Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Likelihood Ratio Test

Description

This lecture introduces the Likelihood Ratio Test in the context of choice models, comparing unrestricted and restricted models through benchmarking and testing generic attributes, taste variations, and nonlinear specifications. The instructor explains the statistical methods and log likelihood calculations, emphasizing the importance of model restrictions and coefficients.

In MOOC

Introduction to Discrete Choice Models

Official source

Ontological neighbourhood

Statistics

Statistical inference: Statistical hypothesis testing

Related concepts (32)

Likelihood function

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.

Likelihood-ratio test

In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models, specifically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods. If the constraint (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should not differ by more than sampling error. Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero.

Relative likelihood

In statistics, when selecting a statistical model for given data, the relative likelihood compares the relative plausibilities of different candidate models or of different values of a parameter of a single model. Assume that we are given some data x for which we have a statistical model with parameter θ. Suppose that the maximum likelihood estimate for θ is . Relative plausibilities of other θ values may be found by comparing the likelihoods of those other values with the likelihood of .

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.

Wald test

In statistics, the Wald test (named after Abraham Wald) assesses constraints on statistical parameters based on the weighted distance between the unrestricted estimate and its hypothesized value under the null hypothesis, where the weight is the precision of the estimate. Intuitively, the larger this weighted distance, the less likely it is that the constraint is true. While the finite sample distributions of Wald tests are generally unknown, it has an asymptotic χ2-distribution under the null hypothesis, a fact that can be used to determine statistical significance.

Related lectures (36)

Maximum Likelihood Estimation: Multivariate Statistics

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

Likelihood Ratio Test: Detection & Estimation

Covers the likelihood ratio test for detection and estimation in statistical analysis.

Likelihood Ratio Test: Hypothesis Testing

Covers the Likelihood Ratio Test and hypothesis testing methods using Maximum Likelihood Estimators.