{ "cells": [ { "cell_type": "markdown", "id": "cd65bf6e-6f46-4eb8-8f3d-be890621d559", "metadata": { "tags": [] }, "source": [ "# Multivariate regression\n", "\n", "*Goal:* Find a relationship that explains variable $y$ in terms of variables, $x_1, x_2, x_3$,...$x_n$" ] }, { "cell_type": "code", "execution_count": 20, "id": "7d82b49e-cc9f-4413-9927-2cd994cdbab9", "metadata": { "tags": [ "remove-input" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import statsmodels.formula.api as sm\n", "from matplotlib import cm\n", "\n", "np.random.seed(232)\n", "x = np.random.normal(6, 3, 100)\n", "y = -np.random.normal(3, 1, 100)\n", "z = 20 + 2*x + 3*y + np.random.normal(0, 2, 100)\n", "\n", "fig = plt.figure(figsize=(7, 7))\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.set_proj_type('persp')\n", "\n", "x_surf = np.arange(0, np.max(x), 0.1)\n", "y_surf = np.arange(np.min(y), 0, 0.1)\n", "x_surf, y_surf = np.meshgrid(x_surf, y_surf)\n", "\n", "z_surf = 20 + 2*x_surf + 3*y_surf\n", "\n", "ax.plot_surface(x_surf, y_surf,\n", " z_surf,\n", " rstride=1,\n", " cstride=1,\n", " alpha = 0.4)\n", "\n", "\n", "ax.scatter(x, y, z,\n", " c='blue',\n", " marker='o',\n", " alpha=1)\n", "\n", "ax.plot3D(x, 0*x, 20 + 2*x, color='darkgray')\n", "ax.plot3D(x*0, y, 20 + 3*y, color='darkgray')\n", "\n", "ax.plot3D(0, 0, 20, marker='o', color='k')\n", "ax.text3D(0, 0, 22, '$c_0$', color='k', fontsize=16)\n", "ax.text3D(9, 0, 41, '$c_1$', color='k', fontsize=16)\n", "ax.text3D(0, -4, 15, '$c_2$', color='k', fontsize=16)\n", "\n", "ax.set_xlabel('$x_1$', fontsize=18)\n", "ax.set_ylabel('$x_2$', fontsize=18)\n", "\n", "ax.set_xlim3d([0, 15])\n", "ax.set_ylim3d([-5, 0]);\n", "\n", "ax.set_zlabel('y', fontsize=18);\n", "ax.view_init(elev=20.);\n", "ax.set_box_aspect(aspect=None, zoom=0.9);" ] }, { "cell_type": "markdown", "id": "a4baef36-6f24-4716-a7a9-efae375eeed3", "metadata": { "tags": [] }, "source": [ "This three dimensional visualization shows how linear model based on two predictor variables, $x_1$ and $x_2$ can be used to model a response variable $y$. A constant and two slopes to define a 2D plane in 3D space with the equation\n", "\n", "$$y = c_0 + c_1 x_1 + c_2 x_2$$\n", "\n", "The sum of squared vertical distances between the model (plane) and observations of $y$ (dots) are minimized. Like fitting a line in 2D space, this procedure assumes the validity of a linear model.\n", "\n", "## Example: Model for aragonite saturation state based on three other oceanographic variables\n", "\n", "As a motivation for multiple linear regression, we consider a model for aragonite saturation state, $\\Omega_A$. The study by Juranek et al. (2009), discussed on greater detail below, uses multiple linear regression to model $\\Omega_A$ for surveys where it is not measured, using more commonly measured parameters. We know that $\\Omega_A$ depends on both physical and biological processes, so one candidate for a model might be:\n", "\n", "$y = c_0 + c_1x_1 + c_2x_2 + c_3x_3 $\n", "\n", "where $y$ = $\\Omega_A$\n", "\n", "$x_1$ = temperature\n", "\n", "$x_2$ = salinity\n", "\n", "$x_3$ = dissolved oxygen\n", "\n", "$k$ = 3 predictor variables\n", "\n", "$N$ = 1011 samples\n", "\n", "Because we have three predictor variables, it is hard to visualize in four-dimensional space. However, the same principles are involved as fitting a 1D line in 2D space, or a 2D plane in 3D space.\n", "\n", "## Equations for linear model\n", "\n", "A linear model can be represented as a system of $N$ equations.\n", "\n", "$$ c_0 + c_1x_{11} + c_2x_{12} + c_3x_{13} = \\hat{y}_1 + \\epsilon_1$$\n", "\n", "$$ c_0 + c_1x_{21} + c_2x_{22} + c_3x_{23} = \\hat{y}_2 + \\epsilon_2$$\n", "\n", "$$ c_0 + c_1x_{31} + c_2x_{32} + c_3x_{33} = \\hat{y}_3 + \\epsilon_3$$ \n", "\n", "$$ \\ldots $$\n", "\n", "$$ c_0 + c_1x_{N1} + c_2x_{N2} + c_3x_{N3} = \\hat{y}_N + \\epsilon_4$$\n", "\n", "where $\\hat{y}_i$ is a modeled value and $\\epsilon_i$ is the difference between the modeled value, $\\hat{y}_i$ and an observation $y_i$. The least squares regression minimizes the sum of $\\epsilon_i^2$, the overall deviation between the linear model and data.\n", "\n", "## Matrix form\n", "\n", "To solve a least squares problem numerically, it helps to write the system of equations for the model in matrix form.\n", "\n", "Form a vector $\\vec{y}$ of $N$ observations.\n", "\n", "$$ \\vec{y} = \\begin{bmatrix}\n", " y_1 \\\\\n", " y_2 \\\\\n", " y_3 \\\\\n", " \\vdots \\\\\n", " y_n \\\\\n", " \\end{bmatrix}$$\n", "\n", "A vector $\\vec{c}$ contains $k+1$ unknown coefficients.\n", "\n", "$$ \\vec{c} = \\begin{bmatrix}\n", " c_0 \\\\\n", " c_1 \\\\\n", " c_2 \\\\\n", " c_3 \\\\\n", " \\end{bmatrix}$$\n", "\n", "The predictor variables are stored as columns in a matrix with $N$ rows and $k+1$ columns\n", "\n", "$$\n", "\\textbf{X} = \\begin{bmatrix}\n", " 1 & x_{11} & x_{12} & x_{13} \\\\\n", " 1 & x_{21} & x_{22} & x_{23} \\\\\n", " 1 & x_{31} & x_{32} & x_{33} \\\\\n", " \\vdots & \\vdots & \\vdots & \\vdots \\\\\n", " 1 & x_{N1} & x_{N2} & x_{N3} \\\\\n", " \\end{bmatrix}$$\n", "\n", "Now the system of equations for the linear model can be written as\n", "\n", "$ X \\vec{c} = \\hat{y} $\n", "\n", "\n", "## Numerical solution\n", "\n", "The least squares problem is solved using a singular value decomposition method. Efficient alorithms for this procedure are typically included in scientfic computing software. In Python, create an array for the vector $\\vec{y}$ and a 2D array for the matrix $X$. Then use `np.linalg,lstsq` to solve for $c$.\n", "\n", "```python\n", "import numpy as np\n", "c = np.linalg.lstsq(X,y)\n", "```" ] }, { "cell_type": "markdown", "id": "11ab16cd-cb99-4e67-a39e-524ac104fb3e", "metadata": { "tags": [] }, "source": [ "## Testing for significance\n", "\n", "### F test \n", "\n", "Similar to ANOVA significance calculation, which also involves ratios of squared values.\n", "\n", "$$ \\hat{y} = c_0 + c_1x_1 + c_2x_2 + c_3x_3$$\n", "\n", "* $H_0 : \\hat{y} = c_0 $ (All non-constant coefficients are zero)\n", "\n", "* $H_1 :$ At least one coefficient is non-zero\n", "\n", "### Total sum of squares\n", "\n", "$$ SST =\\sum_{j=1}^N{(y_j - \\bar{y})^2}$$\n", "\n", "### Regression sum of squares\n", "\n", "$$ SSR =\\sum_{j=1}^N{(\\hat{y_j} - \\bar{y})^2}$$\n", "\n", "where $\\hat{y_j}$ are model values\n", "\n", "\n", "### Error sum of squares\n", "\n", "$$ SSE =\\sum_{j=1}^N{(y_i - \\hat{y})^2}$$\n", "\n", "### F-statistic\n", "\n", "Mean squares statistics, calculated by dividing by degrees of freedom:\n", "\n", "* $MST =\\frac{SST}{N-1}$\n", "\n", "* $MSR =\\frac{SSR}{k}$ , where k is the number of variables\n", "\n", "* $MSE = \\frac{SSE}{N-k-1}$\n", "\n", "$F = \\frac{MSR}{MSE}$\n", "\n", "This test statistic can be compared with a critical F value, which depends on significance level $\\alpha$ and the degrees of freedom in the numerator and denominator. If F is larger, then error is small. Find F using statistical tables, or `stats.f.ppf` in Python.\n" ] }, { "cell_type": "markdown", "id": "49c33a77-5d96-4d5f-a517-47823f5c3669", "metadata": { "tags": [] }, "source": [ "## Multiple regression example: modeling aragonite saturation state\n", "\n", "\n", "![images/arag_sat.png](images/arag_sat.png)\n", "\n", "*Source:* Feeley et al. (2208) Evidence for upwelling of corrosive acidification water onto the continental shelf, Science\n", "\n", "At Aragonite staturation state > 1 aragonite (calcium carbonate will dissolve in seawater)\n", "\n", "Is there a way to estimate aragonite saturation state $\\Omega_{Ar}$ based on more commonly measured parameters?\n", "\n", "$$\\Omega = \\frac{[Ca^{2+}][CO_3^{2-}]}{K'_{sp}}$$\n", "\n", "Where $K'_{sp}$ is the stoichiometric solubility product function of T,S,pr and mineral phase (aragonite, calcite)\n", "\n", "$[Ca^{2+}]$ doesn't change much
\n", "$[CO_3^{2+}]$ can be calculated from chemical measurements of DIC, $pCO_2$, total alkalinity and pH (at least two of these 4 parameters).\n", "\n", "#### Models\n", "\n", "[Juranek et al. (2009)](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2009GL040778) describe a set of least squares regression models for aragonite saturation state, based on more commonly measured oceangraphic variables (temperature, salinity, pressure, oxygen and nitrate).\n", "\n", "Juranek, L. W., R. A. Feely, W. T. Peterson, S. R. Alin, B. Hales, K. Lee, C. L. Sabine, and J. Peterson, 2009: A novel method for determination of aragonite saturation state on the continental shelf of central Oregon using multi-parameter relationships with hydrographic data. Geophys. Res. Lett., 36, doi:10.1029/2009GL040778.\n", "\n", "##### Model 1 \n", "\n", "$$\\Omega_{arag}^e = \\beta_0 + \\beta_1T + \\beta_2S + \\beta_3P + \\beta_4O_2 + \\beta_5NO_3^-$$\n", "\n", "* Has high $R_a^2$ (\"adjusted\" $R^2$)\n", "* High \"variance inflation factor\"\n", "* Indicates multiple collinearity\n", "* Coefficients are ambiguous and not meaningful - When you add more data, you get will get a different answer (this is bad!)\n", "\n", "##### Adjusted $R^2$\n", "\n", "Accounts for reduction of degrees of freedom when using multiple predictor variables.\n", "\n", "$$R_a^2 = R^2 - (1-R^2)\\frac{k}{n-k-1}$$\n", "\n", "$$= 1 - \\frac{MSE}{MST}$$\n", "\n", "If the MSE is low, the adjusted R-squared is going to be high. The more observations you have, the less this adjustment matters.\n", "\n", "\n", "##### Variance Inflation Factor\n", "\n", "Variance Inflation Factor\n", "\n", "$$VIF = \\frac{1}{1 - R^2}$$ \n", "\n", "where $R^2 $ from regression of predictor variables against other predictor variables. There is no clear \"cut-off\" that defines high VIF, but greater than 5 (and definitely greater than 10) is generally considered high.\n", "\n", "![images/arag_sat_table.png](images/arag_sat_table.png)\n", "\n", "*Source:* Juranek et al. (2009)\n", "\n", "##### Final Model\n", "\n", "$$\\Omega_{arag}^e = \\alpha_0 + \\alpha_1(O_2 - O_{2,r}) + \\alpha_2(T - T_r) \\times (O_2 - O_{2,r})$$\n", "\n", "* Less variables, avoids multiple collinearity\n", "* Includes interaction term\n", "* Reference values ($T_r$ and $O_{2,r}$) keep product from getting too big\n", "* Using variables with differing magnitudes can lead to problems like round-off errors\n", "* Standardizing variables (using z-scores) another common strategy\n", "\n", "![images/arag_sat_final.png](images/arag_sat_final.png)\n", "\n", "*Source:* Juranek et al. (2009)\n", "\n", "\n", "__Aragonite saturation state__\n", "\n", "_Red contours:_ from measured DIC and total alkalinaity\n", "\n", "_Blue contours:_ Multiple regression model\n", "\n", "With their multiple regression model, Juranek et al. were able to estimate $\\Omega_{arag}$ for time series that does not always include direct observations of the carbonate system parameters. This helps provide a perspective on the seasonal cycle of $\\Omega_{arag}$, something that cannot be done with one WCOA cruise per year.\n", "\n", "![images/arag_sat_ts.png](images/arag_sat_ts.png)\n" ] }, { "cell_type": "code", "execution_count": null, "id": "bf704896-4635-472d-8dd6-a72c3194e0ec", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.7" }, "vscode": { "interpreter": { "hash": "0ef88d3abb6b62f34a20525ce337090c4512fe8aecf32c74604482b944e1c3bd" } } }, "nbformat": 4, "nbformat_minor": 5 }