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Likelihood ratio tests in behavioral genetics: Problems and solutions
Stockholm University, Faculty of Science, Department of Mathematics.
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2006 (English)In: Behavior Genetics, ISSN 0001-8244, E-ISSN 1573-3297, Behavior Genetics, ISSN 0001-8244, Vol. 36, no 2, 331-340 p.Article in journal (Refereed) Published
Abstract [en]



The likelihood ratio test of nested models for family data plays an important role in the assessment of genetic and environmental influences on the variation in traits. The test is routinely based on the assumption that the test statistic follows a chi-square distribution under the null, with the number of restricted parameters as degrees of freedom. However, tests of variance components constrained to be non-negative correspond to tests of parameters on the boundary of the parameter space. In this situation the standard test procedure provides too large

p-values and the use of the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) for model selection is problematic. Focusing on the classical ACE twin model for univariate traits, we adapt existing theory to show that the asymptotic distribution for the likelihood ratio statistic is a mixture of chi-square distributions, and we derive the mixing probabilities. We conclude that when testing the AE or the CE model against the ACE model, the p-values obtained from using the v2 (1 df) as the reference distribution should be halved. When the E model is tested against the ACE model, a mixture of v2(0 df), v2(1 df) and v2 (2 df) should be used as the reference distribution, and we provide a simple formula to compute the mixing probabilities. Similar results for tests of the AE, DE and E models against the ADE model are also derived. Failing to use the appropriate reference distribution can lead to invalid conclusions.

Place, publisher, year, edition, pages
Springer , 2006. Vol. 36, no 2, 331-340 p.
Keyword [en]
Boundary parameter; chi-square distribution; likelihood ratio test; twin model; variance
National Category
URN: urn:nbn:se:su:diva-25716DOI: 10.1007/s10519-005-9034-7OAI: diva2:200342
Part of urn:nbn:se:su:diva-848Available from: 2006-03-02 Created: 2006-03-02 Last updated: 2010-12-14Bibliographically approved
In thesis
1. Latent variable models for longitudinal twin data
Open this publication in new window or tab >>Latent variable models for longitudinal twin data
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Longitudinal twin data provide important information for exploring sources of variation in human traits. In statistical models for twin data, unobserved genetic and environmental factors influencing the trait are represented by latent variables. In this way, trait variation can be decomposed into genetic and environmental components. With repeated measurements on twins, latent variables can be used to describe individual trajectories, and the genetic and environmental variance components are assessed as functions of age. This thesis contributes to statistical methodology for analysing longitudinal twin data by (i) exploring the use of random change point models for modelling variance as a function of age, (ii) assessing how nonresponse in twin studies may affect estimates of genetic and environmental influences, and (iii) providing a method for hypothesis testing of genetic and environmental variance components. The random change point model, in contrast to linear and quadratic random effects models, is shown to be very flexible in capturing variability as a function of age. Approximate maximum likelihood inference through first-order linearization of the random change point model is contrasted with Bayesian inference based on Markov chain Monte Carlo simulation. In a set of simulations based on a twin model for informative nonresponse, it is demonstrated how the effect of nonresponse on estimates of genetic and environmental variance components depends on the underlying nonresponse mechanism. This thesis also reveals that the standard procedure for testing variance components is inadequate, since the null hypothesis places the variance components on the boundary of the parameter space. The asymptotic distribution of the likelihood ratio statistic for testing variance components in classical twin models is derived, resulting in a mixture of chi-square distributions. Statistical methodology is illustrated with applications to empirical data on cognitive function from a longitudinal twin study of aging.

Place, publisher, year, edition, pages
Stockholm: Matematiska institutionen, 2006. 49 p.
Latent variable models, twin models, variance components, change point models, non-ignorable nonresponse, likelihood ratio tests
National Category
Probability Theory and Statistics
urn:nbn:se:su:diva-848 (URN)91-7155-211-1 (ISBN)
Public defence
2006-03-24, sal 14, hus 5, Kräftriket, Stockholm, 10:00
Available from: 2006-03-02 Created: 2006-03-02Bibliographically approved

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Palmgren, Juni
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