scholarly journals Asymptotic distribution of likelihood ratio test statistics for variance components in nonlinear mixed effects models

2019 ◽  
Vol 135 ◽  
pp. 107-122 ◽  
Author(s):  
Charlotte Baey ◽  
Paul-Henry Cournède ◽  
Estelle Kuhn
Keyword(s):  
Asymptotic Distribution ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Variance Components ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Ratio Test ◽  
Test Statistics ◽  
Nonlinear Mixed Effects ◽  
Nonlinear Mixed Effects Models

scholarly journals Rapid Sample Size Calculations for a Defined Likelihood Ratio Test-Based Power in Mixed-Effects Models

2012 ◽  
Vol 14 (2) ◽  
pp. 176-186 ◽  
Author(s):  
Camille Vong ◽  
Martin Bergstrand ◽  
Joakim Nyberg ◽  
Mats O. Karlsson
Keyword(s):  
Sample Size ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Ratio Test ◽  
Sample Size Calculations

Fitting Growth Model Using Nonlinear Regression with Random Parameters

2011 ◽  
Vol 480-481 ◽  
pp. 1308-1312
Author(s):  
Yao Xiang Li ◽  
Li Chun Jiang
Keyword(s):  
Random Effects ◽  
Repeated Measures ◽  
Fixed Effects ◽  
Model Building ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Ratio Test ◽  
Nonlinear Mixed Effects ◽  
Nonlinear Mixed Effects Models ◽  
Mixed Effect

Mixed Effect models are flexible models to analyze grouped data including longitudinal data, repeated measures data, and multivariate multilevel data. One of the most common applications is nonlinear growth data. The Chapman-Richards model was fitted using nonlinear mixed-effects modeling approach. Nonlinear mixed-effects models involve both fixed effects and random effects. The process of model building for nonlinear mixed-effects models is to determine which parameters should be random effects and which should be purely fixed effects, as well as procedures for determining random effects variance-covariance matrices (e.g. diagonal matrices) to reduce the number of the parameters in the model. Information criterion statistics (AIC, BIC and Likelihood ratio test) are used for comparing different structures of the random effects components. These methods are illustrated using the nonlinear mixed-effects methods in S-Plus software.

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.

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