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On the Likelihood Ratio Tests in Bivariate ACDE Models

Published online by Cambridge University Press:  01 January 2025

Hao Wu and
Michael C. Neale
Hao Wu*
Affiliation:
Boston College
Michael C. Neale
Affiliation:
Virginia Commonwealth University
*
Requests for reprints should be sent to Hao Wu, Boston College, 300 McGuinn Hall, 140 Commonwealth Ave, Chestnut Hill, MA, 02467, USA. E-mail: hao.wu.5@bc.edu
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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 χ2 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 χ2 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.

Keywords

ACE modelvariance componentslikelihood ratio testχ-2 distribution

Information

Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 3 , July 2013, pp. 441 - 463
Copyright
Copyright © 2012 The Psychometric Society

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