Biometrical Letters vol. 43(2), 2006, pp. 109-130
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EVENNESS CONDITIONS FOR FOUR-FACTOR CROSS-NESTED MODELS
C. Fernandes1, P. Ramos1, J. T. Mexia2 1Área Científica de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 01-1959-007 Lisboa, Portugal, cfernandes@deetc.isel.ipl.pt, pramos@deetc.isel.ipl.pt 2Departamento de Matemática, Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, Monte da Caparica 2829-516 Caparica, Portugal, jmt@fct.unl.pt |
Fonseca et al. (2003) obtained UMVUE for the variance components of balanced cross nested models. The estimators were the difference of a positive and a negative part. Unbiased estimators are obtained for the variance components of such models with cross-nesting. Following Michalski & Zmy¶lony (1996) we may use the quotient of the positive by the negative part of the estimators to test the nullity of the variance components. If either the degrees of freedom in the numerator or in the denominator are even we have, (Fonseca et al., 2002) an exact expression for the distribution of the test statistic. It is thus interesting to see if this evenness conditions are a rarity or if they are satisfied in many circumstances. If we name as first evenness condition (1st) that all components of the vector g1 are even and as second evenness condition (2nd) that all components of the vector g2 are even, when at least one of these evenness conditions holds we have an exact expression for the distribution of the test statistic. We will answer this question for four factors models, showing that in more then half of the possible degrees of freedom combinations, at least one of the evenness conditions holds.
Cross nested balanced models, variance components, usual and generalized F tests, evenness conditions.
