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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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On the likelihood ratio tests in bivariate ACDE models.

Hao Wu¹, Michael C Neale

¹Boston College, 300 McGuinn Hall, 140 Commonwealth Ave, Chestnut Hill, MA, 02467, USA, hao.wu.5@bc.edu.

|August 10, 2014

Summary

This study resolves issues with likelihood ratio tests (LRTs) in bivariate genetic models. New methods provide more powerful tests for genetic and environmental influences in twin studies.

Area of Science:

Behavioral Genetics
Quantitative Genetics
Statistical Genetics

Background:

Twin studies commonly use ACE and ADE models to dissect genetic and environmental influences on phenotypes.
Traditional likelihood ratio tests (LRTs) for variance components in these models are statistically problematic due to boundary parameter issues.
Previous work addressed univariate ACDE models, but bivariate models remained unresolved.

Purpose of the Study:

To resolve the statistical challenges of LRTs in bivariate ACDE models.
To develop accurate asymptotic sampling distributions for LRT statistics in bivariate genetic analyses.
To enhance the power of statistical tests for genetic and environmental components in twin studies.

Main Methods:

Applied theoretical frameworks of inequality constrained LRTs using cone approximations.

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Derived asymptotic sampling distributions for test statistics in bivariate ACE/ADE models.

Utilized simulation studies to confirm derived distributions and test statistic properties.

Main Results:

The asymptotic sampling distribution for testing a single bivariate component is a mixture of chi-squared distributions (dfs 0-3).
The distribution for testing both additive genetic (A) and non-additive genetic (C or D) components is a mixture of chi-squared distributions (dfs 0-6).
These novel distributions are stochastically smaller than traditional chi-squared distributions, leading to more powerful LRTs.

Conclusions:

The study provides a statistically sound framework for LRTs in bivariate ACDE models.
The derived distributions and methods increase the power of detecting genetic and environmental effects in twin data.
This work offers a significant advancement for quantitative genetic analyses in twin and family studies.