Lecture

Logistic Regression: Modeling Binary Response Variables

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.

In course

MATH-236: Probability and statistics II

Linear statistical methods, analysis of experiments, logistic regression. ...

Description

This lecture covers logistic regression, a statistical model used to analyze binary response variables. Topics include the exponential family, generalized linear models, logistic regression for horseshoe crab data, odds ratio interpretation, model inference, and parameter estimation. The lecture also discusses the logit transformation, link functions, model fitting, maximum likelihood estimation, confidence intervals, and the relationship between logistic regression and the binomial distribution.

Instructor

Darlene Goldstein

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Data analysis: Regression analysis

Related concepts (32)

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.

Logistic regression

In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination).

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

Logit

In statistics, the logit (ˈloʊdʒɪt ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations. Mathematically, the logit is the inverse of the standard logistic function , so the logit is defined as Because of this, the logit is also called the log-odds since it is equal to the logarithm of the odds where p is a probability. Thus, the logit is a type of function that maps probability values from to real numbers in , akin to the probit function.

Related lectures (64)

Logistic Regression: Statistical Inference and Machine Learning

Covers logistic regression, likelihood function, Newton's method, and classification error estimation.

Horseshoe Crabs: Logistic Regression Analysis

Explores logistic regression analysis of horseshoe crab data, focusing on odds ratio interpretation and model fitting.

Generalised Linear Models: Regression with Exponential Family Responses

Covers regression with exponential family responses using Generalised Linear Models.

Chimpanzee Data Analysis

Covers the analysis of chimpanzee data on learning times and explores generalized linear models and logistic regression.

Mixture Models: Simulation-based Estimation