The Estimation of Skewness and Kurtosis of Random Effects in the Linear Model

Generalising the ANOVA method of estimating variance components in mixed linear models a simple procedure is presented to estimate skewness and kurtosis of the distributions of the random effects of the model. For the model II of a one-way classification this procedure is demonstrated explicitly.     

Joint Modelling of Repeated Measures and Survival Time Data

In many clinical trials both repeated measures data and event history data are simultaneously observed from the same subject. These two types of responses are usually correlated, because they are from the same subject. In this article, we propose a joint model for the combined analysis of repeated measures data and event history data in the framework of hierarchical generalized linear models. The correlation between repeated measures and event time is modelled by introducing a shared random effect. The model parameters are estimated using the hierarchical‐likelihood approach. The proposed model is illustrated using a real data set for the renal transplant patients.     

Weighted Multivariate Regression Estimates Solved by Random Effects Approach

The paper deals with the random effects model, where the expectation vector and the covariance matrix of the effect influencing the population are to be estimated. The iterated estimator of expectation vector is derived, based on the invariant estimator of the combined covariance matrix, and some of its statistical properties are shown.     

Dissecting apple tree architecture into genetic, ontogenetic and environmental effects: QTL mapping

The present study aimed to dissect tree architectural plasticity into genetic, ontogenetic and environmental effects over the first 4 years of growth of an apple F1 progeny by means of quantitative traits loci (QTL) mapping. Both growth and branching processes were phenotyped on the consecutive annual shoots of different axes within a tree. For each studied trait, predicted values (best linear unbiased predictors, BLUPs) of the genotypic (G) effect or its interaction with tree age (G×A) and climatic year (G×Y) were extracted from mixed linear models of repeated data. These BLUPs, which are independent from autocorrelations between repeated measurements, were used for QTL mapping. QTL detection power was improved by this two-step approach. For each architectural process, numerous QTLs were detected and some particularly interesting co-localised in common genomic regions, for internode lengthening, top diameter, and number and percentage of axillary shoots. When several QTLs were detected for a given trait, global models were estimated, which explained a maximum of 40% of the total variance for both internode length and top diameter and 28% for branching. QTLs detected for BLUPs of G×Y effects were interpreted as resulting from the interaction between genetic maximal potential of growth and climatic factors, while those for G×A effects were interpreted in relation to tree ontogeny. Most of the latter ones were found to be concomitant with key development stages during which the trait average started to decrease, but with different magnitudes depending on genotype. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Mapping QTLs with epistatic effects and QTL×environment interactions by mixed linear model approaches

A new methodology based on mixed linear models was developed for mapping QTLs with digenic epistasis and QTL×environment (QE) interactions. Reliable estimates of QTL main effects (additive and epistasis effects) can be obtained by the maximum-likelihood estimation method, while QE interaction effects (additive×environment interaction and epistasis×environment interaction) can be predicted by the-best-linear-unbiased-prediction (BLUP) method. Likelihood ratio and t statistics were combined for testing hypotheses about QTL effects and QE interactions. Monte Carlo simulations were conducted for evaluating the unbiasedness, accuracy, and power for parameter estimation in QTL mapping. The results indicated that the mixed-model approaches could provide unbiased estimates for both positions and effects of QTLs, as well as unbiased predicted values for QE interactions. Additionally, the mixed-model approaches also showed high accuracy and power in mapping QTLs with epistatic effects and QE interactions. Based on the models and the methodology, a computer software program (QTLMapper version 1.0) was developed, which is suitable for interval mapping of QTLs with additive, additive×additive epistasis, and their environment interactions. Received: 23 October 1998 / Accepted: 11 May 1999     

Least Squares and Minimum MSE Estimators of Variance Components in Mixed Linear Models

The paper deals with the quadratic invariant estimators of the linear functions of variance components in mixed linear model. The estimator with locally minimal mean square error with respect to a parameter ? is derived. Under the condition of normality of the vector Y the theoretical values of MSE of several types of estimators are compared in two different mixed models; under a different types of distributions a simulation study is carried out for the behaviour of derived estimators.     

应用混合遗传距离和基因型值遗传距离构建植物遗传资源核心子集

将连续性的基因型值数据和间断性的分子标记数据整合建立混合遗传距离，对比了应用混合遗传距离和单纯应用基因型遗传距离构建植物遗传资源核心子集的效果．应用混合线性模型中的调整无偏预测法（AUP）预测基因型值，结合不加权类平均法（UPGMA）逐步聚类构建遗传资源群体的核心子集，并检测一系列核心子集的代表性评价参数．采用包含8个农艺性状和60个SSR标记信息的水稻群体数据验证混合遗传距离的有效性．结果表明，采用混合数据构建的核心子集比单纯的基因型值数据构建的核心子集更有代表性．主成分分析结果验证了该结论的可知陛．     

Unbiasedness of the Estimator of the Function of Expected Value in the Mixed Linear Model

The traditional method for estimating the linear function of fixed parameters in mixed linear model is a two-stage procedure. In the first stage of this procedure the variance components estimators are calculated and next in the second stage these estimators are taken as true values of variance components to estimating the linear function of fixed parameters according to generalized least squares method. In this paper the general mixed linear model is considered in which a matrix related to fixed parameters and or/a dispersion matrix of observation vector may be deficient in rank. It is shown that the estimators of a set of functions of fixed parameters obtained in second stage are unbiased if only the observation vector is symmetrically distributed about its expected value and the estimators of variance components from first stage are translation-invariant and are even functions of the observation vector.