Lecture

Derivation of the logit model

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Description

This lecture covers the derivation of the logit model in the context of choice models, focusing on the error term, choice sets, availability conditions, and the choice model itself. It explains the concepts of universal and individual choice sets, the generation of choice sets, and the assumptions made in modeling awareness and distance. The instructor discusses the conditions for availability and the formulation of the choice model using probability functions.

In MOOC

Introduction to Discrete Choice Models

Human behavior is complex, and unpredictable. Or is it? Predicting the behavior using mathematical models is the topic of this course. More specifically, we focus on choice modeling, in order to obtain disaggregate demand models. Focusing on the logit model, the course covers in details the specification of the model, the estimation of its parameters, the validation and the application. Exercises using the software Biogeme are also proposed. Concrete case studies with real data sets are provided.

Official source

Related concepts (28)

Discrete choice

In economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives, such as entering or not entering the labor market, or choosing between modes of transport. Such choices contrast with standard consumption models in which the quantity of each good consumed is assumed to be a continuous variable. In the continuous case, calculus methods (e.g. first-order conditions) can be used to determine the optimum amount chosen, and demand can be modeled empirically using regression analysis.

Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

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.

Probability mass function

In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.

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).

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