Locally optimal designs for binary dose‐response models

In this article, we consider the problem of seeking locally optimal designs for nonlinear dose‐response models with binary outcomes. Applying the theory of Tchebycheff Systems and other algebraic tools, we show that the locally D‐, A‐, and c‐optimal designs for three binary dose‐response models are minimally supported in finite, closed design intervals. The methods to obtain such designs are presented along with examples. The efficiencies of these designs are also discussed. The Canadian Journal of Statistics 46: 336–354; 2018 © 2018 Statistical Society of Canada     

Model selection in randomized response techniques for binary responses

Randomized response techniques (RRTs) have been proposed in survey sampling literature as a solution to the problem of social desirability bias (SDB) while dealing with sensitive questions. All RRTs reduce the SDB by introducing privacy protection for the respondents, but the variances of the estimates become larger compared with the ones obtained from direct questioning technique (DQT). The success of RRTs heavily depends on the assumption that the variable of interest is in fact sensitive for the population under study. There might be situations, however, where a presumably sensitive question is not considered to be sensitive in some populations, in which case using an RRT instead of the DQT would inflate the variance of the estimates unreasonably. In this study, we propose a two-stage sampling procedure for a binary response, which enables one to accurately estimate both the prevalence of the sensitive characteristic and the probability of cheating in a population. The proposed model allows one to choose between an RRT and the DQT. We support our theoretical results with numerous simulations.     

Carcinogenic Mixtures

Human populations are generally exposed simultaneously to a number of toxicants present in the environment, including complex mixtures of unknown and variable origin. While scientific methods for evaluating the potential carcinogenic risks of pure compounds are relatively well established, methods for assessing the risks of complex mixtures are somewhat less developed. This article provides a report of a recent workshop on carcinogenic mixtures sponsored by the Committee on Toxicology of the U.S. National Research Council, in which toxicological, epidemiological, and statistical approaches to carcinogenic risk assessment for mixtures were discussed. Complex mixtures, such as diesel emissions and tobacco smoke, have been shown to have carcinogenic potential. Bioassay-directed fractionation based on short-term screening test for genotoxicity has also been used in identifying carcinogenic components of mixtures. Both toxicological and epidemiological studies have identified clear interactions between chemical carcinogens, including synergistic effects at moderate to high doses. To date, laboratory studies have demonstrated over 900 interactions involving nearly 200 chemical carcinogens. At lower doses, theoretical arguments suggest that risks may be near additive. Thus, additivity at low doses has been invoked as as a working hypothesis by regulatory authorities in the absence of evidence to the contrary. Future studies of the joint effects of carcinogenic agents may serve to elucidate the mechanisms by which interactions occur at higher doses.     

Binary designs are not always the best

We give an example of a nonbinary block design which is better than any binary design with respect to the E-optimality criterion. This shows that the class of binary designs is not essentially complete, at least with respect to E-optimality.     

Remark on Construction of Efficiency-Balanced Designs

In this note, all the efficiency-balanced block designs constructed by utilizing two methods of Dey & Singh (1980) are completely presented within a practical range of parameters.     

Three-mode factor analysis with binary core and orthonormality constraints

Summary A constrained version of Three-mode Factor Analysis model is considered in order to make its interpretation easier. The constraints are obtained by fixing some elements of the core to zero and requiring orthonormal factor loadings. An algorithm to solve the related minimization problem and an example of core constraints with theoretically interesting features, are given.     

高维数据的稳健二分类方法

对于实证研究中经常遇到变量维数高和存在异常值的二分类问题,探索稳健的高维二分类方法显得尤为重要。本文提出基于Lasso惩罚的光滑0-1损失函数二分类法,并利用Fabs 算法高效地解决了变量选择和参数估计问题。数值模拟的结果表明,在不同异常值比例下该方法均具有良好的稳健性。基于CHIP 2013年度数据,利用该方法对农民工子女高中入学决定的影响因素进行了实证研究。分析发现,农民工父母的教育水平、教育水平与家庭经济状况的交互作用、农民工子女性别、性别与民族的交互作用均对农民工子女的入学决定有重要影响。     

Estimation of Average Treatment Effects with Misclassification

This paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression, or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified. Failure to account for misclassification is shown to result in attenuation bias in the estimated treatment effect. An identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect. A discrete instrument suffices for nonparametric identification.     

回回民族二元一体的文化结构

伊斯兰文化是回回民族精神文化的另一方面,它是回回人的精神支柱。伊斯兰文化是一个没有中断过的世界性的大文化,它包含着认一论的信仰、伦理道德、价值观念、生活方式、人文科学、自然科学诸多方面,它是一个庞大的文化综合体。同时,中华民族养育了回回民族,使回回民族具有了儒学文化与伊斯兰文化二元一体的文化结构。这二元一体的文化结构,构建了回回民族的精神世界。     

Panel Binary Variables and Sufficiency: Generalizing Conditional Logit

This paper extends the conditional logit approach (Rasch, Andersen, Chamberlain) used in panel data models of binary variables with correlated fixed effects and strictly exogenous regressors. In a two‐period two‐state model, necessary and sufficient conditions on the joint distribution function of the individual‐and‐period specific shocks are given such that the sum of individual binary variables across time is a sufficient statistic for the individual effect. By extending a result of Chamberlain, it is shown that root‐n consistent regular estimators can be constructed in panel binary models if and only if the property of sufficiency holds. In applied work, the estimation method amounts to quasi‐differencing the binary variables as if they were continuous variables and transforming a panel data model into a cross‐section model. Semiparametric approaches can then be readily applied.