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Robust testing for random effects in unbalanced heteroscedastic one-way models

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  • Inkyung Jung
  • Pranab Kumar Sen

Abstract

The usual variance ratio test for random effect, in a balanced design, is quite vulnerable to (i) unbalancedness, (ii) non-normality of either of the two random components, and (iii) heteroscedasticity of the chance errors. A robust rank-based test assuming only continuous, symmetric but otherwise arbitrary distributions for both the random effect and chance errors, and for a general heteroscedastic model is proposed here. Whereas the parametric tests are based on some F-distributional approximations, the proposed rank-based test rests on a normal approximation. Simulation studies, made to support the proposed methodology, suggest that not only the test is robust with respect to its significance level but also performs better in power, for heteroscedastic unbalanced models (even under normality).

Suggested Citation

  • Inkyung Jung & Pranab Kumar Sen, 2008. "Robust testing for random effects in unbalanced heteroscedastic one-way models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(4), pages 305-317.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:4:p:305-317
    DOI: 10.1080/10485250802018477
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    References listed on IDEAS

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    1. Hartung, Joachim & Knapp, Guido, 2000. "Confidence intervals for the between group variance in the unbalanced one-way random effects model of analysis of variance," Technical Reports 2000,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Harris, Ian R. & Burch, Brent D., 2005. "Measuring Relative Importance of Sources of Variation Without Using Variance," The American Statistician, American Statistical Association, vol. 59, pages 217-222, August.
    3. Mark G. Vangel & Andrew L. Rukhin, 1999. "Maximum Likelihood Analysis for Heteroscedastic One-Way Random Effects ANOVA in Interlaboratory Studies," Biometrics, The International Biometric Society, vol. 55(1), pages 129-136, March.
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