Tests concerning a nested mixed model with heteroscedastic random effects

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Abstract

The purpose of this article is to present tests concerning the fixed and random effects for a two-fold nested mixed model under the following conditions:

  • 1.

    (i) The nesting effect is fixed.

  • 2.

    (ii) The nested effect is random with an unknown variance component assumed to depend only on the levels of the nesting effect.

  • 3.

    (iii) All random effects, including the random errors, are independently distributed as normal variates.

  • 4.

    (iv) The subclass frequencies in the last stage are equal (last-stage uniformity).

An example is given to illustrate the proposed tests.

References (23)

  • T.W. Anderson

    A test for equality of means when covariance matrices are unequal

    Ann. Math. Statist.

    (1963)
  • B.M. Bennett

    Note on a solution of the generalized Behrens-Fisher problem

    Ann. Inst. Statist. Math.

    (1951)
  • G.E.P. Box

    Non-normality and tests on variances

    Biometrika

    (1953)
  • G.E.P. Box

    Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effect of inequality of variance in the one-way classificat ion

    Ann. Math. Statist.

    (1954)
  • G.E.P. Box et al.

    Permutation theory in the derivation of robust criteria and the study of departures from assumption

    J. Roy. Statist. Soc. Ser. B

    (1955)
  • K.A. Brownlee

    Statistical Theory and Methodology in Science and Engineering

    (1965)
  • S.R. Dalal

    Simultaneous confidence procedures for univariate and multivariate Behrens-Fisher type problems

    Biometrika

    (1978)
  • M.L. Eaton

    Some remarks on Scheffé's solution to the Behrens-Fisher problem

    J. Amer. Statist. Assoc.

    (1969)
  • M. Hussein et al.

    An unbalanced nested model with random effects having unequal variances

    Biometrical J.

    (1978)
  • K. Ito

    On the effect of heteroscedasticity and nonnormality upon some multivariate test procedures

  • G.S. James

    Tests of linear hypothesis in univariate and multivariate analysis when the ratios of the population variances are unknown

    Biometrika

    (1954)

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