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Cited by 0Statistical Methods and Bayesian InferenceStatistical Methods and ApplicationsAdvanced Statistical Methods and Models

The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.

Analysis of Variance: Estimation of Variance Components (Model II of the Analysis of Variance)

Dieter Rasch, Dieter Schott·2018·Mathematical Statistics
DOI 10.1002/9781119385295.ch6
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Abstract

This chapter considers models of the analysis of variance (ANOVA) where all factors are random. The model in this case is known as model II. The chapter describes a theorem that allows statisticians to calculate the expectations of the mean squares of an ANOVA based on model II, which is of importance to one of the methods for estimating the components σ2i and σ2. The chapter applies the method of Henderson for several classifications. The estimator of a component is reached by replacing all observed values in the corresponding equation of the estimate by the corresponding random variables. The chapter describes components with the estimation tests of hypotheses about the variance. Besides the method of Henderson, three further methods are mainly in use. These include the maximum likelihood method (ML), the restricted ML (REML), and the MINQUE method. Each of these four methods can be performed by SPSS.

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Crossref · 10.1002/9781119385295.ch6

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21 of 21 references verified0 citation errors · 0 not checkable

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Research works printed but not linked: 6

  1. Drygas H., 1980, Mathematical Statistics, Banach Centre Publications, 95
  2. Hammersley J. M., 1949, The unbiased estimate and standard error of the interclass variance, Metron, 15, 189
  3. Herrendörfer G., 1976, Versuchsplanung im linearen Modell – Schätzung von Varianzkomponenten und eingeschränkte Messwerterfassung bei der Schätzung und dem Vergleich von Mittelwerten und Regressionskoeffizienten
  4. 10.2307/2284244 · DOI
  5. Searle S. R., 1971, Linear Models
  6. Townsend E. C., 1968, Unbiased estimators of variance components in simple unbalanced designs

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Metadata

Authors
Rasch, D., & Schott, D.
Affiliations
  • BOKU University (AT)
  • Wismar University of Applied Sciences (DE)
ORCID
Dieter Rasch
Venue
Mathematical Statistics
Publisher
Wiley
Published
2018-01-12
Pages
293-340
DOI
10.1002/9781119385295.ch6
OpenAlex
W4247619294
Cited by
0
References
21
Type
other
Language
en
Open access
closed
Licence
doi.wiley.com/10.1002/tdm_license_1.1 (tdm)
Locations
Wiley eBooks (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
Keywords
random effects models, variance component estimation, maximum likelihood estimation, restricted maximum likelihood, MINQUE, SPSS

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