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Recovery of inter-block information when block sizes are unequal
Abstract
A method is proposed for estimating intra-block and inter-blook weights in the analysis of incomplete block designs with block sizes not necessarily equal. The method consists of maximizing the likelihood, not of all the data, but of a set of selected error contrasts. When block sizes are equal results are identical with those obtained by the method of Nelder (1968) for generally balanced designs. Although mainly concerned with incomplete block designs the paper also gives in outline an extension of the modified maximum likelihood procedure to designs with a more complicated block structure.
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Citations
Cited by
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
“It can be shown that the estimates Of u2, 3l *,s ak+1 found in this way are identical to those described by Patterson and Thompson (1971), Corbeil and Searle (1976) and Harville (1977) under the label REML, or "restricted" maximum likelihood.”
ResultApplied Longitudinal Data Analysis: Modeling Change and Event Occurrence
Singer, J. D., & Willett, J. B. (2003) · doi:10.1093/acprof:oso/9780195152968.001.0001 · Cited by 10,647
GCTA: a tool for genome-wide complex trait analysis
Yang, J., Lee, S. H., Goddard, M. E., & Visscher, P. M. (2011) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2010.11.011 · Cited by 8,279
Random-Effects Models for Longitudinal Data
Laird, N. M., & Ware, J. H. (1982) · Biometrics · doi:10.2307/2529876 · Cited by 8,923
Prediction of Total Genetic Value Using Genome-Wide Dense Marker Maps
Meuwissen, T. H. E., Hayes, B. J., & Goddard, M. E. (2001) · Genetics · doi:10.1093/genetics/157.4.1819 · Cited by 7,917
Metadata
- Authors
- PATTERSON, H. D., & THOMPSON, R.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1971
- Volume
- 58
- Issue
- 3
- Pages
- 545-554
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2000084758
- Cited by
- 4,058
- References
- 0
- FWCI
- 4.30
- Type
- journal article
- Language
- en
- Open access
- closed
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- PATTERSON, H. D., & THOMPSON, R. (1971). Recovery of inter-block information when block sizes are unequal. Biometrika. https://doi.org/10.1093/biomet/58.3.545
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
