{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
" \n",
"\n",
"# Regression interpretation\n",
"\n",
"Let's consider how adjustment works in regression by considering a so called ANCOVA (analysis of covariance) setting. Imagine, there's treatment variable that we're ineterested in, $T_i$, and a regression variable that we have to adjust for, $X_i$. Consider this specific variation of this setting: \n",
"\n",
"$$\n",
"Y_i = \\beta_0 + \\beta_1 X_i + \\beta_2 T_i + \\epsilon_i\n",
"$$\n",
"\n",
"To tie ourselves down with a context, consider $Y_i$ is blood pressure, $T_i$ is a medication and $X_i$ is BMI. Let's look at different settings that could arise using plots.\n",
"\n",
"Since I'm going to be making the same plot over and over, I defined a function that\n",
"\n",
"1. fit the ANCOVA model using sklearn\n",
"2. plotted the data as $X$ versus $Y$ with orange versus blue for treated versus not\n",
"3. added the fitted ANCOVA lines plus the marginal means (the means for each group disregarding $X$) as horizontal lines\n",
"\n",
"Note, the adjusted estimated treatment effect is the difference between the two parallel sloped lines. The unadjusted estimated treatment effect is the difference between the two horizontal lines. Let's look at how adjustment changes things depending on the setting. First we'll do our imports and then define a function that will make our plot for us and fit the ANCOVA model.\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import numpy as np\n",
"import pandas as pd\n",
"from sklearn.linear_model import LinearRegression\n",
"import copy\n",
"\n",
"sns.set()\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def myplot(x, y, t):\n",
" x1 = x[t == 1]\n",
" x0 = x[t == 0]\n",
" y1 = y[t == 1]\n",
" y0 = y[t == 0]\n",
" xm1 = np.mean(x1)\n",
" xm0 = np.mean(x0)\n",
" ym1 = np.mean(y1)\n",
" ym0 = np.mean(y0)\n",
"\n",
" X = np.array([x, t]).transpose()\n",
" out = LinearRegression().fit(X, y)\n",
" b0hat = out.intercept_\n",
" b1hat = out.coef_[0]\n",
" b2hat = out.coef_[1]\n",
" \n",
" plt.scatter(x0, y0)\n",
" plt.scatter(x1, y1)\n",
"\n",
" col = sns.color_palette()\n",
"\n",
" plt.axhline(y = ym0, c = col[0])\n",
" plt.axhline(y = ym1, c = col[1])\n",
"\n",
" xlim = [np.min(x), np.max(x)]\n",
"\n",
" ylim0 = [z * b1hat + b0hat + b2hat for z in xlim]\n",
" ylim1 = [z * b1hat + b0hat for z in xlim]\n",
"\n",
" plt.plot( xlim, ylim1)\n",
" plt.plot( xlim, ylim0) \n",
"\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's consider out model with $\\beta_0 = 0$, $\\beta_1 = 1$ and $\\beta_2 = 4$. So the treated have an intercept 4 units higher. Let's consider simulating from this model where the treatment is randomized."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 100\n",
"x = np.random.normal(size = n)\n",
"e = np.random.normal(size = n)\n",
"t = np.random.binomial(1, .5, n)\n",
"\n",
"beta0 = 0\n",
"beta1 = 1\n",
"beta2 = 4\n",
"\n",
"y = beta0 + beta1 * x + beta2 * t + e\n",
"\n",
"myplot(x, y, t)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that the marginal means (horizontal lines) are about 4 units appart, same as the lines. This is due to the randomization. A goal of randomization is to make our inference for the treatment unrelated to whether or not we adjust for the confounding variable ($X$). So, we get (up to random error) the ssame answer whether we adjust for $X$ or not. Let's consider a different setting."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"myplot(x + t * 4, y, t)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now notice that there is a large unadjusted difference (difference between the horizontal lines) whereas there is not much of a difference between the lines. That is, when adjusting for $X$, the relationship goes away. Of note, treatment assignment is highly related to the $X$ variable. Orange dots tend to have a larger $X$ value than the blue. Because of this, there's pratically no area of overlap between the orange and the blue to directly compare them. The adjusted model is all model, extrapolating the blue line up to the orange and the orange down to the blue assuming that they're parallel."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"myplot(x + t * 4, y - t * 4, t)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Above notice that the result is the reverse. There's little association marginally, but a large one when conditioning. Let's look at one final case."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"myplot(x + t * 6, y - t * 2, t)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Above things are even worse, the relationship has reversed itself. The marginal association is that the orange is above the blue whereas the conditional association is that the blue is above the orange. That is, if you fit the treatment model without $X$ you get one answer, and with $X$ you get the exact opposite answer! This is an example of so-called \"Simpsons paradox\". The \"paradox\" isn't that paradoxical. It simply says the relationship between two variables could reverse itself when factoring in another variable. Once again, note there's no overlap in the distributions."
]
}
],
"metadata": {
"interpreter": {
"hash": "625a8f875bfb3f569e4f618df17e1f8389970b6b26ee2c84acb92c5fbebf95c3"
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.13"
}
},
"nbformat": 4,
"nbformat_minor": 4
}