Likelihood ratio test là gì


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

What is a Likelihood-Ratio Test?

The Likelihood-Ratio kiểm tra (sometimes called the likelihood-ratio chi-squared test) is a hypothesis test 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 to find out which of the following models is the best fit:

Model Two has two predictor variables (age,sex). It is “nested” within Mã Sản Phẩm 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.

The best Mã Sản Phẩm 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 lớn grasp (i.e. the likelihood function is highest nearer the true value for Θ), the calculations lớn find the inputs for the procedure are not.

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

Running the Test

Basically, the kiểm tra compares the fit of two models. The null hypothesis is that the smaller Mã Sản Phẩm is the “best” model; It is rejected when the thử nghiệm statistic is large. In other words, if the null hypothesis is rejected, then the larger model is a significant improvement over the smaller one.

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If you know the log-likelihood functions for the two models, the chạy thử statistic is relatively easy khổng lồ calculate as the ratio between the log-likelihood of the simpler model (s) to lớn the Model with more parameters (g):

You might also see this equation with “s” written as the likelihood for the null Mã Sản Phẩm và “g” written as the likelihood for the alternative sầu Mã Sản Phẩm.

The chạy thử statistic approximates a chi-squared random variable. Degrees of freedom for the kiểm tra equal the difference in the number of parameters for the two models.

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

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