Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

Harville, David A.

doi:10.1080/01621459.1977.10480998

Cited by 2,667Statistical Methods and Bayesian InferenceStatistical and numerical algorithmsAdvanced Statistical Methods and Models

Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

Harville, David A.·1977·Journal of the American Statistical Association

DOI 10.1080/01621459.1977.10480998

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Abstract

Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be considered for computing the ml or reml estimates. The computations on each iteration of these algorithms are those associated with computing estimates of fixed and random effects for given values of the variance components.

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The ReML objective function and the variational energy are formally identical under this model.
“It is interesting to note that the ReML objective function and the variational energy are formally identical under this model [15],[18].”
From Hierarchical Models in the Brain (2008) · cites this paper as [18]
Static cases of the fixed-form scheme reduce to expectation maximisation (EM) and restricted maximum likelihood (ReML) for linear models.
“We have discussed static cases of this fixed-form scheme previously and how it reduces to expectation maximisation (EM; [17]) and restricted maximum likelihood (ReML; [18]) for linear models [15].”
From Hierarchical Models in the Brain (2008) · cites this paper as [18]

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Authors: Harville, D. A.
Affiliations: Iowa State University (US)
Corresponding author: Harville, David A.
Venue: Journal of the American Statistical Association
Publisher: Informa UK Limited
Published: 1977-06
Volume: 72
Issue: 358
Pages: 320-338
ISSN: 0162-1459 (ISSN-L)
1537-274X
DOI: 10.1080/01621459.1977.10480998
OpenAlex: W1982585616
Cited by: 2,667
References: 86
Citations by year: 2026: 56 · 2025: 62 · 2024: 72 · 2023: 86 · 2022: 113 · 2021: 73 · 2020: 71 · 2019: 77 · 2018: 75 · 2017: 79 · 2016: 69 · 2015: 76 · 2014: 114 · 2013: 70 · 2012: 109
FWCI: 16.91
Type: journal article
Language: en
Open access: closed
Locations: Journal of the American Statistical Association (publishedVersion)
Defense Technical Information Center (DTIC) (submittedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
Keywords: variance component estimation, maximum likelihood estimation, restricted maximum likelihood, fixed and random effects, iterative methods, asymptotic theory, mixed models

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Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

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