Monte Carlo Comparison of ANOVA, MIVQUE, REML, and ML Estimators of Variance Components

Swallow, William H.; Monahan, John F.

doi:10.2307/1268415

Cited by 88 publications

(63 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…When comparing the risks (rows 6-9), we see that ANOVA's, MLE and REML's methods are similar in terms of the efficiency except for the risk of Σ g and Σ e . This is consistent with the Monte Carlo simulation study conducted by Swallow and Monahan (1984). The significance of the difference between ANOVA's and MLE's risks decreases when the number of traits, r, increases, while REML's risks maintain good performance even as r increases.…”

Section: Efficiency Of the Proposed Anova Estimator For Variance Compsupporting

confidence: 88%

“…In fact, what could be seen first as an outdated approach is actually a fast and powerful way to estimate variance components. As shown in Swallow & Monahan (1984), the ANOVA VC estimators we propose are unique and efficient, as it is the case with one-way random effect models. Note that one can also include covariates in the model.…”

Section: Discussionmentioning

confidence: 98%

“…The ANOVA estimators of the VC under an unbalanced one way random effect ANOVA model are given in Searle (1971), Swallow & Monahan (1984) and Searle (1992). However, these estimators do not take into account the familial structure in the data.…”

Section: Anova Estimators Of V C Accounting For Familial Dependencementioning

confidence: 99%

“…S t = S b + S w ), where S t is the total scatter Sum of Squares matrix. This leads to independent sums of squares and competent and unique ANOVA estimators (see for instance Swallow & Monahan, 1984, for more details). Note also that the ANOVA estimators we obtained from Proposition 1 are linear combination of S b and S w .…”

Section: Anova Estimators Of V C Accounting For Familial Dependencementioning

confidence: 99%

See 3 more Smart Citations

Principal Components of Heritability for High Dimension Quantitative Traits and General Pedigrees

Oualkacha¹,

Labbe²,

Ciampi³

et al. 2012

Statistical Applications in Genetics and Molecular Biology

View full text Add to dashboard Cite

For many complex disorders, genetically relevant disease definition is still unclear. For this reason, researchers tend to collect large numbers of items related directly or indirectly to the disease diagnostic. Since the measured traits may not be all influenced by genetic factors, researchers are faced with the problem of choosing which traits or combinations of traits to consider in linkage analysis. To combine items, one can subject the data to a principal component analysis. However, when family date are collected, principal component analysis does not take family structure into account. In order to deal with these issues, Ott & Rabinowitz (1999) introduced the principal components of heritability (PCH), which capture the familial information across traits by calculating linear combinations of traits that maximize heritability. The calculation of the PCHs is based on the estimation of the genetic and the environmental components of variance. In the genetic context, the standard estimators of the variance components are Lange's maximum likelihood estimators, which require complex numerical calculations. The objectives of this paper are the following: i) to review some standard strategies available in the literature to estimate variance components for unbalanced data in mixed models; ii) to propose an ANOVA method for a genetic random effect model to estimate the variance components, which can be applied to general pedigrees and high dimensional family data within the PCH framework; iii) to elucidate the connection between PCH analysis and Linear Discriminant Analysis. We use computer simulations to show that the proposed method has similar asymptotic properties as Lange's method when the number of traits is small, and we study the efficiency of our method when the number of traits is large. A data analysis involving schizophrenia and bipolar quantitative traits is finally presented to illustrate the PCH methodology.

show abstract

Section: Efficiency Of the Proposed Anova Estimator For Variance Compsupporting

confidence: 88%

Section: Discussionmentioning

confidence: 98%

Section: Anova Estimators Of V C Accounting For Familial Dependencementioning

confidence: 99%

Section: Anova Estimators Of V C Accounting For Familial Dependencementioning

confidence: 99%

See 2 more Smart Citations

Principal Components of Heritability for High Dimension Quantitative Traits and General Pedigrees

Oualkacha¹,

Labbe²,

Ciampi³

et al. 2012

Statistical Applications in Genetics and Molecular Biology

View full text Add to dashboard Cite

show abstract

“…(1992). To summarize, REML has been shown in simulation studies to perform better in terms of bias and mean-squared error than method-of-moments (Swallow and Monahan, 1984). A Newton-type implementation of REML produces an asymptotic covariance matrix for the estimated parameters; this is absent in most method-of-moments procedures.…”

Section: Why Reml?mentioning

confidence: 99%

Analyzing Split-Plot Andrepeated-Measures Designsusing Mixed Models

Wolfinger¹,

Miles-McDermott²,

Kendall³

1992

Conference on Applied Statistics in Agriculture

View full text Add to dashboard Cite

Abstract\Ve first introduce the general linear llllxed model and provide a j ustificatioll for using REML to fit it. Then, for an irrigation example, we present sevt~raJ mixed models of increasiug complexity. The initial model corresponds to a typical split-plot analysis. Next, we present covariance structureI' that directly describe the variability of repeated measures within whole plots. Finally, we combine the above types into more complicated mixed models, and compare them using likelihood-based criteria.

show abstract

Non-Iterative Robust Estimators of Variance Components in Within-Subject Designs

Mehrotra¹

1997

Statist. Med.

View full text Add to dashboard Cite

Classic estimators of variance components break down in the presence of outliers and perform less efficiently under non-normality. In this article I present simple non-iterative estimators of variance components that are resistant to outliers and robust to systematic departures from normality, such as heavy tailedness of the distribution of responses. The proposed estimators are based on a robust extension of Hocking's AVE approach and are thus called RAVE estimators. I present results from a Monte Carlo comparison of RAVE versus classic estimation methods including maximum likelihood (ML), restricted maximum likelihood (REML) and minimum variance quadratic unbiased estimation (MIVQUE). Under simulated deviations from normality, RAVE estimators are associated with smaller mean squared errors than all the comparators, and in the normal case they exhibit a minimal loss in relative efficiency. A numerical example illustrates the proposed methodology.

show abstract

Monte Carlo Comparison of ANOVA, MIVQUE, REML, and ML Estimators of Variance Components

Cited by 88 publications

References 0 publications

Principal Components of Heritability for High Dimension Quantitative Traits and General Pedigrees

Principal Components of Heritability for High Dimension Quantitative Traits and General Pedigrees

Analyzing Split-Plot Andrepeated-Measures Designsusing Mixed Models

Non-Iterative Robust Estimators of Variance Components in Within-Subject Designs

Contact Info

Product

Resources

About