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A Statistical Model which Combines Features of Factor Analytic and Analysis of Variance Techniques
Open accessAbstract
This paper describes a method of matrix decomposition which retains the ability of factor analytic techniques to summarize data in terms of a relatively low number of coordinates; but at the same time, does not sacrifice the useful analysis of variance heuristic of partitioning data matrices into independent sources of variation which are relatively simple to interpret. The basic model is essentially a two-way analysis of variance model which requires that the matrix of interaction parameters be decomposed by using factor analytic techniques. Problems of judging statistical significance are discussed; and an illustrative example is presented.
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Research works printed but not linked: 18
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- Scheffé, 1959, The analysis of variance
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- Gollob, H. F. A combined additive and multiplicative model of word combination in sentences. Unpublished Ph.D. dissertation, Yale University, 1965.
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Statistical Analyses of Multilocation Trials
Crossa, J. (1990) · Advances in Agronomy · doi:10.1016/s0065-2113(08)60818-4 · Cited by 640
Functional measurement and psychophysical judgment.
Anderson, N. H. (1970) · Psychological Review · doi:10.1037/h0029064 · Cited by 576
Malosetti, M., Ribaut, J.-M., & van Eeuwijk, F. A. (2013) · Frontiers in Physiology · doi:10.3389/fphys.2013.00044 · Cited by 539
“A popular model of this type is the additive main effects and multiplicative interaction (AMMI) model (Gollob, 1968; Mandel, 1969; Gabriel, 1978; Gauch, 1988; van Eeuwijk, 1995).”
MethodOlivoto, T., Lúcio, A. D. C., da Silva, J. A. G., Marchioro, V. S., de Souza, V. Q., & Jost, E. (2019) · Agronomy Journal · doi:10.2134/agronj2019.03.0220 · Cited by 490
Metadata
- Authors
- Gollob, H. F.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1968-03
- Volume
- 33
- Issue
- 1
- Pages
- 73-115
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2025091503
- Cited by
- 595
- References
- 0
- FWCI
- 6.58
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
