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

Open Journal of Statistics 2015年第4期5卷 233-244页

作者： Yanyan Wu Augustine Wong Georges Monette laurent briollais 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

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.

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

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Parameter Estimation in Logistic Regression for Transition, Reverse Transition and Repeated Transition from Repeated Outcomes

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Applied Mathematics 2012年第11期3卷 1739-1749页

作者： Rafiqul I. Chowdhury M. Ataharul Islam Shahariar Huda laurent briollais Department of Epidemiology and Biostatistics Western University London Canada Department of Statistics and OR King Saud University Riyadh KSA Department of Statistics and OR Kuwait University Kuwait City Kuwait Samuel Lunenfeld Research Institute Mount Sinai Hospital Toronto Canada

Covariate dependent Markov models dealing with estimation of transition probabilities for higher orders appear to be restricted because of over-parameterization. An improvement of the previous methods for handling runs of events by expressing the conditional probabilities in terms of the transition probabilities generated from Markovian assumptions was proposed using Chapman-Kolmogorov equations. Parameter estimation of that model needs extensive pre-processing and computations to prepare data before using available statistical softwares. A computer program developed using SAS/IML to estimate parameters of the model are demonstrated, with application to Health and Retirement Survey (HRS) data from USA.

关键词： Computer Program Markov Model Transition Reverse Transition Repeated Transition

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