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The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.
There is nothing magical about a sample size of 1 000, it's just a nice round number that is well within the range where an exact test, chi-square test, and G–test will give almost identical p values. Spreadsheets, web-page calculators, and SAS shouldn't have any problem doing an exact test on a sample size of 1 000 . — John H. McDonald [2]
In practice, the likelihood ratio is often used directly to construct tests — see likelihood-ratio test.However it can also be used to suggest particular test-statistics that might be of interest or to suggest simplified tests — for this, one considers algebraic manipulation of the ratio to see if there are key statistics in it related to the size of the ratio (i.e. whether a large ...
This expression is simply 2 times the log-likelihood ratio of the full model compared to the reduced model. The deviance is used to compare two models – in particular in the case of generalized linear models (GLM) where it has a similar role to residual sum of squares from ANOVA in linear models .
Likelihood Ratio: An example "test" is that the physical exam finding of bulging flanks has a positive likelihood ratio of 2.0 for ascites. Estimated change in probability: Based on table above, a likelihood ratio of 2.0 corresponds to an approximately +15% increase in probability.
Two other standard generalizations of the likelihood ratio are (a) the generalized likelihood ratio as used in the standard, classical likelihood ratio test and (b) the Bayes factor. Importantly, neither (a) nor (b) are e-variables in general: generalized likelihood ratios in sense (a) are not e-variables unless the alternative is simple (see ...
To be clear: These limitations on Wilks’ theorem do not negate any power properties of a particular likelihood ratio test. [3] The only issue is that a χ 2 {\displaystyle \chi ^{2}} distribution is sometimes a poor choice for estimating the statistical significance of the result.
Rather than the Wald method, the recommended method [21] to calculate the p-value for logistic regression is the likelihood-ratio test (LRT), which for these data give (see § Deviance and likelihood ratio tests below).