Confidence Intervals on the Total Variance in an Unbalanced Two-fold Nested Design

Confidence intervals on the total variance in an unbalanced random two-fold nested design are constructed and compared. Computer simulation indicates the proposed intervals provide confidence coefficients that are generally close to the stated level.     

Approximate Confidence Interval on Ratio of Two Variances in a Two-way Crossed Model

The model considered is a two-factor cross-classification variance components model with one observation per cell. Let the two factors be A and B, the problem is to obtain an approximate confidence interval for the ratio of variance component A over variance component B. In this paper, a method of solving this problem is established and simulations are performed to check the method.     

Confidence Intervals on Ratios of Variance Components for the Unbalanced Two Factor Nested Model

The model considered in this article is the two-factor nested unbalanced variance component model: for p = 1, 2, …, P; q = 1, 2, …, Q_p; and r = 1, 2, …, R_pq. The random variables Y_pqr are observable. The constant μ is an unknown parameter, and A_p, B_pq and C_pqr are (unobservable) normal and independently distributed random variables with zero means and finite variances σ²_A, σ²_B, and σ²_C, respectively. Approximate confidence intervals on ?_A and ?_B using unweighted means are derived, where The performance of these approximate confidence intervals are evaluated using computer simulation. The simulated results indicate that these proposed confidence intervals perform satisfactorily and can be used in applied problems.     

Lower Confidence Limits for the Positive Linear Combination of two Variances

An alternative method for determining the approximate lower confidence limits for the positive linear combination of two variances based on an approach similar to BULMER (1957) has been proposed. The probability coverage of the proposed alternative limits has been compared with the other existing methods.     

Confidence Intervals and Tests of Hypotheses on Variance Components in an Unbalanced Two-fold Nested Design

Confidence intervals and tests of hypotheses on variance components are required in studies that employ a random effects design. The unbalanced random two-fold nested design is considered in this paper and confidence intervals are proposed for the variance components σ2/A and σ2/B. Computer simulation is used to show that even in very unbalanced designs, these intervals generally maintain the stated confidence coefficient. The hypothesis test for σ2/A based on the lower bound of the recommended confidence interval is shown to be better than previously proposed approximate tests.     

Relative efficiency of North Carolina designs I and II and standard design III in three wheat crosses

Summary The efficiency of three analyses, namely, Designs I and II of Comstock and Robinson (1952) and standard Design III analysis of Kearsey and Jinks (1968), was compared in the F₂s of three wheat crosses (Norteno 67 x HD 1982, HD 1982 x Moti and Sonalika x Moti) for plant height, spikelets per spike and yield per plant. The three analyses showed a remarkable agreement in estimating the additive (D) component for all three characters in all three crosses. But, as regards the estimation of dominance ] (H) component, standard Design III analysis proved to be more efficient than the other two analyses in crosses 2 (HD 1982 x Moti) and 3 (Sonalika x Moti) for all three characters except spikelets per spike in cross 3.     

Genetic Analysis of Line x Tester Progenies Compared in Orthogonally Supplemented Efficiency Balanced Incomplete Block Designs

The theory which analyses the progenies of line X tester crossing procedure and one group of homozygous parents is presented. This analysis allows to conclude on genetics of a quantitative character of parents included in the experiment. The statistics like variance among parents, mean variance of progenies of lines, variance of tester progeny means and covariance of testers with means of their progenies can be derived. On that base one can get four different genetic parameters of variance. In a special case of experiment, it is possible to test the significance of additive variance.     

巢式设计的多元分析

本文把经典巢式设计的统计分析方法由单变量推广到多变量,使得试验或调查的多性状数据能综合在一起进行分析,以得出考虑了性状间相关性在内的统计结论并用一烟草栽培试验数据示明具体步骤。     

Predicting mean and variance of all possible lines and hybrids from designs with partially inbred progenies

Two-factor mating designs at consecutive S_n and S_(n+1) levels (S₀ and S₁ S₁ and S₂, or F₂ and F₃) allow estimation of all components of the variation among homozygous lines and F₁ hybrids that can be derived from a given population. They also allow for the prediction of the mean of these lines and single-cross hybrids. Some tests for the presence of epistasis are possible at the levels of means and of variances. Such mating designs can be very useful for predicting the value of the best possible lines or the best possible F₁ hybrids when it is difficult to produce, at an experimental level for exploratory purposes, either lines or hybrids.     

Design of a binary biomarker study from the results of a pilot study

Biomarkers are increasingly used in clinical and epidemiologic studies. Prior to these studies, small pilot studies are often conducted to assess the reproducibility of the biomarker. This article discusses how the results of a pilot study can be used to design subsequent studies when the biomarker is a binary assessment. We consider situations in which the pilot study has two factors (e.g., laboratory and individual) that are either crossed or nested. We discuss how binary random-effects models can be used for estimating the sources of variation and how parameter estimates from these models can be used to appropriately design future studies. We also show that fitting a linear variance components model that ignores the binary nature of the data is a simple alternative method that results in nearly unbiased and moderately efficient estimators of important design parameters. We illustrate the methodology with data from a study assessing the reproducibility of p53 immunohistochemistry in bladder tumors.     

两栖类皮肤石蜡切片样本量探讨——以峨眉髭蟾毛细血管丰富度为例

石蜡切片是量化两栖动物各种皮肤特征的常用技术,但在两栖动物中缺乏取样标准。血管密度等无法直接度量的特性可能需要较大的样本量,探讨这类特征的取样标准有利于实践工作。本研究对雄性峨眉髭蟾Leptobrachium boringii表皮下毛细血管丰富度进行量化,并通过重抽样分析该特征所需样本量。实验获得2只个体10个部位数据,每个部位模拟29种抽样。结果显示,体型较小个体多数部位需接近20条组织或更高的样本量,体型较大个体多数部位所需样本量接近15条或更高。建议在两栖类皮肤石蜡切片工作中对全部有效切片进行制片,以满足不同特征对样本量的要求。表皮下毛细血管丰富度与所需样本量呈负相关关系,可能缘于高密度部位的血管分布更均匀。如在其他两栖动物类群中亦观察到该相关性,则有助于在量化该特征时合理选取样本量。     

Estimation of Design and Genetic Components of Variance in Double Cross Mating Designs

The present paper deals with the estimation of design and genetic components of variance based on full double crosses and partial tetra-allel crosses. We have presented the explicit experissions for the symmetric sums estimators of design components of variance based on Hinkelmann's model. Consequently we have also presented explicitly the genetic components of variance based on full double crosses and partial tetra-allel crosses. The procedure is also illustrated with the help of a hypothetical data.     

Estimation of Variance Components Based on Partial Triallel Mating Design

The higher order mating designs like triallel and double crosses have been found to be useful in exploiting the epistatic gene action. However, it is equally important to note that enormous amount of resources are necessary to develop triallel crosses even for a small number of genetic lines p as it involves developing p(p—1)(p—2)/2 distinct three way hybrids. A simple answer to this problem is to consider a sample of triallel crosses known as partial triallel crosses (PTC) which retains the salient properties of triallel crosses at less cost. In this paper we consider the estimation of variance components (design and genetic) based on partial triallel mating designs.     

The Design and Use of Variance Component Models in the Analysis of Human Quantitative Pedigree Data

The use of variance components and multivariate linear models in genetics applications has a long history that dates back to (at least) Fisher's seminal 1918 paper “The correlation between relatives on the supposition of Mendelian inheritance” [Phil. Trans. 52: 399–433]. Although extensions and elaborations of Fisher's insights have been offered in recent times, relatively few studies exist which examine the theoretical and operational properties variance component models possess in complicated genetic analysis settings. In this paper variance component models, as well as some of their properties (e.g., power, efficiency, and sample size considerations) are discussed in the context of each of the following genetic analysis settings: 1. the detection of general polygenic additive and dominance effects; 2. the detection of genetic effects in the presence of environmental effects (and vice versa); 3. the detection of pleiotropic gene action; 4. aspects of the detection of genotype by environment interaction; and 5. sequential tests for general hypotheses framed in the context of settings 1 through 4. Exposition of the proposed methods and results are facilitated through a special emphasis placed on pedigree covariance structure modeling.     

A Comparison of Formulae for Calculating Cost‐Efficient Sample Sizes of Case‐Control Studies with an Internal Validation Scheme

When a case‐control study is planned to include an internal validation study, the sample size of the study and the proportion of validated observations has to be calculated. There are a variety of alternative methods to accomplish this. In this article some possible procedures will be compared in order to clarify whether considerable differences in the suggested optimal designs occur, dependent on the used method.     

The Effect of Sample Design in the Discriminant Analysis for Two Groups

This paper shows the effect of sample design on the Discriminant Analysis for two groups by means of a simulation study involving stratified design. Four criteria of discrimination are used and compared. Also, the equivalency between the Multiple Linear Regression using the Generalized Estimating Equations and the Discriminant Analysis for two normal populations from a Complex Design is proved. The results are applied to an epidemiological problem.     

Spatial variation and effects of habitat on temperate reef fish assemblages in northeastern New Zealand

Reef-associated fishes can respond to changes in habitat structure and the nature of their response can change with different spatial scales of observation. A structured hierarchical mensurative sampling design was used to sample temperate reef fish assemblages in northeastern New Zealand at several spatial scales over 2 years. The three spatial scales examined were tens of meters (transects), hundreds to thousands of meters (sites) and hundreds of kilometers (locations). We tested the hypothesis that fish assemblages differed between kelp forest habitat (relatively dense stands of the kelp, Ecklonia radiata (C. Agardh) J. Agardh, median depth=13.5 m) and barrens habitat (rocky reef dominated by turfing and encrusting red algae and the grazing urchin, Evechinus chloroticus (Valenciennes), median depth=6.7 m). Recently developed multivariate techniques were used to test for and quantify multivariate variation at different spatial scales. There were significant effects of habitat on the spatial distribution of fish assemblages, characterised by greater abundances or frequencies of Parika scaber, Chromis dispilus, Trachurus novaezelandiae, Nemadactylus douglasii, Bodianus unimaculatus, Odax pullus and Pseudolabrus miles in kelp forest habitat, and greater abundances or frequencies of Notolabrus celidotus, Notolabrus fucicola, Girella tricuspidata, Coris sandageri, Chironemus marmoratus, Parma alboscapularis, Scorpis violaceus and Kyphosus sydneyanus in barrens habitat. Some of the more common species, including Upeneichthys lineatus, Scorpis lineolatus and Cheilodactylus spectabilis showed no strong consistent effects of these two differing habitats on their distributions. There was, however, a significant Habitat×Locations interaction: effects of habitat did not occur at all locations. Variability was highest at the scale of individual transects and variability from site to site and from location to location was comparable. Spatial variation was large compared to inter-annual variation, which was minimal, and spatial patterns were consistent in the 2 years examined. Further experiments, including manipulations, are required to understand what mechanisms and processes might be driving these patterns. This study, coupled with results from previous studies, suggests that there may be a dynamic inter-play between effects of habitat on fish and effects of fish on biogenic habitat, such as kelp forests.     

fullfact: an R package for the analysis of genetic and maternal variance components from full factorial mating designs

Full factorial breeding designs are useful for quantifying the amount of additive genetic, nonadditive genetic, and maternal variance that explain phenotypic traits. Such variance estimates are important for examining evolutionary potential. Traditionally, full factorial mating designs have been analyzed using a two‐way analysis of variance, which may produce negative variance values and is not suited for unbalanced designs. Mixed‐effects models do not produce negative variance values and are suited for unbalanced designs. However, extracting the variance components, calculating significance values, and estimating confidence intervals and/or power values for the components are not straightforward using traditional analytic methods. We introduce fullfact – an R package that addresses these issues and facilitates the analysis of full factorial mating designs with mixed‐effects models. Here, we summarize the functions of the fullfact package. The observed data functions extract the variance explained by random and fixed effects and provide their significance. We then calculate the additive genetic, nonadditive genetic, and maternal variance components explaining the phenotype. In particular, we integrate nonnormal error structures for estimating these components for nonnormal data types. The resampled data functions are used to produce bootstrap‐t confidence intervals, which can then be plotted using a simple function. We explore the fullfact package through a worked example. This package will facilitate the analyses of full factorial mating designs in R, especially for the analysis of binary, proportion, and/or count data types and for the ability to incorporate additional random and fixed effects and power analyses.