Likelihood-ratio test

A hypothesis test that compares the maximum likelihood under a restricted model with the maximum under a less restricted model. The ratio measures how much better the broader model fits the observed data.

Likelihood function: A function of model parameters that measures how well their values account for observed data. The test compares the largest likelihood values allowed by its two models.
Statistical hypothesis testing: A framework for using data to assess claims about a probability model or population. The likelihood comparison is a way to test a specified null claim.
Logistic regression: A regression model that represents a binary outcome's probability through a link function, commonly the logit. Likelihood-ratio tests compare nested logistic regression models and their predictors.
Wald test: A hypothesis test based on the estimated parameter's distance from a null value, scaled by estimated uncertainty. It tests parameter estimates directly rather than comparing maximized likelihoods.
Maximum likelihood estimation: A method for estimating model parameters by choosing values that maximize the likelihood of observed data. Each model is fitted by maximizing its likelihood before the comparison.
Null hypothesis: A statistical claim treated as the reference condition in a hypothesis test. The restricted model encodes the conditions imposed by the null hypothesis.
Poisson regression: A regression model for count outcomes that commonly uses a log link for the expected count. Nested count models can be assessed by comparing their maximized likelihoods.
Score test: A hypothesis test based on the likelihood's slope at the null-model estimate. It needs a fit under the null, unlike the likelihood-ratio test's fit under both models.
Deviance: A measure of model misfit commonly defined as twice the log-likelihood gap from a saturated model. Twice the log-likelihood difference between nested fits is a deviance statistic.
Nested models: Models in which one is obtained from another by imposing parameter constraints. The standard test compares models related by such constraints.

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