Likelihood Ratio Là Gì


This article is about Likelihood-Ratio Tests used in probability và mathematical Statistics. If you’re looking for information about the ratio used to assess diagnostic tests in medicine, see this other article: What is a Likelihood Ratio?

What is a Likelihood-Ratio Test?

The Likelihood-Ratio thử nghiệm (sometimes called the likelihood-ratio chi-squared test) is a hypothesis demo that helps you choose the “best” mã sản phẩm between two nested models. “Nested models” means that one is a special case of the other. For example, you might want khổng lồ find out which of the following models is the best fit:

Model Two has two predictor variables (age,sex). It is “nested” within model one because it has just two of the predictor variables (age, sex).

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This theory cam also be applied to matrices. For example, a scaled identity matrix is nested within a more complex compound symmetry matrix.

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The best model is the one that makes the data most likely, or maximizes the likelihood function“>likelihood function, fn(X – 1, … , Xn|Θ).Although the concept is relatively easy khổng lồ grasp (i.e. The likelihood function is highest nearer the true value for Θ), the calculations to find the inputs for the procedure are not.

Likelihood-ratio tests use log-likelihood functions, which are difficult và lengthy khổng lồ calculate by hand. Most statistical software packages have built in functions lớn handle them; On the other hand, log-likelihood functions pose other serious challenges, like the difficulty of calculating global maximums. These often involve hefty computations with complicated, multi-dimensional integrals.

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Running the Test

If you know the log-likelihood functions for the two models, the test statistic is relatively easy lớn calculate as the ratio between the log-likelihood of the simpler model (s) to lớn the mã sản phẩm with more parameters (g):


You might also see this equation with “s” written as the likelihood for the null mã sản phẩm and “g” written as the likelihood for the alternative model.

CITE THIS AS:Stephanie Glen. "Likelihood-Ratio Tests (Probability và Mathematical Statistics)" From Elementary Statistics for the rest of us!