A Graphical Tool for Interpreting Regression Coefficients of Trinomial Logit Models

Multinomial logit (also termed multi-logit) models permit the analysis of the statistical relation between a categorical response variable and a set of explicative variables (called covariates or regressors). Although multinomial logit is widely used in both the social and economic sciences, the interpretation of regression coefficients may be tricky, as the effect of covariates on the probability distribution of the response variable is nonconstant and difficult to quantify. The ternary plots illustrated in this article aim at facilitating the interpretation of regression coefficients and permit the effect of covariates (either singularly or jointly considered) on the probability distribution of the dependent variable to be quantified. Ternary plots can be drawn both for ordered and for unordered categorical dependent variables, when the number of possible outcomes equals three (trinomial response variable); these plots allow not only to represent the covariate effects over the whole parameter space of the dependent variable but also to compare the covariate effects of any given individual profile. The method is illustrated and discussed through analysis of a dataset concerning the transition of master’s graduates of the University of Trento (Italy) from university to employment.     

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution

Summary . A fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is sufficiently general to encompass some recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew t -density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.     

Assessment of modeling longitudinal binary data based on graphical methods

Longitudinal categorical data are commonly applied in a variety of fields and are frequently analyzed by generalized estimating equation (GEE) method. Prior to making further inference based on the GEE model, the assessment of model fit is crucial. Graphical techniques have long been in widespread use for assessing the model adequacy. We develop alternative graphical approaches utilizing plots of marginal model-checking condition and local mean deviance to assess the GEE model with logit link for longitudinal binary responses. The applications of the proposed procedures are illustrated through two longitudinal binary datasets.     

A modified LGB method for detecting significant effects based on a half-normal probability plot

In analyzing data from unreplicated factorial designs, the half-normal probability plot is commonly used to screen for the ‘vital few’ effects. Recently, many formal methods have been proposed to overcome the subjectivity of this plot. Lawson (1998) (hereafter denoted as LGB) suggested a hybrid method based on the half-normal probability plot, which is a blend of Lenth (1989) and Loh (1992) method. The method consists of fitting a simple least squares line to the inliers, which are determined by the Lenth method. The effects exceeding the prediction limits based on the fitted line are candidates for the vital few effects. To improve the accuracy of partitioning the effects into inliers and outliers, we propose a modified LGB method (hereafter denoted as the Mod_LGB method), in which more outliers can be classified by using both the Carling’s modification of the box plot (Carling, 2000) and Lenth method. If no outlier exists or there is a wide range in the inliers as determined by the Lenth method, more outliers can be found by the Carling method. A simulation study is conducted in unreplicated $2^4$ designs with the number of active effects ranging from 1 to 6 to compare the efficiency of the Lenth method, original LGB methods, and the proposed modified version of the LGB method.     

Visualization for Large‐scale Gaussian Updates

In geostatistics and also in other applications in science and engineering, it is now common to perform updates on Gaussian process models with many thousands or even millions of components. These large‐scale inferences involve modelling, representational and computational challenges. We describe a visualization tool for large‐scale Gaussian updates, the ‘medal plot’. The medal plot shows the updated uncertainty at each observation location and also summarizes the sharing of information across observations, as a proxy for the sharing of information across the state vector (or latent process). As such, it reflects characteristics of both the observations and the statistical model. We illustrate with an application to assess mass trends in the Antarctic Ice Sheet, for which there are strong constraints from the observations and the physics.     

世界主要国家钢铁工业节能环保发展战略

钢铁工业的发展必须充分考虑本国面临的能源供应和环境污染等方面的压力,世界主要钢铁工业国家在节能环保方面都取得了长足的进步. 综合媒体6月21日报道,与世界主要产钢国钢铁工业的能源结构相比,中国煤炭所占比例高于其它国家,而天然气和燃料油的比重明显低于发达国家.     

Inference on a progressive type I interval-censored truncated normal distribution

In this paper, we consider the problem of making statistical inference for a truncated normal distribution under progressive type I interval censoring. We obtain maximum likelihood estimators of unknown parameters using the expectation-maximization algorithm and in sequel, we also compute corresponding midpoint estimates of parameters. Estimation based on the probability plot method is also considered. Asymptotic confidence intervals of unknown parameters are constructed based on the observed Fisher information matrix. We obtain Bayes estimators of parameters with respect to informative and non-informative prior distributions under squared error and linex loss functions. We compute these estimates using the importance sampling procedure. The highest posterior density intervals of unknown parameters are constructed as well. We present a Monte Carlo simulation study to compare the performance of proposed point and interval estimators. Analysis of a real data set is also performed for illustration purposes. Finally, inspection times and optimal censoring plans based on the expected Fisher information matrix are discussed.     

论小说创作

如果可能,请别写小说.小说创作是一种非社会行为,一旦动笔,小说家会时刻为小说中的人物所困扰;而且,真正写起来,小说指南一类书籍并不管用.假如非写不可,那么,小说家需考虑是以情节为主还是以人物为主.如果以情节为主,小说家即在虚构的事情中间而非在所谓的真实生活中寻找人物的时候,抓住情节不放;如果以人物为主,那么,小说家则需对适于情节的某些特征加以强调,使人物在新环境中显得真实可信,从而赋予他们生命.小说家无论重情节抑或是重人物,都还要考虑以何种形式、何种风格呈现情节和人物的问题;当然,在优秀的小说家笔下,故事和人物本身会以最适合的形式出现.小说家应对形式、人物和语言保持一种敏锐的感觉.此外,小说家可能会对道德教诲产生迷恋.尽管应当通过作品给读者以教益,但是,真诚的艺术家并不能专注于说教.     

《红楼梦》情节的"对照美"--以贾瑞挨整与薛蟠遭打的对照为个案

"犯而不犯"是明清人对"犯"与"避"这一对待性范畴的对立统一的辩证关系的界定,当时的小说评论家们充分地认识到了这一创作方法的审美功能.<红楼梦>中贾瑞挨整与薛蟠遭打这一对情节,也体现了这一对范畴的辩证关系,具有"对照"美.     

Deletion residuals in the detection of heterogeneity of variances in linear regression

The heterogeneity of error variance often causes a huge interpretive problem in linear regression analysis. Before taking any remedial measures we first need to detect this problem. A large number of diagnostic plots are now available in the literature for detecting heteroscedasticity of error variances. Among them the ‘residuals’ and ‘fits’ (R–F) plot is very popular and commonly used. In the R–F plot residuals are plotted against the fitted responses, where both these components are obtained using the ordinary least squares (OLS) method. It is now evident that the OLS fits and residuals suffer a huge setback in the presence of unusual observations and hence the R–F plot may not exhibit the real scenario. The deletion residuals based on a data set free from all unusual cases should estimate the true errors in a better way than the OLS residuals. In this paper we propose ‘deletion residuals’ and the ‘deletion fits’ (DR–DF) plot for the detection of the heterogeneity of error variances in a linear regression model to get a more convincing and reliable graphical display. Examples show that this plot locates unusual observations more clearly than the R–F plot. The advantage of using deletion residuals in the detection of heteroscedasticity of error variance is investigated through Monte Carlo simulations under a variety of situations.