{ "cells": [ { "cell_type": "markdown", "id": "dramatic-illustration", "metadata": {}, "source": [ "(moderation_analysis)=\n", "# Bayesian moderation analysis\n", "\n", ":::{post} March, 2022\n", ":tags: moderation, path analysis, \n", ":category: beginner\n", ":author: Benjamin T. Vincent\n", ":::\n", "\n", "This notebook covers Bayesian [moderation analysis](https://en.wikipedia.org/wiki/Moderation_(statistics)). This is appropriate when we believe that one predictor variable (the moderator) may influence the linear relationship between another predictor variable and an outcome. Here we look at an example where we look at the relationship between hours of training and muscle mass, where it may be that age (the moderating variable) affects this relationship.\n", "\n", "This is not intended as a one-stop solution to a wide variety of data analysis problems, rather, it is intended as an educational exposition to show how moderation analysis works and how to conduct Bayesian parameter estimation in PyMC.\n", "\n", "Note that this is sometimes mixed up with [mediation analysis](https://en.wikipedia.org/wiki/Mediation_(statistics)). Mediation analysis is appropriate when we believe the effect of a predictor variable upon an outcome variable is (partially, or fully) mediated through a 3rd mediating variable. Readers are referred to the textbook by {cite:t}hayes2017introduction as a comprehensive (albeit Frequentist) guide to moderation and related models as well as the PyMC example {ref}mediation_analysis." ] }, { "cell_type": "code", "execution_count": 1, "id": "characteristic-eight", "metadata": {}, "outputs": [], "source": [ "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import pymc as pm\n", "import xarray as xr\n", "\n", "from matplotlib.cm import ScalarMappable\n", "from matplotlib.colors import Normalize" ] }, { "cell_type": "code", "execution_count": 2, "id": "collaborative-product", "metadata": {}, "outputs": [], "source": [ "az.style.use(\"arviz-darkgrid\")\n", "%config InlineBackend.figure_format = 'retina'" ] }, { "cell_type": "markdown", "id": "split-staff", "metadata": {}, "source": [ "First in the (hidden) code cell below, we define some helper functions for plotting that we will use later." ] }, { "cell_type": "code", "execution_count": 3, "id": "strange-touch", "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "def make_scalarMap(m):\n", " \"\"\"Create a Matplotlib ScalarMappable so we can use a consistent colormap across both data points and posterior predictive lines. We can use scalarMap.cmap to use as a colormap, and scalarMap.to_rgba(moderator_value) to grab a colour for a given moderator value.\"\"\"\n", " return ScalarMappable(norm=Normalize(vmin=np.min(m), vmax=np.max(m)), cmap=\"viridis\")\n", "\n", "\n", "def plot_data(x, moderator, y, ax=None):\n", " if ax is None:\n", " fig, ax = plt.subplots(1, 1)\n", " else:\n", " fig = plt.gcf()\n", "\n", " h = ax.scatter(x, y, c=moderator, cmap=scalarMap.cmap)\n", " ax.set(xlabel=\"x\", ylabel=\"y\")\n", " # colourbar for moderator\n", " cbar = fig.colorbar(h)\n", " cbar.ax.set_ylabel(\"moderator\")\n", " return ax\n", "\n", "\n", "def posterior_prediction_plot(result, x, moderator, m_quantiles, ax=None):\n", " \"\"\"Plot posterior predicted y\"\"\"\n", " if ax is None:\n", " fig, ax = plt.subplots(1, 1)\n", "\n", " post = az.extract(result)\n", " xi = xr.DataArray(np.linspace(np.min(x), np.max(x), 20), dims=[\"x_plot\"])\n", " m_levels = result.constant_data[\"m\"].quantile(m_quantiles).rename({\"quantile\": \"m_level\"})\n", "\n", " for p, m in zip(m_quantiles, m_levels):\n", " y = post.β0 + post.β1 * xi + post.β2 * xi * m + post.β3 * m\n", " region = y.quantile([0.025, 0.5, 0.975], dim=\"sample\")\n", " ax.fill_between(\n", " xi,\n", " region.sel(quantile=0.025),\n", " region.sel(quantile=0.975),\n", " alpha=0.2,\n", " color=scalarMap.to_rgba(m),\n", " edgecolor=\"w\",\n", " )\n", " ax.plot(\n", " xi,\n", " region.sel(quantile=0.5),\n", " color=scalarMap.to_rgba(m),\n", " linewidth=2,\n", " label=f\"{p*100}th percentile of moderator\",\n", " )\n", "\n", " ax.legend(fontsize=9)\n", " ax.set(xlabel=\"x\", ylabel=\"y\")\n", " return ax\n", "\n", "\n", "def plot_moderation_effect(result, m, m_quantiles, ax=None):\n", " \"\"\"Spotlight graph\"\"\"\n", "\n", " if ax is None:\n", " fig, ax = plt.subplots(1, 1)\n", "\n", " post = az.extract(result)\n", "\n", " # calculate 95% CI region and median\n", " xi = xr.DataArray(np.linspace(np.min(m), np.max(m), 20), dims=[\"x_plot\"])\n", " rate = post.β1 + post.β2 * xi\n", " region = rate.quantile([0.025, 0.5, 0.975], dim=\"sample\")\n", "\n", " ax.fill_between(\n", " xi,\n", " region.sel(quantile=0.025),\n", " region.sel(quantile=0.975),\n", " alpha=0.2,\n", " color=\"k\",\n", " edgecolor=\"w\",\n", " )\n", "\n", " ax.plot(xi, region.sel(quantile=0.5), color=\"k\", linewidth=2)\n", "\n", " # plot points at each percentile of m\n", " percentile_list = np.array(m_quantiles) * 100\n", " m_levels = np.percentile(m, percentile_list)\n", " for p, m in zip(percentile_list, m_levels):\n", " ax.plot(\n", " m,\n", " np.mean(post.β1) + np.mean(post.β2) * m,\n", " \"o\",\n", " c=scalarMap.to_rgba(m),\n", " markersize=10,\n", " label=f\"{p}th percentile of moderator\",\n", " )\n", "\n", " ax.legend(fontsize=9)\n", "\n", " ax.set(\n", " title=\"Spotlight graph\",\n", " xlabel=\"$moderator$\",\n", " ylabel=r\"$\\beta_1 + \\beta_2 \\cdot moderator$\",\n", " )" ] }, { "cell_type": "markdown", "id": "light-trustee", "metadata": {}, "source": [ "# Does the effect of training upon muscularity decrease with age?\n", "\n", "I've taken inspiration from a blog post {cite:t}vandenbergSPSS which examines whether age influences (moderates) the effect of training on muscle percentage. We might speculate that more training results in higher muscle mass, at least for younger people. But it might be the case that the relationship between training and muscle mass changes with age - perhaps training is less effective at increasing muscle mass in older age?\n", "\n", "The schematic box and arrow notation often used to represent moderation is shown by an arrow from the moderating variable to the line between a predictor and an outcome variable.\n", "\n", "![](moderation_figure.png)\n", "\n", "It can be useful to use consistent notation, so we will define:\n", "- $x$ as the main predictor variable. In this example it is training.\n", "- $y$ as the outcome variable. In this example it is muscle percentage.\n", "- $m$ as the moderator. In this example it is age.\n", "\n", "## The moderation model\n", "\n", "While the visual schematic (above) is a useful shorthand to understand complex models when you already know what moderation is, you can't derive it from the diagram alone. So let us formally specify the moderation model - it defines an outcome variable $y$ as:\n", "\n", "$$\n", "y \\sim \\mathrm{Normal}(\\beta_0 + \\beta_1 \\cdot x + \\beta_2 \\cdot x \\cdot m + \\beta_3 \\cdot m, \\sigma^2)\n", "$$\n", "\n", "where $y$, $x$, and $m$ are your observed data, and the following are the model parameters:\n", "- $\\beta_0$ is the intercept, its value does not have that much importance in the interpretation of this model.\n", "- $\\beta_1$ is the rate at which $y$ (muscle percentage) increases per unit of $x$ (training hours). \n", "- $\\beta_2$ is the coefficient for the interaction term $x \\cdot m$.\n", "- $\\beta_3$ is the rate at which $y$ (muscle percentage) increases per unit of $m$ (age). \n", "- $\\sigma$ is the standard deviation of the observation noise.\n", "\n", "We can see that the mean $y$ is simply a multiple linear regression with an interaction term between the two predictors, $x$ and $m$. \n", "\n", "We can get some insight into why this is the case by thinking about this as a multiple linear regression with $x$ and $m$ as predictor variables, but where the value of $m$ influences the relationship between $x$ and $y$. This is achieved by making the regression coefficient for $x$ is a function of $m$:\n", "\n", "$$\n", "y \\sim \\mathrm{Normal}(\\beta_0 + f(m) \\cdot x + \\beta_3 \\cdot m, \\sigma^2)\n", "$$\n", "\n", "and if we define that as a linear function, $f(m) = \\beta_1 + \\beta_2 \\cdot m$, we get\n", "\n", "$$\n", "y \\sim \\mathrm{Normal}(\\beta_0 + (\\beta_1 + \\beta_2 \\cdot m) \\cdot x + \\beta_3 \\cdot m, \\sigma^2)\n", "$$\n", "\n", "We can use $f(m) = \\beta_1 + \\beta_2 \\cdot m$ later to visualise the moderation effect." ] }, { "cell_type": "markdown", "id": "weighted-announcement", "metadata": {}, "source": [ "## Import data\n", "First, we will load up our example data and do some basic data visualisation. The dataset is taken from {cite:t}vandenbergSPSS but it is unclear if this corresponds to real life research data or if it was simulated." ] }, { "cell_type": "code", "execution_count": 4, "id": "prime-construction", "metadata": {}, "outputs": [], "source": [ "def load_data():\n", " try:\n", " df = pd.read_csv(\"../data/muscle-percent-males-interaction.csv\")\n", " except:\n", " df = pd.read_csv(pm.get_data(\"muscle-percent-males-interaction.csv\"))\n", "\n", " x = df[\"thours\"].values\n", " m = df[\"age\"].values\n", " y = df[\"mperc\"].values\n", " return (x, y, m)\n", "\n", "\n", "x, y, m = load_data()\n", "\n", "# Make a scalar color map for this dataset (Just for plotting, nothing to do with inference)\n", "scalarMap = make_scalarMap(m)" ] }, { "cell_type": "code", "execution_count": 5, "id": "pretty-croatia", "metadata": {}, "outputs": [ { "data": { "image/png": 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