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所在平台: Udemy |
课程主页: https://www.udemy.com/course/linear-regression-glms-and-gams-with-r/
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Coursera 课程《R 语言的线性回归、广义线性模型（GLMs）和广义可加模型（GAMs）》 本课程旨在教授如何利用 R 语言，在基础线性回归模型的基础上，扩展其假设和约束，从而指定、建模并解释广义线性模型（GLMs）和广义可加模型（GAMs）。课程将结合 Simon N. Wood 的著作《Generalized Additive Models: An Introduction with R》，通过一系列实际案例，演示 GLMs 和 GAMs 的估计过程。 线性统计模型将响应变量建模为预测变量的线性函数，并假定其误差项服从零均值正态分布。然而，线性假设常常构成局限。广义线性模型（GLMs）打破了这一线性假设，允许响应变量的期望值成为预测变量线性组合的平滑（非线性）单调函数。此外，GLMs 还放宽了响应变量服从正态分布的限制，支持多种分布（如正态、泊松、二项、对数线性等）。 广义可加模型（GAMs）是 GLMs 的进一步扩展，允许估计非参数平滑函数形式的回归系数。例如，局部加权散点平滑（lowess）等非参数平滑方法，通过对数据进行局部子集拟合，从而得到平滑曲线。 课程将概述如何使用 R 语言进行 GLMs 和 GAMs 的建模。GLMs，尤其是 GAMs，已发展成为灵活且常用的统计方法。本课程将介绍建模、估计和解释 GAMs 的最新方法，重点在于使用 R 语言进行 GLMs 和 GAMs 的建模与解释。通过使用免费的 R 软件，将直观展示线性和广义线性、广义可加模型的实际应用。
Linear Regression, GLMs and GAMs with R demonstrates how to use R to extend the basic assumptions and constraints of linear regression to specify, model, and interpret the results of generalized linear (GLMs) and generalized additive (GAMs) models. The course demonstrates the estimation of GLMs and GAMs by working through a series of practical examples from the book Generalized Additive Models: An Introduction with R by Simon N. Wood (Chapman & Hall/CRC Texts in Statistical Science, 2006). Linear statistical models have a univariate response modeled as a linear function of predictor variables and a zero mean random error term. The assumption of linearity is a critical (and limiting) characteristic. Generalized linear models (GLMs) relax this assumption of linearity. They permit the expected value of the response variable to be a smoothed (e.g. non-linear) monotonic function of the linear predictors. GLMs also relax the assumption that the response variable is normally distributed by allowing for many distributions (e.g. normal, poisson, binomial, log-linear, etc.). Generalized additive models (GAMs) are extensions of GLMs. GAMs allow for the estimation of regression coefficients that take the form of non-parametric smoothers. Nonparametric smoothers like lowess (locally weighted scatterplot smoothing) fit a smooth curve to data using localized subsets of the data. This course provides an overview of modeling GLMs and GAMs using R. GLMs, and especially GAMs, have evolved into standard statistical methodologies of considerable flexibility. The course addresses recent approaches to modeling, estimating and interpreting GAMs. The focus of the course is on modeling and interpreting GLMs and especially GAMs with R. Use of the freely available R software illustrates the practicalities of linear, generalized linear, and generalized additive models.
