How Large is the Probability for the Estimate of a Variance Component to be Negative?

Verdooren, L.R.

doi:10.1002/bimj.4710240404

Cited by 24 publications

(5 citation statements)

References 6 publications

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“…Laidig et al (2008) reported a fivefold larger ratio (14.2 compared with 14.4, a ratio of 1:1) from German long-term data on cultivar evaluation trials in wheat. The current simulation study showed that increasing the ratio of genotype VC to error VC decreased the REML-based bias of the genotype VC, and thus is in line with van Tassel et al (1995) and Verdooren (1982). Furthermore, it decreases the probability that the genotype VC is bounded at zero.…”

Section: Crop Sciencesupporting

confidence: 90%

Effect of missing values in multi‐environmental trials on variance component estimates

Hartung

Piepho

2021

Crop Science

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A common task in the analysis of multi-environmental trials (MET) by linear mixed models (LMM) is the estimation of variance components (VCs). Most often, MET data are imbalanced, e.g., due to selection. The imbalance mechanism can be missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR). If the missing-data pattern in MET was caused by selection, it is usually MAR. In this case, likelihood-based methods are the preferred methods for analysis as they can account for a MAR data pattern. Likelihood-based methods used to estimate VCs in LMM have the This article is protected by copyright. All rights reserved. 2property that all VC estimates are constrained to be non-negative and thus the estimators are generally biased. Therefore, there are two potential causes of bias in MET analysis: a data pattern not being MCAR and the bias of likelihood-based VC estimators. The current study tries to dissect and quantify both possible sources of bias. A simulation study with MET data typical for cultivar evaluation trials was conducted, in which the missing data pattern and the size of VCs were varied. The results showed that for the simulated MET, bias in VC estimates was similar under MCAR and MAR. Thus, the bias is solely due to the likelihoodbased estimation. Bias increase when increasing the ratio of genotype variance to error variance is small. Bias was similar for MAR and MCAR data patterns. Thus, it may be concluded that selection does not increase bias in VC estimation.

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Section: Crop Sciencesupporting

confidence: 90%

Effect of missing values in multi‐environmental trials on variance component estimates

Hartung

Piepho

2021

Crop Science

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“…For selected models, under the Normality assumption, some exact tests and procedures for constructing confidence intervals are available, see SEELY and EL-BASSIOUNI (1983), HARVILLE and FENECH (1985), KHURI and LITTELL (1987) and VERDOOREN (1988). Nesting is generally a favourable feature.…”

Section: Componenrs Of Variancementioning

confidence: 99%

The analysis of unbalanced linear models with variance components

Engel¹

1990

Statistica Neerlandica

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“…Negative variance components should therefore be allowed only with balanced data (Spilke, Hu, & Piepho, ). The probability of a negative variance estimate due to chance variation alone can be quite large in small data sets (Verdooren, ).…”

Section: Mixed Model Analysis Of Example 1 By Remlmentioning

confidence: 99%

A tutorial on the statistical analysis of factorial experiments with qualitative and quantitative treatment factor levels

Piepho

Edmondson²

2018

J Agronomy Crop Science

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Agronomic experiments are often complex and difficult to interpret, and the proper use of appropriate statistical methodology is essential for an efficient and reliable analysis. In this paper, the basics of the statistical analysis of designed experiments are discussed using real examples from agricultural field trials. Factorial designs allow for the study of two or more treatment factors in the same experiment, and here we discuss the analysis of factorial designs for both qualitative and quantitative level treatment factors. Where treatment factors have quantitative levels, models of treatment effects are essential for efficient analysis and in this paper we discuss the use experimental data is now readily available, and we demonstrate the use of two alternative software packages, the SAS package and the R language. The main purpose of the paper is to exemplify standard statistical methodology for routine analysis of designed experiments in agricultural research, but in our discussion we also provide some references for the study of more advanced methodology.factorial analysis, linear mixed models, polynomial regression, R, repeated-measures analysis, response surface models, SAS, split-plot analysis | INTRODUCTIONAgronomic experiments are often difficult and complex both to plan and to execute and may depend on many factors that can affect both efficiency and reliability. They are usually expensive and may sometimes take many years to accomplish. In addition, agronomic experiments are typically subject to high background variability due to effects such as fertility trends in fields or initial weight differences between animals or year-to-year variability in weather as well as to the high natural variability of biological and agronomic systems. wileyonlinelibrary.com/journal/jac | 1 the aims of the experiment and produces accurate and efficient information that provides a simple and parsimonious description of the results while still taking proper account of the error structure of the design. A properly chosen analysis will provide not only a full summary of the observed data but will also give additional insight into the effects of the treatments on the system under study.The focus of this paper is on designed experiments with treatment structures that can be modelled by polynomial regression methods. All the experiments considered are comparative, meaning that the focus is exclusively on comparisons between treatments in the same experiment (Bailey, 2008;Giesbrecht & Gumpertz, 2004;Hinkelmann & Kempthorne, 1994). Polynomial regression is a standard linear model methodology that fits naturally within the standard analysis of variance. We will show how modern mixed model computer software can be used for the routine analysis of blocked experiments based on a range of block and treatment structures, including designs with repeated observations on the same experimental units.The paper does not explicitly discuss the design of experiments, but it will be assumed that the example data sets have been col...

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How Large is the Probability for the Estimate of a Variance Component to be Negative?

Cited by 24 publications

References 6 publications

Effect of missing values in multi‐environmental trials on variance component estimates

Effect of missing values in multi‐environmental trials on variance component estimates

The analysis of unbalanced linear models with variance components

A tutorial on the statistical analysis of factorial experiments with qualitative and quantitative treatment factor levels

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