Lecture

Generalized Additive Models: Applications and Techniques

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers Generalized Additive Models (GAMs), starting with the basics of linear models and multiple regression. It then delves into the concept of GAMs, explaining how they extend GLMs by incorporating smooth functions of covariates. The lecture demonstrates the use of polynomial and cubic spline bases for modeling smooth functions, along with controlling model smoothness through penalties. Practical examples using the mgcv package in R are provided to illustrate fitting GAMs and visualizing the results. Additionally, the lecture introduces linear mixed models as an extension of the linear model, incorporating random effects. The instructor emphasizes practical applications through examples and code snippets.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Generalized linear model

In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression.

Generalized linear mixed model

In statistics, a generalized linear mixed model (GLMM) is an extension to the generalized linear model (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects. They also inherit from GLMs the idea of extending linear mixed models to non-normal data. GLMMs provide a broad range of models for the analysis of grouped data, since the differences between groups can be modelled as a random effect. These models are useful in the analysis of many kinds of data, including longitudinal data.

R package

R packages are extensions to the R statistical programming language. R packages contain code, data, and documentation in a standardised collection format that can be installed by users of R, typically via a centralised software repository such as CRAN (the Comprehensive R Archive Network). The large number of packages available for R, and the ease of installing and using them, has been cited as a major factor driving the widespread adoption of the language in data science.

General linear model

The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as where Y is a matrix with series of multivariate measurements (each column being a set of measurements on one of the dependent variables), X is a matrix of observations on independent variables that might be a design matrix (each column being a set of observations on one of the independent variables), B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors (noise).

Related lectures (64)

ANOVA & Moderation

Covers ANOVA, mediation, and moderation analyses in R for CS-411 Digital Education.

Regression: Linear Models

Introduces linear regression, generalized linear models, and mixed-effect models for regression analysis.

Linear Models: Least Squares

Explores linear models, least squares, Gaussian vectors, and model selection methods.

Regression Diagnostics

Covers regression diagnostics for linear models, emphasizing the importance of checking assumptions and identifying outliers and influential observations.

Likelihood Estimation and Least Squares