title: On the likelihood ratio tests in bivariate ACDE models.
abstract: The ACE and ADE models have been heavily exploited in twin studies to identify the genetic and environmental components in phenotypes. However, the validity of the likelihood ratio test (LRT) of the existence of a variance component, a key step in the use of such models, has been doubted because the true values of the parameters lie on the boundary of the parameter space of the alternative model for such tests, violating a regularity condition required for a LRT (e.g., Carey in Behav. Genet. 35:653-665, 2005; Visscher in Twin Res. Hum. Genet. 9:490-495, 2006). Dominicus, Skrondal, Gjessing, Pedersen, and Palmgren (Behav. Genet. 36:331-340, 2006) solve the problem of testing univariate components in ACDE models. Our current work as presented in this paper resolves the issue of LRTs in bivariate ACDE models by exploiting the theoretical frameworks of inequality constrained LRTs based on cone approximations. Our derivation shows that the asymptotic sampling distribution of the test statistic for testing a single bivariate component in an ACE or ADE model is a mixture of χ (2) distributions of degrees of freedom (dfs) ranging from 0 to 3, and that for testing both the A and C (or D) components is one of dfs ranging from 0 to 6. These correct distributions are stochastically smaller than the χ (2) distributions in traditional LRTs and therefore LRTs based on these distributions are more powerful than those used naively. Formulas for calculating the weights are derived and the sampling distributions are confirmed by simulation studies. Several invariance properties for normal data (at most) missing by person are also proved. Potential generalizations of this work are also discussed.
authors.affiliation: Boston College, 300 McGuinn Hall, 140 Commonwealth Ave, Chestnut Hill, MA, 02467, USA, hao.wu.5@bc.edu.
authors.forename: Hao
authors.initials: H
authors.lastname: Wu
authors.forename: Michael C
authors.initials: MC
authors.lastname: Neale
mesh_terms: D003198:Computer Simulation; D004777:Environment; D006801:Humans; D016013:Likelihood Functions; D008957:Models, Genetic; D015233:Models, Statistical; D010641:Phenotype; D018433:Twin Studies as Topic; D014427:Twins / Q000235:genetics
references.citation: Am J Cardiol. 1989 Dec 1;64(19):1333-7
references.pmid: 2686389
references.citation: Psychometrika. 2011 Apr 1;76(2):306-317
references.pmid: 23258944
references.citation: Behav Genet. 2006 Mar;36(2):331-40
references.pmid: 16474914
references.citation: Twin Res Hum Genet. 2006 Aug;9(4):490-5
references.pmid: 16899155
references.citation: Behav Genet. 2005 Sep;35(5):653-65
references.pmid: 16184491
references.citation: Biometrics. 1994 Dec;50(4):1171-7
references.pmid: 7786999
references.citation: Biostatistics. 2010 Apr;11(2):226-41
references.pmid: 20029057