Likelihood Distance Test
- Compares how likely the observed data are under a proposed model versus a reference model.
- Requires computing the likelihoods for both models and comparing them.
- A higher likelihood for the proposed model indicates a better fit to the observed data.
Definition
Section titled “Definition”Likelihood distance test is a statistical method used to evaluate the fit of a proposed model to observed data by comparing the likelihood of the observed data under the proposed model to the likelihood of the observed data under a reference model.
Explanation
Section titled “Explanation”- Specify a proposed model that describes the relationship of interest and a reference model that represents the data without the proposed effect.
- Calculate the likelihood of the observed data under each model by assessing the probability of the observed values given the models’ predicted values.
- Compare the two likelihoods: if the likelihood under the proposed model is higher than under the reference model, the proposed model is considered a better fit to the data and more likely to describe the relationship between the variables.
Examples
Section titled “Examples”Drug effectiveness (blood pressure) example
Section titled “Drug effectiveness (blood pressure) example”Researchers collect blood pressure measurements for patients before and after taking a drug. They propose a model predicting change in blood pressure based on factors such as age, gender, and baseline blood pressure. The reference model predicts change based only on age and gender (not considering baseline blood pressure). The researchers compute the likelihood of the observed data under both models; a higher likelihood under the proposed model indicates it fits the data better and suggests the drug may be effective in reducing blood pressure.
Genetic data example
Section titled “Genetic data example”Researchers propose a model that predicts the likelihood of developing a disease based on genetic makeup. The reference model predicts disease likelihood based only on environmental factors, without genetics. By comparing the likelihood of the observed data under both models, researchers determine whether the genetic-based model fits better and whether genetic makeup is a significant predictor of the disease.
Related terms
Section titled “Related terms”- Reference model
- Likelihood