Evaluation of Third-Order Method for the Tests of Variance Component in Linear Mixed Models

作     者：Yanyan Wu Augustine Wong Georges Monette Laurent Briollais 

作者机构：Department of Public Health Sciences University of Hawaii at Manoa Honolulu HI USA Department of Mathematics and Statistics York University Toronto ON Canada Lunenfeld-Taunenbaum Research Institute Mount Sinai Hospital Toronto ON Canada 

出 版 物：《Open Journal of Statistics》 (统计学期刊（英文）)

年 卷 期：2015年第5卷第4期

页      面：233-244页

学科分类：1002[医学-临床医学] 100214[医学-肿瘤学] 10[医学] 

主　　题：Family Data Genetic Variant Likelihood Ratio Test Random Effects Third-Order Method Variance Component 

摘      要：Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boundary conditions. It is well documented in literature that the traditional first-order methods: likelihood ratio statistic, Wald statistic and score statistic, provide an excessively conservative approximation to the null distribution. However, the magnitude of the conservativeness has not been thoroughly explored. In this paper, we propose a likelihood-based third-order method to the mixed models for testing the null hypothesis of zero and non-zero variance component. The proposed method dramatically improved the accuracy of the tests. Extensive simulations were carried out to demonstrate the accuracy of the proposed method in comparison with the standard first-order methods. The results show the conservativeness of the first order methods and the accuracy of the proposed method in approximating the p-values and confidence intervals even when the sample size is small.