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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.
The likelihood ratio is central to likelihoodist statistics: the law of likelihood states that the degree to which data (considered as evidence) supports one parameter value versus another is measured by the likelihood ratio. In frequentist inference, the likelihood ratio is the basis for a test statistic, the so-called likelihood-ratio test.
It is possible to do a calculation of likelihood ratios for tests with continuous values or more than two outcomes which is similar to the calculation for dichotomous outcomes. For this purpose, a separate likelihood ratio is calculated for every level of test result and is called interval or stratum specific likelihood ratios. [4]
The likelihood ratio is a function of the data ; therefore, it is a statistic, although unusual in that the statistic's value depends on a parameter, . The likelihood-ratio test rejects the null hypothesis if the value of this statistic is too small.
^ = the maximized value of the likelihood function of the model , i.e. ^ = (^,), where {^} are the parameter values that maximize the likelihood function and is the observed data; n {\displaystyle n} = the number of data points in x {\displaystyle x} , the number of observations , or equivalently, the sample size;
Clearly, the difference between the unbiased estimator and the maximum likelihood estimator diminishes for large n. In the general case, the unbiased estimate of the covariance matrix provides an acceptable estimate when the data vectors in the observed data set are all complete: that is they contain no missing elements. One approach to ...
In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing.It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.
Specifically, at each stage, after the removal of the highest ordered interaction, the likelihood ratio chi-square statistic is computed to measure how well the model is fitting the data. The highest ordered interactions are no longer removed when the likelihood ratio chi-square statistic becomes significant. [2]
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