Testing Linear Contrasts of Means in Experimental Design Without Assuming Normality and Homogeneity of Variances

We investigate the efficiencies of TIKU'S (1967, 1980) modified maximum likelihood (MML) estimators of location and scale parameters of symmetric distributions and show that they are remarkably efficient (jointly). We develop test statistics (based on MML estimators), analogous to the classical tests based on sample means and variances, for testing the equality of two means (the population variances not necessarily equal). We show that these tests are remarkably robust to distributional assumptions and generally more powerful than the well-known nonparametric tests (WILCOXON , normal-score, KOLMOGOROV -SMIRNOV ). We generalize the results to testing linear contrasts of means in experimental design (the error variances not necessarily equal). We show that the analogous tests based on ‘adaptive’ robust estimators (wave, bisquare, HAMPEL ,) etc., GROSS (1976, and other ‘adaptive’ robust estimators) give misleading Type I errors.     

Further Results in Indices for Diagnostic Screening II

This article is in continuation of a previous one on properties of diagnostic indices (Bennett, 1976). Results are presented on biases in sample estimates of the sensitivity (ξ) and specificity (η) of a diagnostic test T for a disease, as well as their asymptotic variances. The problem of combining estimates of ξ, η from various clinical centres and obtaining appropriate confidence limits is also discussed. A numerical example is also given. (Tables 1a, b). The log-linear model for ξ, η is also discussed.     

A Stochastic Model for the Predatory Behaviour of Naive Spiderlings (Araneas: Salticidae)

A stochastic model is proposed for the hunting behaviour of jumping spiders when they are newly emerged from the egg-sac. The model takes into account the fact that the spiders are often unsuccessful when they attempt to catch prey for the first time and also the fact that their rate of response to prey slows down with time if they are unsuccessful. It is shown that the spiderlings ability to catch perceived prey improves with the number of prey captured. The model has been fitted to experimental data using the method of maximum likelihood and a good fit has been obtained. The model could be used as part of a model for the whole predation system.     

Model fitting and hypothesis testing for age-specific mortality data

Demographic studies focusing on age-specific mortality rates are becoming increasingly common throughout the fields of life-history evolution, ecology and biogerontology. Well-defined statistical techniques for quantifying patterns of mortality within a cohort and identifying differences in age-specific mortality among cohorts are needed. Here I discuss using maximum likelihood (ML) statistical methods to estimate the parameters of mathematical models, which are used to describe the change in mortality with age. ML provides a convenient and powerful framework for choosing an adequate mortality model, estimating model parameters and testing hypotheses about differences in parameters among experimental or ecological treatments. Simulations suggest that experiments designed to estimate age-specific mortality should involve at least 100-500 individuals per cohort per treatment. Significant bias in the estimation of model parameters is introduced when the mortality model is misspecified and samples are too small to detect the true mortality pattern. Furthermore, the lack of simple and efficient procedures for comparing different mortality models has forced the use of the Gompertz model, which specifies an exponentially increasing mortality with age, and which may not apply to the majority of experimental systems.     

Goodness-of-Fit Tests for the Logistic Regression Model for Matched Case-Control Studies

A number of statistics have recently been proposed to asssess the fit of the multiple logistic regression model in both prospective and retrospective studies involving two independent samples as well as in cross sectional studies. These statistics are not appropriate for assessing fit with matched case-control studies. This paper presents methods for assessing fit for matched case-control studies. Both parametric and nonparametric approaches are suggested even though none are directly analogous to the statistics proposed in the unmatched situation. Several examples are included to illustrate the methods.     

家畜抗性等级性状的QTL定位方法

在广义线性模型的框架内模拟研究了家畜抗性等级性状的QTL定位方法,QTL参数的估计采用最大似然方法,比较了阈模型方法与一般线性方法的QTL定位效率,并对影响等级性状QTL定位效率的主要因素（QTL效应、性状的遗传力）进行了模拟研究,实验设计为多个家系的女儿设计,资源群体大小为500头。研究结果表明：在QTL位置参数估计及检验功效方面,阈模型方法具有一定的优势,对抗性等级性状QTL定位的功效也高于线性方法。另外,性状遗传力和QTL效应的大小对QTL定位的准确度也有直接的影响,随着性状遗传力QTL效应的     

Analysis of a Generalized Linear Mixed Model: A Case Study and Simulation Results

A class of generalized linear mixed models can be obtained by introducing random effects in the linear predictor of a generalized linear model, e.g. a split plot model for binary data or count data. Maximum likelihood estimation, for normally distributed random effects, involves high-dimensional numerical integration, with severe limitations on the number and structure of the additional random effects. An alternative estimation procedure based on an extension of the iterative re-weighted least squares procedure for generalized linear models will be illustrated on a practical data set involving carcass classification of cattle. The data is analysed as overdispersed binomial proportions with fixed and random effects and associated components of variance on the logit scale. Estimates are obtained with standard software for normal data mixed models. Numerical restrictions pertain to the size of matrices to be inverted. This can be dealt with by absorption techniques familiar from e.g. mixed models in animal breeding. The final model fitted to the classification data includes four components of variance and a multiplicative overdispersion factor. Basically the estimation procedure is a combination of iterated least squares procedures and no full distributional assumptions are needed. A simulation study based on the classification data is presented. This includes a study of procedures for constructing confidence intervals and significance tests for fixed effects and components of variance. The simulation results increase confidence in the usefulness of the estimation procedure.     

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.     

单位点孢子体-配子体互作模型中不育基因的位置和效应的估计方法

水稻籼粳亚种间杂交F1通常表现为高度不育,这种不育性的一种遗传学解释称为单位点孢子体-配子体互作模型.为了研究这种不育性,提出了一种统计方法,可以估计单位点孢子体-配子体互作模型中不育基因位点的位置和效应.该方法利用回交群体中呈现异常分离的标记位点,用最大似然法对不育基因与标记位点之间的重组率和雌配子存活率进行估计.由于所依据的是非连续变异的遗传标记的分离,而不是连续分布的配子育性指标,因此可以避免由育性直接估计所带来的重组率结果的不稳定.     

The General Linear Model as a Framework for Models in Configural Frequency Analysis

The present paper discusses models of Configural Frequency Analysis (CFA). For most models of CFA maximum likelihood estimators are given. For all of these models least squares estimators are also given. These estimators are equivalent to each other if quasiparametric conditions prevail. Using the second approach, the general linear model can be used to systematize CFA models. Numerical examples are given, using both artificial and psychiatric data.     

Estimation of Fixed and Random Effects in the Functional Nonlinear Errors-in-Variable Model

Consider an experiment where a nonlinear continuous functional relationship exists between y and X. Assume that this relationship has been measured at n replicated points of X from each of t treatments or populations. Assume further that the X are fixed unknown vectors and that the location parameter v is either a fixed unknown vector or a vector of random variables. In the first case various linear hypotheses are to be tested about v, such as tests for main effects and interaction; in the second case, the mean and variance of the random variable v are to be estimated. A two-step procedure based on asymptotic theory is presented to test hypotheses or develop estimates for the fixed effects or random effects functional errors-in-variable model. An example of a one-way random effects model is given.