{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Regression"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"What function we use to estimate a relationship between $y$ and the regressor(s) depends on the data that we have. As practice using multiple x-variables, let's simulate a dataset that is generated by the following equation\n",
"$$\n",
"y = 4 + 0.5 x + 3 x^2 + u\n",
"$$\n",
"\n",
"The relationship between $y$ and $x$ in the above equation is said to be *nonlinear* in $x$."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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y
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x
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x2
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0
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15.159244
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4.006576
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4
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"text/plain": [
" y x x2\n",
"0 15.159244 1.764052 3.111881\n",
"1 4.006576 0.400157 0.160126\n",
"2 6.727911 0.978738 0.957928\n",
"3 20.669952 2.240893 5.021602\n",
"4 14.810536 1.867558 3.487773"
]
},
"execution_count": 1,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import seaborn as sns\n",
"import statsmodels.formula.api as smf\n",
"\n",
"np.random.seed(0)\n",
"\n",
"df = pd.DataFrame(columns=['y', 'x', 'x2'])\n",
"df['x'] = np.random.normal(0, 1, 100)\n",
"df['x2'] = df['x'] ** 2\n",
"df['y'] = 4 + 0.5 * df['x'] + 3 * df['x2'] + np.random.normal(0, 0.5, 100)\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"Note that to square column `'x'` to produce `'x2'`, all we need to do is type `df2['x'] ** 2` since `**` is the command for exponentiation.\n",
"\n",
"Next, plot a relationship between just `y` and `x`, assuming a linear fit."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {
},
"output_type": "execute_result"
},
{
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",
"text/plain": [
"
"
]
},
"execution_count": 2,
"metadata": {
"image/png": {
"height": 351,
"width": 352
},
"needs_background": "light"
},
"output_type": "execute_result"
}
],
"source": [
"sns.lmplot(x='x', y='y', data=df)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"The estimated straight line gets things horribly wrong! The line is pretty far away from a lot of the actual data points.\n",
"\n",
"The scatter plot of the data above makes clear that the data demonstrates a non-linear relationship.\n",
"\n",
"What we ought do to is fit a line given by\n",
"$$\n",
"\\hat{y} = c + \\hat{\\beta}_1 x + \\hat{\\beta}_2 x^2\n",
"$$\n",
"\n",
"where there are two beta coefficients. One for $x$, and one for $x^2$."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: y R-squared: 0.983\n",
"Model: OLS Adj. R-squared: 0.983\n",
"Method: Least Squares F-statistic: 2885.\n",
"Date: Sun, 26 Sep 2021 Prob (F-statistic): 3.91e-87\n",
"Time: 19:42:50 Log-Likelihood: -75.005\n",
"No. Observations: 100 AIC: 156.0\n",
"Df Residuals: 97 BIC: 163.8\n",
"Df Model: 2 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept 4.0714 0.066 61.584 0.000 3.940 4.203\n",
"x 0.5615 0.052 10.829 0.000 0.459 0.664\n",
"x2 2.9666 0.040 73.780 0.000 2.887 3.046\n",
"==============================================================================\n",
"Omnibus: 7.876 Durbin-Watson: 2.003\n",
"Prob(Omnibus): 0.019 Jarque-Bera (JB): 3.580\n",
"Skew: 0.188 Prob(JB): 0.167\n",
"Kurtosis: 2.152 Cond. No. 2.47\n",
"==============================================================================\n",
"\n",
"Notes:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
]
}
],
"source": [
"model = smf.ols('y ~ x + x2', data=df).fit()\n",
"print(model.summary())"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"The variable `model2` stores a lot of data. Beyond holding summary output for the performance of the regression (which we've accessed via the `model2.summary()` command), we can reference the estimated parameters directly via `.params`. For example:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Intercept: 4.07135075409863\n",
"beta for x: 0.5615154693913419\n",
"beta for x2: 2.966624223933464\n"
]
}
],
"source": [
"print('Intercept: ', model.params['Intercept'])\n",
"print('beta for x:', model.params['x'])\n",
"print('beta for x2:', model.params['x2'])"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"As an aside, the fact that we're using square brackets to reference items inside of `squared.params` is a clue that the `.params` component of the variable `squared` was built using a dictionary-like structure.\n",
"\n",
"One way to tell that the estimates of `squared` are better than the estimates of `straight` is to look at the `R-squared` value in the summary output. This measure takes a value between 0 and 1, with a score of 1 indicating perfect fit. For comparison purposes, consider the linear fit model below:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: y R-squared: 0.056\n",
"Model: OLS Adj. R-squared: 0.046\n",
"Method: Least Squares F-statistic: 5.767\n",
"Date: Sun, 26 Sep 2021 Prob (F-statistic): 0.0182\n",
"Time: 19:45:33 Log-Likelihood: -277.26\n",
"No. Observations: 100 AIC: 558.5\n",
"Df Residuals: 98 BIC: 563.7\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept 7.0734 0.392 18.054 0.000 6.296 7.851\n",
"x 0.9318 0.388 2.401 0.018 0.162 1.702\n",
"==============================================================================\n",
"Omnibus: 49.717 Durbin-Watson: 1.848\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 128.463\n",
"Skew: 1.877 Prob(JB): 1.27e-28\n",
"Kurtosis: 7.091 Cond. No. 1.06\n",
"==============================================================================\n",
"\n",
"Notes:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
]
}
],
"source": [
"model_linear = smf.ols('y ~ x', data=df).fit()\n",
"print(model_linear.summary())"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"The linear-fit model produced an R-squared of 0.056 while the quadratic-fit model yielded a R-squared of 0.983.\n",
"\n",
"Another informative way to jude a modeled relationship is by plotting the **residuals**. The residuals are the \"un-expected\" part of the equation. For example, in the linear-fit model, the residual is defined as\n",
"$$\n",
"\\hat{u} := y - \\hat{y} = y - \\hat{c} - \\hat{\\beta} x\n",
"$$\n",
"and in the quadratic-fit model the residual, $\\hat{u}$, is given by\n",
"$$\n",
"\\hat{u} := y - \\hat{y} = y- \\hat{c} - \\hat{\\beta}_1 x - \\hat{\\beta}_2 x^2\n",
"$$\n",
"Using the information in `.params`, we can calculate residuals."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"df['resid'] = model.resid\n",
"df['resid_linear'] = model_linear.resid"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"Next, plot the two sets of residuals."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
"
"
]
},
"execution_count": 8,
"metadata": {
"image/png": {
"height": 424,
"width": 717
},
"needs_background": "light"
},
"output_type": "execute_result"
}
],
"source": [
"sns.scatterplot(x='x', y='resid_linear', data=df)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"In the straight-line model, we can see that the errors have a noticeable pattern to them. This is an indication that a more complicated function of $x$ would be a better description for the relationship between $x$ and $y$."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"
"
]
},
"execution_count": 9,
"metadata": {
"image/png": {
"height": 424,
"width": 728
},
"needs_background": "light"
},
"output_type": "execute_result"
}
],
"source": [
"sns.scatterplot(x='x', y='resid', data=df)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"In comparison, the residuals from the squared model look more random. Additionally, they're substantially smaller on average, with almost all residuals having an absolute value less than one. This indicates a much better fit than the straight-line model in which the residual values were often much larger."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### Looking Beyond OLS\n",
"\n",
"OLS works well when the $y$ variable in our model is a linear combination of $x$ variables. Note that the relationship between $y$ and a given regressor may be nonlinear, as in the case of $y$ being a function of $x$ and $x^2$. However, while we may say that $y$ is a nonlinear function of $x$ in this case, the variable $y$ is still a linear function of $x$ and $x^2$. To clarify:\n",
"$$\n",
"y = \\alpha + \\beta x + u\n",
"$$\n",
"is linear in $x$. Likewise:\n",
"$$\n",
"y = \\alpha + \\beta_1 x + \\beta_2 x^2 + u\n",
"$$\n",
"is linear in $x$ and $x^2$. In contrast, the function\n",
"$$\n",
"y = \\frac{e^{\\alpha + \\beta x + u}}{1 + e^{\\alpha + \\beta x + u}}\n",
"$$ is *nonlinear*. This last equation may look terrifyingly unnatural, but it's actually very useful. Let's get a sense of what the equation looks like by plotting the function\n",
"$$\n",
"y = \\frac{e^{x}}{1 + e^{x}}.\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" x y\n",
"0 2 0.880797\n",
"1 5 0.993307\n",
"2 -10 0.000045\n",
"3 -7 0.000911\n",
"4 -7 0.000911\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"
"
]
},
"execution_count": 10,
"metadata": {
"image/png": {
"height": 424,
"width": 720
},
"needs_background": "light"
},
"output_type": "execute_result"
}
],
"source": [
"np.random.seed(0)\n",
"curve = pd.DataFrame(columns=['x','y'])\n",
"curve['x'] = np.random.randint(low=-10, high=10, size=100)\n",
"curve['y'] = np.exp(curve['x']) / (1 + np.exp(curve['x']))\n",
"print(curve.head())\n",
"sns.lineplot(x='x', y='y', data=curve)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"The function $y = e^{x}/(1+e^{x})$ creates an S-curve with a lower bound of $0$ and an upper bound of $1$.\n",
"\n",
"These bounds are useful in analytics. Often, our task is to estimate probabilities. For instance, what is the likelihood that a borrower defaults on their mortgage, the likelihood that a credit card transaction is fraudulent, or the likelihood that a company will violate its capital expenditure covenant on an outstanding loan? All of these questions require us to estimate a probability. The above function is useful because it considers a situation in which the $y$ variable is necessarily between $0$ and $1$ (i.e. $0\\%$ probability and $100\\%$ probability).\n",
"\n",
"Suppose that we instead took the `curve` data above and tried to fit it with linear regression."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {
},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
"
"
]
},
"execution_count": 11,
"metadata": {
"image/png": {
"height": 351,
"width": 352
},
"needs_background": "light"
},
"output_type": "execute_result"
}
],
"source": [
"sns.lmplot(x='x', y='y', data=curve)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"Note that in the above plot, there are estimated \"probabilities\" (the $\\hat{y}$ values) that are either lower than $0$ or higher than $1$. This is statistically impossible.\n",
"\n",
"That fancy S-shaped function above is called the *inverse logit* function. That is because $e^x / (1+e^x)$ is the inverse of the *logit* function given by $log(x / (1-x)$. Just like we can invert the equation $y = f(x)$ to get $f^{-1}(y) = x$, the inverse of $y = e^x / (1+e^x)$ is given by $log(y / (1-y)) = x$.\n",
"\n",
"When we model probabilities, the $y$ variable will be either $0$ or $1$ for any observations. Observations where the event occurred are recorded with $y=1$. For instance, in a dataset about mortgage default, those borrowers who default on their mortgage would have $y=1$ and everyone else would have $y=0$.\n",
"\n",
"Suppose that we estimate a model given by\n",
"$$\n",
"log\\Big(\\frac{y}{1-y}\\Big) = \\alpha + \\beta x + u\n",
"$$.\n",
"Then, the estimated value $\\hat{\\alpha} + \\hat{\\beta}x$ for a given observation would be $log(\\hat{y}/(1-\\hat{y}))$. This is what we refer to as the *log odds ratio*. The odds ratio is the probability that $y$ equals $1$ divided by the probability that $y$ equals $0$; this is what $\\hat{y}/(1-\\hat{y})$ tells us. Ultimately, our estimate for $\\hat{y}$ then tells us the likelihood that the true value for $y$ is equal to $1$.\n",
"\n",
"This type of model is called a logistic regression model. Let's simulate some data."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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7.963573
\n",
"
\n",
"
\n",
"
4
\n",
"
3.867558
\n",
"
1
\n",
"
6.470232
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" x y xb\n",
"0 3.764052 1 6.056209\n",
"1 2.400157 0 0.600629\n",
"2 2.978738 1 2.914952\n",
"3 4.240893 1 7.963573\n",
"4 3.867558 1 6.470232"
]
},
"execution_count": 12,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"np.random.seed(0)\n",
"df2 = pd.DataFrame(columns=['x', 'y'])\n",
"df2['x'] = np.random.normal(2, 1, 1000)\n",
"df2['xb'] = -9 + 4 * df2['x']\n",
"df2['y'] = np.random.binomial(n=1, p= np.exp(df2['xb']) / (1+np.exp(df2['xb'])) )\n",
"df2.head()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"Now try fitting a model using linear regression (ordinary least squares). When OLS is applied to a $y$ variable that only takes value 0 or 1, the model is referred to as a linear probability model (LPM)."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: y R-squared: 0.514\n",
"Model: OLS Adj. R-squared: 0.514\n",
"Method: Least Squares F-statistic: 1056.\n",
"Date: Sun, 26 Sep 2021 Prob (F-statistic): 1.41e-158\n",
"Time: 19:59:38 Log-Likelihood: -346.17\n",
"No. Observations: 1000 AIC: 696.3\n",
"Df Residuals: 998 BIC: 706.2\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept -0.2928 0.024 -12.187 0.000 -0.340 -0.246\n",
"x 0.3564 0.011 32.493 0.000 0.335 0.378\n",
"==============================================================================\n",
"Omnibus: 113.684 Durbin-Watson: 2.045\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 37.844\n",
"Skew: 0.207 Prob(JB): 6.06e-09\n",
"Kurtosis: 2.142 Cond. No. 5.70\n",
"==============================================================================\n",
"\n",
"Notes:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
]
}
],
"source": [
"lpm = smf.ols('y ~ x', data=df2).fit()\n",
"print(lpm.summary())"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"Now fit the model using logistic regression."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 0.292801\n",
" Iterations 8\n",
" Logit Regression Results \n",
"==============================================================================\n",
"Dep. Variable: y No. Observations: 1000\n",
"Model: Logit Df Residuals: 998\n",
"Method: MLE Df Model: 1\n",
"Date: Sun, 26 Sep 2021 Pseudo R-squ.: 0.5660\n",
"Time: 20:00:42 Log-Likelihood: -292.80\n",
"converged: True LL-Null: -674.60\n",
"Covariance Type: nonrobust LLR p-value: 4.432e-168\n",
"==============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept -8.5975 0.567 -15.154 0.000 -9.709 -7.486\n",
"x 3.8987 0.259 15.062 0.000 3.391 4.406\n",
"==============================================================================\n"
]
}
],
"source": [
"logit = smf.logit('y ~ x', data=df2).fit()\n",
"print(logit.summary())"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"The estimated parameters (intercept and $\\beta$ coefficient) are much closer to their true value using logistic regression. While popular, linear probability models *do not* often give meaningful estimates. This is especially true when outcomes are rare (meaning most $y$ values are either 0 or 1, and there is not a relatively even balance between the two)."
]
}
],
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