A Comparison of Variance Component Estimators

Corbeil, R. R.; Searle, S. R.

doi:10.2307/2529264

Cited by 111 publications

(26 citation statements)

References 11 publications

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“…In the balanced case, REML estimators without restrictions on the parameter space have closed form and are identical to their counterparts from (M)ANOVA (e.g., Corbeil and Searle 1976;Lee and Kapadia 1984). For normally distributed data, restricting the eigenvalues of W À1 B in the one-way classification to a minimum of unity in fact is equivalent to REML estimation of S B and S W constrained to the parameter space (Amemiya 1985, Appendix).…”

Section: Bias Due To Sampling Variancementioning

confidence: 99%

Perils of Parsimony: Properties of Reduced-Rank Estimates of Genetic Covariance Matrices

Meyer

Kirkpatrick

2008

Genetics

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Eigenvalues and eigenvectors of covariance matrices are important statistics for multivariate problems in many applications, including quantitative genetics. Estimates of these quantities are subject to different types of bias. This article reviews and extends the existing theory on these biases, considering a balanced one-way classification and restricted maximum-likelihood estimation. Biases are due to the spread of sample roots and arise from ignoring selected principal components when imposing constraints on the parameter space, to ensure positive semidefinite estimates or to estimate covariance matrices of chosen, reduced rank. In addition, it is shown that reduced-rank estimators that consider only the leading eigenvalues and -vectors of the ''between-group'' covariance matrix may be biased due to selecting the wrong subset of principal components. In a genetic context, with groups representing families, this bias is inverse proportional to the degree of genetic relationship among family members, but is independent of sample size. Theoretical results are supplemented by a simulation study, demonstrating close agreement between predicted and observed bias for large samples. It is emphasized that the rank of the genetic covariance matrix should be chosen sufficiently large to accommodate all important genetic principal components, even though, paradoxically, this may require including a number of components with negligible eigenvalues. A strategy for rank selection in practical analyses is outlined.

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Section: Bias Due To Sampling Variancementioning

confidence: 99%

Perils of Parsimony: Properties of Reduced-Rank Estimates of Genetic Covariance Matrices

Meyer

Kirkpatrick

2008

Genetics

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“…A mixed-model unbalanced nested analysis of variance (ANOVA; BMDP3V, 1987 version) based on the maximum likeli hood technique [Corbeil and Searle, 1976;Harville, 1977: Dixon et al, 1985 was used to estimate the variance components for each of the 9 EMG parameters. This nested ANOVA had three levels: spe- cies (fixed factor), individual (random factor) and implant (ran dom factor).…”

Section: Statistical a Nalysismentioning

confidence: 99%

Variation in Neuromuscular Activity during Prey Capture by Trophic Specialists and Generalists (Pisces: Labridae)

Sl¹

1988

Brain Behav Evol

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Members of the marine teleost family Labridae are among the most abundant and morphologically diverse fish on coral reefs. A quantitative analysis was conducted of the neuromuscular activity patterns controlling movement of the jaws during prey capture by 4 labrid species ranging from trophic specialists to trophic generalists. A total of more than 800 captures of 3 prey types was analyzed. All 4 species showed significant modulation of electromyographic parameters in response to different prey types. Significant variation was also found between replicate experiments on the same individuals. To obtain valid assessments of interspecific variability, statistical analyses must take into account this potentially high degree of intraspecific variability. By partitioning the variance in a nested analysis of variance, a lack of significant differences in electromyographic parameters between species became apparent. In contrast to the closely related Cichlidae, trophic diversification in the Labridae has not been accompanied by the acquisition of unique neuromuscular activity patterns for prey capture. The dramatic adaptive radiation that has occurred in these 2 families has involved different processes of evolutionary diversification. Neuromuscular stereotypy of labrids may be associated with the lack of structural flexibility in their ‘coupled jaw’, Additional study is needed to establish the extent to which labrid radiation into various trophic niches is related to the evolution of specialized morphologies and foraging behaviors.

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“…(11) and (12) were solved with the restricted maximum likelihood method (Corbeil and Searle, 1976) to ensure an unbiased estimation of V.…”

Section: Group Comparisonmentioning

confidence: 99%

Dynamic Bayesian network modeling of fMRI: A comparison of group-analysis methods

Wang

Palmer

et al. 2008

NeuroImage

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Bayesian network (BN) modeling has recently been introduced as a tool for determining the dependencies between brain regions from functional-magnetic-resonance-imaging (fMRI) data. However, studies to date have yet to explore the optimum way for meaningfully combining individually determined BN models to make group inferences. We contrasted the results from three broad approaches: the "virtual-typical-subject" (VTS) approach which pools or averages group data as if they are sampled from a single, hypothetical virtual typical subject; the "individual-structure" (IS) approach that learns a separate BN for each subject, and then finds commonality across the individual structures, and the "common-structure" (CS) approach that imposes the same network structure on the BN of every subject, but allows the parameters to differ across subjects. To explore the effects of these three approaches, we applied them to an fMRI study exploring the motor effect of L-dopa medication on ten subjects with Parkinson's disease (PD), as the profound clinical effects of this medication suggest that fMRI activation in PD subjects after medication should start approaching that of age-matched controls. We found that none of these approaches is generally superior over the others, according to Bayesian-information-criterion (BIC) scores, and that they led to considerably different group-level results. The IS approach was more sensitive to the normalization effect of the L-dopa medication on brain connectivity. However, for the more homogeneous control population, the VTS approach was superior. Group-analysis approaches should be selected carefully with consideration of both statistical and biomedical evidence.

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A Comparison of Variance Component Estimators

Abstract: June, 1975 Explicit solutions are given for the maxi111tm likelihood (ML) and restricted maximm likelihood (RDn.) equations under normality for four conn:non variance com-

Cited by 111 publications

References 11 publications

Perils of Parsimony: Properties of Reduced-Rank Estimates of Genetic Covariance Matrices

Perils of Parsimony: Properties of Reduced-Rank Estimates of Genetic Covariance Matrices

Variation in Neuromuscular Activity during Prey Capture by Trophic Specialists and Generalists (Pisces: Labridae)

Dynamic Bayesian network modeling of fMRI: A comparison of group-analysis methods

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