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Calculating Asymptotic Significance Levels of the Constrained Likelihood Ratio Test with Application to Multivariate Genetic Linkage Analysis

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Listed:
  • Morris Nathan J

    (Case Western Reserve University)

  • Elston Robert

    (Case Western Reserve University)

  • Stein Catherine M

    (Case Western Reserve University)

Abstract

The asymptotic distribution of the multivariate variance component linkage analysis likelihood ratio test has provoked some contradictory accounts in the literature. In this paper we confirm that some previous results are not correct by deriving the asymptotic distribution in one special case. It is shown that this special case is a good approximation to the distribution in many situations. We also introduce a new approach to simulating from the asymptotic distribution of the likelihood ratio test statistic in constrained testing problems. It is shown that this method is very efficient for small p-values, and is applicable even when the constraints are not convex. The method is related to a multivariate integration problem. We illustrate how the approach can be applied to multivariate linkage analysis in a simulation study. Some more philosophical issues relating to one-sided tests in variance components linkage analysis are discussed.

Suggested Citation

  • Morris Nathan J & Elston Robert & Stein Catherine M, 2009. "Calculating Asymptotic Significance Levels of the Constrained Likelihood Ratio Test with Application to Multivariate Genetic Linkage Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-34, September.
    • Handle: RePEc:bpj:sagmbi:v:8:y:2009:i:1:n:39
    DOI: 10.2202/1544-6115.1456
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    References listed on IDEAS

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    1. Wolak, Frank A, 1991. "The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models," Econometrica, Econometric Society, vol. 59(4), pages 981-995, July.
    2. Geert Verbeke & Geert Molenberghs, 2003. "The Use of Score Tests for Inference on Variance Components," Biometrics, The International Biometric Society, vol. 59(2), pages 254-262, June.
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