The models being compared need not be F-test or a likelihood ratio test.
2.
The Likelihood ratio test has better behavior for small sample sizes, so it is generally preferred.
3.
There are several reasons to prefer the likelihood ratio test or the Lagrange multiplier to the Wald test:
4.
The tenability of each model can be tested statistically by using a likelihood ratio test or other indices of fit.
5.
Further, it can be used in a hypothesis test for whether evolutionary rates are constant ( by using likelihood ratio tests ).
6.
Durbin's h-test ( see below ) or likelihood ratio tests, that are valid in large samples, should be used.
7.
Another result, also called likelihood ratio tests, where Wilks showed the distribution of log likelihood ratios is asymptotically \ chi ^ 2.
8.
An additional reason that the chi-squared distribution is widely used is that it is a member of the class of likelihood ratio tests ( LRT ).
9.
In the form stated here, the likelihood ratio is small if the alternative model is better than the null model and the likelihood ratio test provides the decision rule as follows:
10.
Rather than the Wald method, the recommended method to calculate the p-value for logistic regression is the Likelihood Ratio Test ( LRT ), which for this data gives p = 0.0006.
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