A Monte Carlo study of local identifiability and degrees of freedom in the asymptotic likelihood ratio test

1979 ◽  
Vol 32 (1) ◽  
pp. 121-132 ◽  
Author(s):  
Roderick P. McDonald ◽  
William R. Krane
Keyword(s):  
Monte Carlo ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Degrees Of Freedom ◽  
Monte Carlo Study ◽  
Ratio Test ◽  
Local Identifiability ◽  
Asymptotic Likelihood

A Note on the Asymptotic Distribution of Likelihood Ratio Tests to Test Variance Components

2006 ◽  
Vol 9 (4) ◽  
pp. 490-495 ◽  
Author(s):  
Peter M. Visscher
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Variance Components ◽  
Degrees Of Freedom ◽  
Likelihood Ratio Tests ◽  
Likelihood Ratio Test Statistic ◽  
Ratio Test ◽  
Test Statistic

AbstractWhen using maximum likelihood methods to estimate genetic and environmental components of (co)variance, it is common to test hypotheses using likelihood ratio tests, since such tests have desirable asymptotic properties. In particular, the standard likelihood ratio test statistic is assumed asymptotically to follow a χ2 distribution with degrees of freedom equal to the number of parameters tested. Using the relationship between least squares and maximum likelihood estimators for balanced designs, it is shown why the asymptotic distribution of the likelihood ratio test for variance components does not follow a χ2 distribution with degrees of freedom equal to the number of parameters tested when the null hypothesis is true. Instead, the distribution of the likelihood ratio test is a mixture of χ2 distributions with different degrees of freedom. Implications for testing variance components in twin designs and for quantitative trait loci mapping are discussed. The appropriate distribution of the likelihood ratio test statistic should be used in hypothesis testing and model selection.

Interpretable Statistical Tests for Growth Comparisons using Parameters in the von Bertalanffy Equation

1990 ◽  
Vol 47 (7) ◽  
pp. 1416-1426 ◽  
Author(s):  
Robert M. Cerrato
Keyword(s):  
Monte Carlo ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Statistical Tests ◽  
Confidence Region ◽  
Principal Factor ◽  
Ratio Test ◽  
Von Bertalanffy ◽  
Empirical Comparison ◽  
Degree Of Heterogeneity

Likelihood ratio, t-, univariate χ2-, and T2-tests have been proposed to compare von Bertalanffy parameters among stocks. As commonly applied, all of these tests are approximate, with the accuracy of each dependent on the nonlinearity of the von Bertalanffy equation, sample size, and if present, the degree of heterogeneity in the error variances. An empirical comparison of these procedures shows that the likelihood ratio test often differs in outcome from the others. Analysis of the conflicting cases by confidence region comparisons and Monte Carlo simulations almost always resolved the outcome in favor of the likelihood ratio test. The parameter effects component of nonlinearity was found to be the principal factor biasing the t-, univariate χ2-, and T2-tests. Reparameterizations of the von Bertalanffy equation substantially reduced, but did not completely eliminate, conflicting outcomes. It is concluded that the likelihood ratio test is the most accurate of the procedures considered in this study, and whenever possible, it should be the approach of choice.

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