 5.705 14.689 0.000\n", "hr[11] 105.4234 5.722 18.424 0.000\n", "hr[12] 137.2837 5.740 23.916 0.000\n", "hr[13] 136.0359 5.760 23.617 0.000\n", "hr[14] 126.6361 5.776 21.923 0.000\n", "hr[15] 132.0865 5.780 22.852 0.000\n", "hr[16] 178.5206 5.772 30.927 0.000\n", "hr[17] 296.2670 5.749 51.537 0.000\n", "hr[18] 269.4409 5.736 46.976 0.000\n", "hr[19] 186.2558 5.714 32.596 0.000\n", "hr[20] 125.5492 5.704 22.012 0.000\n", "hr[21] 87.5537 5.693 15.378 0.000\n", "hr[22] 59.1226 5.689 10.392 0.000\n", "hr[23] 26.8376 5.688 4.719 0.000\n", "workingday 1.2696 1.784 0.711 0.477\n", "temp 157.2094 10.261 15.321 0.000\n", "weathersit[cloudy/misty] -12.8903 1.964 -6.562 0.000\n", "weathersit[heavy rain/snow] -109.7446 76.667 -1.431 0.152\n", "weathersit[light rain/snow] -66.4944 2.965 -22.425 0.000" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = MS(['mnth',\n", " 'hr',\n", " 'workingday',\n", " 'temp',\n", " 'weathersit']).fit_transform(Bike)\n", "Y = Bike['bikers']\n", "M_lm = sm.OLS(Y, X).fit()\n", "summarize(M_lm)" ] }, { "cell_type": "markdown", "id": "d165f13c", "metadata": {}, "source": [ "There are 24 levels in `hr` and 40 rows in all.\n", "In `M_lm`, the first levels `hr[0]` and `mnth[Jan]` are treated\n", "as the baseline values, and so no coefficient estimates are provided\n", "for them: implicitly, their coefficient estimates are zero, and all\n", "other levels are measured relative to these baselines. For example,\n", "the Feb coefficient of $6.845$ signifies that, holding all other\n", "variables constant, there are on average about 7 more riders in\n", "February than in January. Similarly there are about 16.5 more riders\n", "in March than in January.\n", "\n", "The results seen in Section~\\ref{sec:bikeshare.linear}\n", "used a slightly different coding of the variables `hr` and `mnth`, as follows:" ] }, { "cell_type": "code", "execution_count": 67, "id": "3b8a24b4", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.734388Z", "iopub.status.busy": "2024-06-04T23:19:11.734170Z", "iopub.status.idle": "2024-06-04T23:19:11.738116Z", "shell.execute_reply": "2024-06-04T23:19:11.737083Z" } }, "outputs": [], "source": [ "hr_encode = contrast('hr', 'sum')\n", "mnth_encode = contrast('mnth', 'sum')" ] }, { "cell_type": "markdown", "id": "ee108ad7", "metadata": {}, "source": [ "Refitting again:" ] }, { "cell_type": "code", "execution_count": 68, "id": "276ec935", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.741132Z", "iopub.status.busy": "2024-06-04T23:19:11.740955Z", "iopub.status.idle": "2024-06-04T23:19:11.806258Z", "shell.execute_reply": "2024-06-04T23:19:11.805740Z" } }, "outputs": [ { "data": { "text/html": [ "
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coefstd errtP>|t|
intercept73.59745.13214.3400.000
mnth[Jan]-46.08714.085-11.2810.000
mnth[Feb]-39.24193.539-11.0880.000
mnth[March]-29.53573.155-9.3610.000
mnth[April]-4.66222.741-1.7010.089
mnth[May]26.47002.8519.2850.000
mnth[June]21.73173.4656.2720.000
mnth[July]-0.76263.908-0.1950.845
mnth[Aug]7.15603.5352.0240.043
mnth[Sept]20.59123.0466.7610.000
mnth[Oct]29.74722.70011.0190.000
mnth[Nov]14.22292.8604.9720.000
hr[0]-96.14203.955-24.3070.000
hr[1]-110.72133.966-27.9160.000
hr[2]-117.72124.016-29.3100.000
hr[3]-127.28284.081-31.1910.000
hr[4]-133.04954.117-32.3190.000
hr[5]-120.27754.037-29.7940.000
hr[6]-75.54243.992-18.9250.000
hr[7]23.95113.9696.0350.000
hr[8]127.51993.95032.2840.000
hr[9]24.43993.9366.2090.000
hr[10]-12.34073.936-3.1350.002
hr[11]9.28143.9452.3530.019
hr[12]41.14173.95710.3970.000
hr[13]39.89393.97510.0360.000
hr[14]30.49403.9917.6410.000
hr[15]35.94453.9958.9980.000
hr[16]82.37863.98820.6550.000
hr[17]200.12493.96450.4880.000
hr[18]173.29893.95643.8060.000
hr[19]90.11383.94022.8720.000
hr[20]29.40713.9367.4710.000
hr[21]-8.58833.933-2.1840.029
hr[22]-37.01943.934-9.4090.000
workingday1.26961.7840.7110.477
temp157.209410.26115.3210.000
weathersit[cloudy/misty]-12.89031.964-6.5620.000
weathersit[heavy rain/snow]-109.744676.667-1.4310.152
weathersit[light rain/snow]-66.49442.965-22.4250.000
\n", "
" ], "text/plain": [ " coef std err t P>|t|\n", "intercept 73.5974 5.132 14.340 0.000\n", "mnth[Jan] -46.0871 4.085 -11.281 0.000\n", "mnth[Feb] -39.2419 3.539 -11.088 0.000\n", "mnth[March] -29.5357 3.155 -9.361 0.000\n", "mnth[April] -4.6622 2.741 -1.701 0.089\n", "mnth[May] 26.4700 2.851 9.285 0.000\n", "mnth[June] 21.7317 3.465 6.272 0.000\n", "mnth[July] -0.7626 3.908 -0.195 0.845\n", "mnth[Aug] 7.1560 3.535 2.024 0.043\n", "mnth[Sept] 20.5912 3.046 6.761 0.000\n", "mnth[Oct] 29.7472 2.700 11.019 0.000\n", "mnth[Nov] 14.2229 2.860 4.972 0.000\n", "hr[0] -96.1420 3.955 -24.307 0.000\n", "hr[1] -110.7213 3.966 -27.916 0.000\n", "hr[2] -117.7212 4.016 -29.310 0.000\n", "hr[3] -127.2828 4.081 -31.191 0.000\n", "hr[4] -133.0495 4.117 -32.319 0.000\n", "hr[5] -120.2775 4.037 -29.794 0.000\n", "hr[6] -75.5424 3.992 -18.925 0.000\n", "hr[7] 23.9511 3.969 6.035 0.000\n", "hr[8] 127.5199 3.950 32.284 0.000\n", "hr[9] 24.4399 3.936 6.209 0.000\n", "hr[10] -12.3407 3.936 -3.135 0.002\n", "hr[11] 9.2814 3.945 2.353 0.019\n", "hr[12] 41.1417 3.957 10.397 0.000\n", "hr[13] 39.8939 3.975 10.036 0.000\n", "hr[14] 30.4940 3.991 7.641 0.000\n", "hr[15] 35.9445 3.995 8.998 0.000\n", "hr[16] 82.3786 3.988 20.655 0.000\n", "hr[17] 200.1249 3.964 50.488 0.000\n", "hr[18] 173.2989 3.956 43.806 0.000\n", "hr[19] 90.1138 3.940 22.872 0.000\n", "hr[20] 29.4071 3.936 7.471 0.000\n", "hr[21] -8.5883 3.933 -2.184 0.029\n", "hr[22] -37.0194 3.934 -9.409 0.000\n", "workingday 1.2696 1.784 0.711 0.477\n", "temp 157.2094 10.261 15.321 0.000\n", "weathersit[cloudy/misty] -12.8903 1.964 -6.562 0.000\n", "weathersit[heavy rain/snow] -109.7446 76.667 -1.431 0.152\n", "weathersit[light rain/snow] -66.4944 2.965 -22.425 0.000" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X2 = MS([mnth_encode,\n", " hr_encode,\n", " 'workingday',\n", " 'temp',\n", " 'weathersit']).fit_transform(Bike)\n", "M2_lm = sm.OLS(Y, X2).fit()\n", "S2 = summarize(M2_lm)\n", "S2" ] }, { "cell_type": "markdown", "id": "f7e31352", "metadata": {}, "source": [ "What is the difference between the two codings? In `M2_lm`, a\n", "coefficient estimate is reported for all but level `23` of `hr`\n", "and level `Dec` of `mnth`. Importantly, in `M2_lm`, the (unreported) coefficient estimate\n", "for the last level of `mnth` is not zero: instead, it equals the\n", "negative of the sum of the coefficient estimates for all of the\n", "other levels. Similarly, in `M2_lm`, the coefficient estimate\n", "for the last level of `hr` is the negative of the sum of the\n", "coefficient estimates for all of the other levels. This means that the\n", "coefficients of `hr` and `mnth` in `M2_lm` will always sum\n", "to zero, and can be interpreted as the difference from the mean\n", "level. For example, the coefficient for January of $-46.087$ indicates\n", "that, holding all other variables constant, there are typically 46\n", "fewer riders in January relative to the yearly average.\n", "\n", "It is important to realize that the choice of coding really does not\n", "matter, provided that we interpret the model output correctly in light\n", "of the coding used. For example, we see that the predictions from the\n", "linear model are the same regardless of coding:" ] }, { "cell_type": "code", "execution_count": 69, "id": "c8b43ab6", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.812237Z", "iopub.status.busy": "2024-06-04T23:19:11.811979Z", "iopub.status.idle": "2024-06-04T23:19:11.819745Z", "shell.execute_reply": "2024-06-04T23:19:11.819144Z" } }, "outputs": [ { "data": { "text/plain": [ "1.0334731385542263e-18" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum((M_lm.fittedvalues - M2_lm.fittedvalues)**2)" ] }, { "cell_type": "markdown", "id": "f17733ac", "metadata": {}, "source": [ "The sum of squared differences is zero. We can also see this using the\n", "`np.allclose()` function:" ] }, { "cell_type": "code", "execution_count": 70, "id": "bcc538c2", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.823477Z", "iopub.status.busy": "2024-06-04T23:19:11.823254Z", "iopub.status.idle": "2024-06-04T23:19:11.830397Z", "shell.execute_reply": "2024-06-04T23:19:11.829852Z" } }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(M_lm.fittedvalues, M2_lm.fittedvalues)" ] }, { "cell_type": "markdown", "id": "41fb2787", "metadata": {}, "source": [ "To reproduce the left-hand side of Figure~\\ref{Ch4:bikeshare}\n", "we must first obtain the coefficient estimates associated with\n", "`mnth`. The coefficients for January through November can be obtained\n", "directly from the `M2_lm` object. The coefficient for December\n", "must be explicitly computed as the negative sum of all the other\n", "months. We first extract all the coefficients for month from\n", "the coefficients of `M2_lm`." ] }, { "cell_type": "code", "execution_count": 71, "id": "33a75971", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.833582Z", "iopub.status.busy": "2024-06-04T23:19:11.833376Z", "iopub.status.idle": "2024-06-04T23:19:11.840363Z", "shell.execute_reply": "2024-06-04T23:19:11.839611Z" } }, "outputs": [ { "data": { "text/plain": [ "mnth[Jan] -46.0871\n", "mnth[Feb] -39.2419\n", "mnth[March] -29.5357\n", "mnth[April] -4.6622\n", "mnth[May] 26.4700\n", "mnth[June] 21.7317\n", "mnth[July] -0.7626\n", "mnth[Aug] 7.1560\n", "mnth[Sept] 20.5912\n", "mnth[Oct] 29.7472\n", "mnth[Nov] 14.2229\n", "Name: coef, dtype: float64" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coef_month = S2[S2.index.str.contains('mnth')]['coef']\n", "coef_month" ] }, { "cell_type": "markdown", "id": "7caad472", "metadata": {}, "source": [ "Next, we append `Dec` as the negative of the sum of all other months." ] }, { "cell_type": "code", "execution_count": 72, "id": "eeac39db", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.843459Z", "iopub.status.busy": "2024-06-04T23:19:11.843230Z", "iopub.status.idle": "2024-06-04T23:19:11.850225Z", "shell.execute_reply": "2024-06-04T23:19:11.849688Z" } }, "outputs": [ { "data": { "text/plain": [ "mnth[Jan] -46.0871\n", "mnth[Feb] -39.2419\n", "mnth[March] -29.5357\n", "mnth[April] -4.6622\n", "mnth[May] 26.4700\n", "mnth[June] 21.7317\n", "mnth[July] -0.7626\n", "mnth[Aug] 7.1560\n", "mnth[Sept] 20.5912\n", "mnth[Oct] 29.7472\n", "mnth[Nov] 14.2229\n", "mnth[Dec] 0.3705\n", "dtype: float64" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "months = Bike['mnth'].dtype.categories\n", "coef_month = pd.concat([\n", " coef_month,\n", " pd.Series([-coef_month.sum()],\n", " index=['mnth[Dec]'\n", " ])\n", " ])\n", "coef_month" ] }, { "cell_type": "markdown", "id": "55a5ff99", "metadata": {}, "source": [ "Finally, to make the plot neater, we’ll just use the first letter of each month, which is the $6$th entry of each of\n", "the labels in the index." ] }, { "cell_type": "code", "execution_count": 73, "id": "e86a3652", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.853511Z", "iopub.status.busy": "2024-06-04T23:19:11.853047Z", "iopub.status.idle": "2024-06-04T23:19:11.977554Z", "shell.execute_reply": "2024-06-04T23:19:11.976958Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_month, ax_month = subplots(figsize=(8,8))\n", "x_month = np.arange(coef_month.shape[0])\n", "ax_month.plot(x_month, coef_month, marker='o', ms=10)\n", "ax_month.set_xticks(x_month)\n", "ax_month.set_xticklabels([l[5] for l in coef_month.index], fontsize=20)\n", "ax_month.set_xlabel('Month', fontsize=20)\n", "ax_month.set_ylabel('Coefficient', fontsize=20);" ] }, { "cell_type": "markdown", "id": "6c68761a", "metadata": {}, "source": [ "Reproducing the right-hand plot in Figure~\\ref{Ch4:bikeshare} follows a similar process." ] }, { "cell_type": "code", "execution_count": 74, "id": "5abb32ed", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.980369Z", "iopub.status.busy": "2024-06-04T23:19:11.980198Z", "iopub.status.idle": "2024-06-04T23:19:11.985705Z", "shell.execute_reply": "2024-06-04T23:19:11.984785Z" } }, "outputs": [], "source": [ "coef_hr = S2[S2.index.str.contains('hr')]['coef']\n", "coef_hr = coef_hr.reindex(['hr[{0}]'.format(h) for h in range(23)])\n", "coef_hr = pd.concat([coef_hr,\n", " pd.Series([-coef_hr.sum()], index=['hr[23]'])\n", " ])" ] }, { "cell_type": "markdown", "id": "bc51083b", "metadata": {}, "source": [ "We now make the hour plot." ] }, { "cell_type": "code", "execution_count": 75, "id": "0f5698be", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:11.989339Z", "iopub.status.busy": "2024-06-04T23:19:11.988415Z", "iopub.status.idle": "2024-06-04T23:19:12.111821Z", "shell.execute_reply": "2024-06-04T23:19:12.111533Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_hr, ax_hr = subplots(figsize=(8,8))\n", "x_hr = np.arange(coef_hr.shape[0])\n", "ax_hr.plot(x_hr, coef_hr, marker='o', ms=10)\n", "ax_hr.set_xticks(x_hr[::2])\n", "ax_hr.set_xticklabels(range(24)[::2], fontsize=20)\n", "ax_hr.set_xlabel('Hour', fontsize=20)\n", "ax_hr.set_ylabel('Coefficient', fontsize=20);" ] }, { "cell_type": "markdown", "id": "c43958c3", "metadata": {}, "source": [ "### Poisson Regression\n", "\n", "Now we fit instead a Poisson regression model to the\n", "`Bikeshare` data. Very little changes, except that we now use the\n", "function `sm.GLM()` with the Poisson family specified:" ] }, { "cell_type": "code", "execution_count": 76, "id": "1262ac4f", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:12.113270Z", "iopub.status.busy": "2024-06-04T23:19:12.113151Z", "iopub.status.idle": "2024-06-04T23:19:12.187994Z", "shell.execute_reply": "2024-06-04T23:19:12.187097Z" } }, "outputs": [], "source": [ "M_pois = sm.GLM(Y, X2, family=sm.families.Poisson()).fit()" ] }, { "cell_type": "markdown", "id": "8552fb8b", "metadata": {}, "source": [ "We can plot the coefficients associated with `mnth` and `hr`, in order to reproduce Figure~\\ref{Ch4:bikeshare.pois}. We first complete these coefficients as before." ] }, { "cell_type": "code", "execution_count": 77, "id": "feeea491", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:12.191417Z", "iopub.status.busy": "2024-06-04T23:19:12.191189Z", "iopub.status.idle": "2024-06-04T23:19:12.211795Z", "shell.execute_reply": "2024-06-04T23:19:12.211208Z" } }, "outputs": [], "source": [ "S_pois = summarize(M_pois)\n", "coef_month = S_pois[S_pois.index.str.contains('mnth')]['coef']\n", "coef_month = pd.concat([coef_month,\n", " pd.Series([-coef_month.sum()],\n", " index=['mnth[Dec]'])])\n", "coef_hr = S_pois[S_pois.index.str.contains('hr')]['coef']\n", "coef_hr = pd.concat([coef_hr,\n", " pd.Series([-coef_hr.sum()],\n", " index=['hr[23]'])])" ] }, { "cell_type": "markdown", "id": "a52b9a03", "metadata": {}, "source": [ "The plotting is as before." ] }, { "cell_type": "code", "execution_count": 78, "id": "09926adc", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:12.215056Z", "iopub.status.busy": "2024-06-04T23:19:12.214817Z", "iopub.status.idle": "2024-06-04T23:19:12.405617Z", "shell.execute_reply": "2024-06-04T23:19:12.405120Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_pois, (ax_month, ax_hr) = subplots(1, 2, figsize=(16,8))\n", "ax_month.plot(x_month, coef_month, marker='o', ms=10)\n", "ax_month.set_xticks(x_month)\n", "ax_month.set_xticklabels([l[5] for l in coef_month.index], fontsize=20)\n", "ax_month.set_xlabel('Month', fontsize=20)\n", "ax_month.set_ylabel('Coefficient', fontsize=20)\n", "ax_hr.plot(x_hr, coef_hr, marker='o', ms=10)\n", "ax_hr.set_xticklabels(range(24)[::2], fontsize=20)\n", "ax_hr.set_xlabel('Hour', fontsize=20)\n", "ax_hr.set_ylabel('Coefficient', fontsize=20);" ] }, { "cell_type": "markdown", "id": "812fed8c", "metadata": {}, "source": [ "We compare the fitted values of the two models.\n", "The fitted values are stored in the `fittedvalues` attribute\n", "returned by the `fit()` method for both the linear regression and the Poisson\n", "fits. The linear predictors are stored as the attribute `lin_pred`." ] }, { "cell_type": "code", "execution_count": 79, "id": "bf9e9f1d", "metadata": { "execution": { "iopub.execute_input": "2024-06-04T23:19:12.409134Z", "iopub.status.busy": "2024-06-04T23:19:12.408900Z", "iopub.status.idle": "2024-06-04T23:19:12.505338Z", "shell.execute_reply": "2024-06-04T23:19:12.505080Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = subplots(figsize=(8, 8))\n", "ax.scatter(M2_lm.fittedvalues,\n", " M_pois.fittedvalues,\n", " s=20)\n", "ax.set_xlabel('Linear Regression Fit', fontsize=20)\n", "ax.set_ylabel('Poisson Regression Fit', fontsize=20)\n", "ax.axline([0,0], c='black', linewidth=3,\n", " linestyle='--', slope=1);" ] }, { "cell_type": "markdown", "id": "dc683c95", "metadata": {}, "source": [ "The predictions from the Poisson regression model are correlated with\n", "those from the linear model; however, the former are non-negative. As\n", "a result the Poisson regression predictions tend to be larger than\n", "those from the linear model for either very low or very high levels of\n", "ridership.\n", "\n", "In this section, we fit Poisson regression models using the `sm.GLM()` function with the argument\n", "`family=sm.families.Poisson()`. Earlier in this lab we used the `sm.GLM()` function\n", "with `family=sm.families.Binomial()` to perform logistic regression. Other\n", "choices for the `family` argument can be used to fit other types\n", "of GLMs. For instance, `family=sm.families.Gamma()` fits a Gamma regression\n", "model." ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "-all", "formats": "Rmd,ipynb", "main_language": "python" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }