Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON ASYMPTOTIC TESTS IN TEREE-FACTOR FACTORIAL DESIGNS WITH NO REPLICATIONS

  • See, Kyoung-Ah (Department of Mathematics and Statistics Miami university)
  • Published : 1999.03.01

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Abstract

We revisit the problems of testing three-factor classifica-tion models with a single observation per cell. A common approach in analyzing such nonreplicated data is to omit the highest order in-teraction and regard it as error. This paper discusses the use of a multiplicative model(See and Smith 1996 and 1998) which is applied on residuals in order to separate the variablility due to three-factor interaction from what is counted as random error. in particualr to test the significance of the interaction term we derived an approxi-mated distribution of the likelihood ratio test statistic based on the quadrilinear model known as Tucher's three-mode principal compo-nent model. The derivation utilizes the distribution of the eignevalues of the Wishart matrix.

Keywords

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