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A method for detecting hidden additivity in two-factor unreplicated experiments

Author

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  • Franck, Christopher T.
  • Nielsen, Dahlia M.
  • Osborne, Jason A.

Abstract

Assessment of interaction in unreplicated two-factor experiments is a challenging problem that has received considerable attention in the literature. A model is proposed in which the levels of one factor belong in two or more groups. Within each group the effects of the two factors are additive but the groups may interact with the ungrouped factor. This structure is called “hidden additivity” if group membership is latent. To identify plausible groupings a search is performed over the space of all possible configurations, or placement of units into two or more groups. A multiplicity-adjusted all-configurations maximum interaction F (ACMIF) test to detect hidden additivity is developed. The method is illustrated using two data sets taken from the literature and a third taken from a recent study of copy number variation due to lymphoma. A simulation study demonstrates the power of the test for hidden additivity and compares it with other well-known tests from the literature.

Suggested Citation

  • Franck, Christopher T. & Nielsen, Dahlia M. & Osborne, Jason A., 2013. "A method for detecting hidden additivity in two-factor unreplicated experiments," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 95-104.
    • Handle: RePEc:eee:csdana:v:67:y:2013:i:c:p:95-104
    DOI: 10.1016/j.csda.2013.05.002
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    References listed on IDEAS

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    1. Tusell, Fernando, 1990. "Testing for interaction in two-way ANOVA tables with no replication," Computational Statistics & Data Analysis, Elsevier, vol. 10(1), pages 29-45, August.
    2. Harry Gollob, 1968. "A statistical model which combines features of factor analytic and analysis of variance techniques," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 73-115, March.
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    Cited by:

    1. Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2021. "REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 987-1013, December.
    2. Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2023. "E-ReMI: Extended Maximal Interaction Two-mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 298-331, July.

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