Lecture

Non nested hypotheses

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Description

This lecture covers the concept of non-nested hypotheses in the context of choice models, where restricted and unrestricted models are compared using the likelihood ratio test. An example is provided to illustrate the comparison between two models and the Cox test. The lecture concludes with recommendations on model selection.

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 (10)

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.

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 principle

In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density function considered as a function of its distributional parameterization argument.

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 .

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.

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Likelihood Ratio Test MOOC: Introduction to Discrete Choice Models

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