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Symbolic Description of Factorial Models for Analysis of Variance

Author

Listed:
  • G. N. Wilkinson
  • C. E. Rogers

Abstract

The paper describes the symbolic notation and syntax for specifying factorial models for analysis of variance in the control language of the genstat statistical program system at Rothamsted. The notation generalizes that of Nelder (1965). Algorithm AS 65 (Rogers, 1973) converts factorial model formulae in this notation to a list of model terms represented as binary integers. A further extension of the syntax is discussed for specifying models generally (including non‐linear forms).

Suggested Citation

  • G. N. Wilkinson & C. E. Rogers, 1973. "Symbolic Description of Factorial Models for Analysis of Variance," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 392-399, November.
    • Handle: RePEc:bla:jorssc:v:22:y:1973:i:3:p:392-399
    DOI: 10.2307/2346786
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    3. Wei Pan & Xianbin Wang & Wenwei Zhou & Bowen Hang & Liwen Guo, 2023. "Linguistic Analysis for Identifying Depression and Subsequent Suicidal Ideation on Weibo: Machine Learning Approaches," IJERPH, MDPI, vol. 20(3), pages 1-12, February.
    4. Christian Kleiber & Achim Zeileis, 2005. "Validating multiple structural change models-a case study," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 685-690.
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    6. Großmann, Heiko, 2014. "Automating the analysis of variance of orthogonal designs," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 1-18.
    7. Zardetto Diego, 2015. "ReGenesees: an Advanced R System for Calibration, Estimation and Sampling Error Assessment in Complex Sample Surveys," Journal of Official Statistics, Sciendo, vol. 31(2), pages 177-203, June.
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    9. Jamie Cummins & Jan De Houwer, 2019. "An inkblot for beliefs: The Truth Misattribution Procedure," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-21, June.
    10. Jesper Ryden & Sven Erick Alm, 2010. "The effect of interaction and rounding error in two-way ANOVA: example of impact on testing for normality," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(10), pages 1695-1701.
    11. Riehl, Kevin & Kiesel, Florian & Schiereck, Dirk, 2022. "Political and Socioeconomic Factors That Determine the Financial Outcome of Successful Green Innovation," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 132099, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    12. Nitzan Shahar & Tobias U Hauser & Michael Moutoussis & Rani Moran & Mehdi Keramati & NSPN consortium & Raymond J Dolan, 2019. "Improving the reliability of model-based decision-making estimates in the two-stage decision task with reaction-times and drift-diffusion modeling," PLOS Computational Biology, Public Library of Science, vol. 15(2), pages 1-25, February.
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    14. Zeileis, Achim & Kleiber, Christian & Kramer, Walter & Hornik, Kurt, 2003. "Testing and dating of structural changes in practice," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 109-123, October.
    15. Bent Nielsen, 2014. "Deviance analysis of age-period-cohort models," Economics Papers 2014-W03, Economics Group, Nuffield College, University of Oxford.
    16. Cansino, José M. & Dugo, Víctor & Gálvez-Ruiz, David & Román-Collado, Rocío, 2023. "What drove electricity consumption in the residential sector during the SARS-CoV-2 confinement? A special focus on university students in southern Spain," Energy, Elsevier, vol. 262(PB).
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    19. Artur Araujo & Steven Julious & Stephen Senn, 2016. "Understanding Variation in Sets of N-of-1 Trials," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-24, December.
    20. Payne, Roger W., 1998. "Design keys, pseudo-factors and general balance," Computational Statistics & Data Analysis, Elsevier, vol. 29(2), pages 217-229, December.
    21. Emil Exenberger & Michaela Kav?áková, 2020. "Evaluation of financial health of companies through data envelopment analysis: Selection of variables for the DEA model in R," Proceedings of Economics and Finance Conferences 10913067, International Institute of Social and Economic Sciences.
    22. Kevser Cetin & Wolfram Mauser, 2023. "The Role of Recent Climate Change in Explaining the Statistical Yield Increase of Maize in Northern Bavaria—A Model Study," Agriculture, MDPI, vol. 13(7), pages 1-19, July.

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