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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.
In statistics, the likelihood-ratio test is a hypothesis test that involves comparing the goodness of fit of two competing statistical models, typically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods.
Thus, the Fisher information may be seen as the curvature of the support curve (the graph of the log-likelihood). Near the maximum likelihood estimate, low Fisher information will indicates that the maximum appears to be "blunt", that is, there are many points in the neighborhood that provide a similar log-likelihood. Conversely, a high Fisher ...
The commonly used chi-squared tests for goodness of fit to a distribution and for independence in contingency tables are in fact approximations of the log-likelihood ratio on which the G-tests are based. [4] The general formula for Pearson's chi-squared test statistic is
If the likelihood ratio chi-square statistic is significant, then the model does not fit well (i.e., calculated expected frequencies are not close to observed frequencies). Backward elimination is used to determine which of the model components are necessary to retain in order to best account for the data.
In this example, the ratio (probability of living during an interval) / (duration of the interval) is approximately constant, and equal to 2 per hour (or 2 hour −1). For example, there is 0.02 probability of dying in the 0.01-hour interval between 5 and 5.01 hours, and (0.02 probability / 0.01 hours) = 2 hour −1.
It is the most widely used of many chi-squared tests (e.g., Yates, likelihood ratio, portmanteau test in time series, etc.) – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900. [1]