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Topic: Likelihood ratio test

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Likelihood

Maximum likelihood

Principle of maximum entropy

Posterior probability

Conditional probability

Statistical significance

Bayesian statistics

Bayes theorem

Sunrise problem

Bayesian probability theory

Information entropy

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Probability interpretations

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Bayesian probability

	ERP 9:1 Comparison of Likelihood Ratio and Pearsonian Rasch Fit
		This test of fit is based on a systematic analysis of the difference between the number of correct responses given by a group of examinees with a similar raw score and the number of correct responses predicted from the model for that group.
		Gustafsson (1980) contended that the tests of fit based on the comparison between observed and theoretical expected frequencies (Wright and Panchapakesan, 1969; Mead, 1976a,b) are inappropriate since the distribution of the test statistics based on the unconditional estimation procedure is unknown.
		The likelihood ratio test is based on the ratio of the likelihood of the response pattern based on a single overall ability estimate and the likelihood of the response pattern based on the J estimated subset abilities.
	www.rasch.org /erp4.htm (4071 words)

	StudyGroup9 List Archive: RE: Likelihood Ratio Test
		Hogg/Klugman and Cummings likelihood ratio tests are slightly different.
		testing whether a set of groups from a population is from a distribution
		the degrees of freedom for the likelihood ratio test is the number of
	www.casact.org /lists/studygroup9/00000209.htm (421 words)

	8.2.3.3. Likelihood ratio tests
		Likelihood functions for reliability data are described in Section 4.
		Calculate the maximum likelihood of the sample data based on an assumed distribution model (the maximum occurs when unknown parameters are replaced by their maximum likelihood estimates).
		The unrestricted likelihood of the data is the product of the two likelihoods, with 4 unknown parameters (the shape and characteristic life for each vendor population).
	www.itl.nist.gov /div898/handbook/apr/section2/apr233.htm (677 words)

	Statistics Solutions : Binomial Logistic Regression
		The likelihood ratio test is a test of the significance of the difference between the likelihood ratio (-2LL) for the researcher's model minus the likelihood ratio for a reduced model.
		Note that the likelihood ratio test of individual parameters is a better criterion than the alternative Wald statistic when considering which variables to drop from the logistic regression model.
		Wald statistic (test): The Wald statistic is an alternative test which is commonly used to test the significance of individual logistic regression coefficients for each independent variable (that is, to test the null hypothesis in logistic regression that a particular logit (effect) coefficient is zero).
	www.statisticssolutions.com /Binomial-Logistic-Regression.htm (3474 words)

	Maximum Likelihood
		The likelihood ratio for a test of the null hypothesis that p = 0.5 is
		Likelihood: The likelihood function is used to obtain maximum likelihood estimates (MLEs) of parameters and is the probabiity of the observed sequences as a function
		The likelihood ratio test statistic is -2logL = 117.946, which is asymptotically c2 distributed under the null hypothesis with 1 degrees of freedom.
	ucjeps.berkeley.edu /bryolab/ib200/maximumlikelihood.html (2941 words)

	Likelihood-ratio test - Definition, explanation
		A likelihood-ratio test is a statistical test relying on a test statistic computed by taking the ratio of the maximum value of the likelihood function under the constraint of the null hypothesis to the maximum with that constraint relaxed.
		If that ratio is Λ and the null hypothesis holds, then for commonly occurring families of probability distributions, −2 log Λ has a particularly handy asymptotic distribution.
		Many common test statistics such as the Z-test, the F-test, Pearson's chi-square test and the G-test can be phrased as log-likelihood ratios or approximations thereof.
	www.calsky.com /lexikon/en/txt/l/li/likelihood_ratio_test.php (649 words)

	Sibling
		Likelihood Ratio: the probability that some event will occur under a set of conditions or assumptions divided by the probability that the same event will occur under a set of different mutually exclusive conditions or assumptions.
		In sibling testing it would be the chance that an allele (s) would occur if two children were siblings divided by the chance the allele occurring if the two were unrelated (see Table 1).
		In a paternity or maternity test, there are certain obligatory paternal and maternal genes which must be observed in both the child and his/her biological parents.
	genetic-identity.com /Sibling/sibling.html (1225 words)

	Genelex: The Paternity DNA Testing Site
		We wanted to compare the results of testing using both RFLP and STR in order to be sure we are using the best method in the complicated cases we are frequently called upon to perform.
		Likelihood ratios for half-sibship were calculated using RFLP, PowerPlex 1, and a combination of PowerPlex 1 and 2.
		STR testing is reserved for cases involving unusual and degraded samples such as decomposed bone and tissue, amniotic fluid, where turnaround is crucial, and in cases requiring extended typing as a result of mutations.
	www.genelex.com /paternitytesting/PromegaKin.html (1721 words)

	New Sensitivity Test & Analysis Software
		Testing material for fracture toughness and analysis of the effects of brain pressure on stroke are other applications.
		The Adaptive Langlie test, developed during the 1970s, is, as the name implies, an adaptation of the original Langlie test.
		The test protocol is the same, except that the levels shift up if a test level near the upper limit results in a failure, with a similar shift down if a test level near the lower level results in a success.
	neyersoftware.com /SensitivityTest/SensitivityTestFlyer.htm (1261 words)

	Other Options
		It goes along the chromosome, and determines whether the likelihood ratio test statistic is increasing or decreasing.
		The default behavior of the QTL Cartographer system is to use a likelihood ratio test statistic (LR) rather than a LOD score.
		be the likelihood of the data given the hypothesis.
	statgen.ncsu.edu /qtlcart/manual/node111.html (173 words)

	Likelihood ratio test (Site not responding. Last check: )
		A likelihood-ratio test is a statistical test relying on a test statistic computed by taking the ratio of the maximum value of the likelihood function under the constraint of the null hypothesis to the maximum with that constraintrelaxed.
		If that ratio is Λ and the null hypothesis holds, thenfor commonly occurring families of probabilitydistributions, −2 log Λ has a particularly handy asymptotic distribution.
		Many common test statistics such as the Z-test, the F-test and Pearson's chi-square test can be phrased aslog-likelihood ratios or approximations thereof.
	www.therfcc.org /likelihood-ratio-test-34373.html (466 words)

	Model discrimination, model selection, generalized likelihood ratio test - Zabel Dissertation
		The generalized likelihood ratio test (GLRT) (Mood, et al., 1974; Bickel and Doksum, 1977; Hogg and Tannis, 1983), as its name implies, is based on the ratio of the likelihoods.
		The likelihood ratio is useful because of the following result (Bickel and Doksum, 1977).
		This test can be extended to the case where the difference between the dimension of the null and alternative models is greater than 1.
	www.cbr.washington.edu /papers/zabel/chp3.doc7.html (769 words)

	Likelihood Ratio Test
		The likelihood ratio test (LRT) is a statistical test of the goodness-of-fit between two models.
		The LRT is explained in more detail by Felsenstein (1981), Huelsenbeck and Crandall (1997), Huelsenbeck and Rannala (1997), and Swofford et al.
		In testing a molecular clock, the degrees of freedom work out to be s-2, where s is the number of taxa in the phylogeny (Felsenstein 1981).
	workshop.molecularevolution.org /resources/lrt.php (608 words)

	Common Shape Parameter Likelihood Ratio Test
		The likelihood ratio test is performed by first obtaining the LR test statistic,
		test stress levels (with two or more exact failure times).
		The individual likelihood values for each of the test stresses can be found in the Results tab of the Likelihood Ratio Test window.
	www.weibull.com /AccelTestWeb/common_shape_parameter_likelihood_ration_test.htm (344 words)

	The Likelihood Ratio Test
		Thus, when two models are hypothesized, the likelihood ratio test can be succinctly expressed as the comparison of the likelihood ratio with a threshold.
		Furthermore, note that only the value of the likelihood ratio relative to the threshold matters; to simplify the computation of the likelihood ratio, we can perform any positively monotonic operations simultaneously on the likelihood ratio and the threshold without affecting the comparison.
		The likelihood ratio is plotted in Figure 1 and the threshold value η, which is computed from the a priori probabilities and the costs to be 1/3, is indicated.
	cnx.org /content/m11234/latest (1043 words)

	Statistics Solutions : Logistic Regression
		The ratio of odds ratios of the independents is the ratio of relative importance of the independent variables in terms of effect on the dependent variable's odds.
		Recall that when the 95% confidence interval around the odds ratio includes the value of 1.0, indicating that a change in value of the independent variable is not associated in change in the odds of the dependent variable assuming a given value, then that variable is not considered a useful predictor in the logistic model.
		If the odds ratio is 4.3 for hs_degree (1=having a high school degree, 0 = not), for instance, where the dependent is employed (0=not employed, 1=employed), we say that the odds of a person with a high school degree being employed are 4.3 times the odds of a person without a high school degree.
	www.statisticssolutions.com /Logistic_Regression.htm (9721 words)

	Likelihood Ratio Tests
		Our first use of likelihood ratio tests will be to investigate which of two models of evolution that best fits a set of DNA sequences.
		This means that once the parameters have been estimated by maximum likelihood, it is possible to interpret them in terms of the ratio between synonymous and non-synonymous mutation rates.
		It should be noted that actually, this is one case where the LRT statistic will not follow a chi-squared distribution due to the so-called boundary problem: M0 corresponds to M3 with two of its parameters constrained at the boundary of the parameter space.
	www.cbs.dtu.dk /courses/PR/lrt.php (3455 words)

	Testing the Molecular Clock (Site not responding. Last check: )
		are the likelihoods under the null and alternative hypotheses, respectively.
		The likelihood under the alternative hypothesis is higher than under the null hypothesis because there are more free parameters in the substitution model (i.e., no constraints on branch lengths).
		The maximum likelihood estimate of phylogeny is consistent with the monophyly of mammals and amniotes (though the tree is unrooted).
	www.sciencemag.org /feature/data/phylo/clock.html (304 words)

	Re: st: no log likelihood ratio test after nbreg??
		The problem MAY be that the data is Poisson and not overdispersed.
		I ran a test of Poisson simulated data, showing the fact that there is no extra dispersion (that is why I used GLM rather than POISSON, which does not give you many diagnostics).
		But in my case, I didn't see the ratio reported after the regression, and there is no z score for alpha.
	www.stata.com /statalist/archive/2005-03/msg00374.html (334 words)

	The Likelihood Ratio Test Procedure
		The notion of using the magnitude of the ratio of two probability density functions as the basis of a best test or of a uniformly most powerful test can be modified, and made intuitively appealing, to provide a method of constructing a test where either or both of the hypothesis and alternative are composite.
		The method leads to tests called likelihood ratio tests, and although not necessarily uniformly most powerful, they often have desirable properties.
		The test involves a comparison of the maximum value the likelihood can take when
	mcs.une.edu.au /~stat354/notes/node86.html (278 words)

	Likelihood Ratio Test (Site not responding. Last check: )
		Full-Model / Restricted Model tests are possible with ML methods.
		which shows that the test is based on the ratio of likelihoods under the full and restricted models; hence, it is sometimes called the "likelihood ratio test."
		If the restricted model is true (and under certain regularity conditions), the test statistic has an asymptotically Chi-squared distribution with P1-P2 degrees of freedom, where P1 and P2 are the number of parameters estimated in the full and restricted models, respectively.
	www2.tltc.ttu.edu /westfall/images/5347/likelihood_ratio_test.htm (147 words)

	Profile Likelihood Confidence Intervals
		Wald-based and likelihood ratio-based confidence intervals are available in the MODEL procedure for computing a confidence interval on an estimated parameter.
		Note that the likelihood ratio test reported the probability that zo = 40.47543 is 5% but zo = 40.47543 is the upper bound of a 95% confidence interval.
		To understand this conundrum, note that the TEST statement is using the likelihood ratio statistic to test the null hypothesis H
	www.asu.edu /sas/sasdoc/sashtml/ets/chap14/sect47.htm (326 words)

	SWS Generalized Likelihood Ratio Test (Site not responding. Last check: )
		The quantity on the left side of Equation 2.2 is called the likelihood ratio and is denoted by
		Because the natural logarithm is a monotonic function and both sides of Equation 2.2 are positive, an equivalent test is shown in Equation 2.3.
		Therefore it is necessary to introduce a modified test known as the generalized likelihood ratio test (GLRT) which is described by Equation 2.4 (also see Chapter 3).
	webpages.charter.net /witek/thesis/node12.html (813 words)

	BGIM : Maximum Likelihood Estimation Primer
		The likelihood ratio test provides the means for comparing the likelihood of the data under one hypothesis (usually called the alternate hypothesis) against the likelihood of the data under another, more restricted hypothesis (usually called the null hypothesis, for the experimenter tries to nullify this hypothesis in order to provide support for the former).
		The likelihood ratio test answers this question: are the data significantly less likely to have arisen if the null hypothesis is true than if the alternate hypothesis is true?
		This is why it is called a likelihood ratio test, but we look at the difference between log-likelihoods.
	statgen.iop.kcl.ac.uk /bgim/mle/sslike_5.html (400 words)

	G-test for goodness-of-fit
		The test statistic is calculated by taking an observed number (O), dividing it by the expected number (E), then taking the natural log of this ratio.
		The test statistic is usually called G, and thus this is a G-test, although it is also sometimes called a log-likelihood test or a likelihood ratio test.
		The usual rule of thumb is that you should use the exact test or randomization test when the smallest expected value is less than 5, and the chi-square and G-tests are accurate enough for larger expected values.
	udel.edu /~mcdonald/statgtestgof.html (1288 words)

	Likelihood Ratio Tests
		However, in other cases, the tests may not be parametric, or there may not be an obvious statistic to start with.
		Likelihood functions, similar to those used in maximum likelihood estimation, will play a key role.
		The likelihood ratio statistic can be generalized to composite hypotheses.
	www.ds.unifi.it /VL/VL_EN/hypothesis/hypothesis6.html (749 words)

	DNAML: Output of the Program
		With 20 tests, one is expected to reach significance at the P =.05 level purely by chance.
		One can, for example, compare runs with different values of the expected transition/transversion ratio to determine which value is the maximum likelihood estimate, and what is the allowable range of values (using a likelihood ratio test, which you will find described in mathematical statistics books).
		This use of the empirical variance of log-likelihood differences is more robust and nonparametric than the classical likelihood ratio test, and may to some extent compensate for the any lack of realism in the model underlying this program.
	www.cmbi.kun.nl /cammsa/PHYLIP/dnaml-4.html (1353 words)

	8 Likelihood ratio tests
		Code is also provided for doing likelihood ratio tests between different nested, and perhaps also, non-nested alternative models.
		As we see, under the fitted (false) islandmodel, the rate of migration from the `mainland' has to be as large as 0.04 to account for the small between-population differentiation generated by the high rate of migration between neighbouring population in the true (steppingstone) model.
		Nothing prevents the user from carrying out likelihood ratio tests between non-nested models, although the interpretation of such tests may be questionable from a theoretical point of view (see e.g.
	www.math.ntnu.no /~jarlet/migration/node13.html (352 words)

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