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A Reformulation of Linear Models
Open accessAbstract
Dissatisfaction is expressed with aspects of the current exposition of linear models, including the neglect of marginality, unnecessary differences between models for finite and infinite populations, failure to distinguish different kinds of random terms, impositon of unnecessary and inconsistent constraints on parameters, and lack of an adequate notation for negative components of variance.The reformulation, exemplified for crossed and nested classifications of balanced data, and for simple orthogonal designed experiments, is designed to integrate finite and infinite populations, random and fixed effects, excess and deficit of variance, to avoid unnecessary constraints on parameters, and to lead naturally to interesting hypotheses about the model terms.
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Cites
Average Values of Mean Squares in Factorials
Cornfield, J., & Tukey, J. W. (1956) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728067 · Cited by 292
Cited by
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McCullagh, P. (2002) · The Annals of Statistics · doi:10.1214/aos/1035844977 · Cited by 248
Controversies concerning randomization and additivity in clinical trials.
Senn, S. (2004) · Statistics in Medicine · doi:10.1002/sim.2074 · Cited by 132
Shell, M. D., Gazelle, H., & Faldowski, R. A. (2014) · Developmental Psychology · doi:10.1037/a0035528 · Cited by 99
Analysis of variance—why it is more important than ever
Gelman, A. (2005) · The Annals of Statistics · doi:10.1214/009053604000001048 · Cited by 861
Meinhardt, L.-M., Elhaidary, M., Colley, M., Rietzler, M., Rixen, J. O., Purohit, A. K., & Rukzio, E. (2025) · Proceedings of the 2025 CHI Conference on Human Factors in Computing Systems · doi:10.1145/3706598.3713187 · Cited by 16
Metadata
- Authors
- Nelder, J. A.
- Venue
- Journal of the Royal Statistical Society. Series A (General)
- Publisher
- JSTOR
- Published
- 1977
- Volume
- 140
- Issue
- 1
- Pages
- 48
- ISSN
- 0035-9238 (ISSN-L)
- OpenAlex
- W2339398872
- Cited by
- 338
- References
- 1
- FWCI
- 3.87
- Type
- journal article
- Language
- en
- Open access
- green
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