A characteristic function approach to the biased sampling model,with application to robust logistic regression

Many sampling problems from multiple populations can be considered under the semiparametric framework of the biased, or weighted, sampling model. Included under this framework is logistic regression under case–control sampling. For any model, atypical observations can greatly influence the maximum likelihood estimate of the parameters. Several robust alternatives have been proposed for the special case of logistic regression. However, some current techniques can exhibit poor behavior in many common situations. In this paper a new family of procedures are constructed to estimate the parameters in the semiparametric biased sampling model. The procedures incorporate a minimum distance approach, but are instead based on characteristic functions. The estimators can also be represented as the minimizers of quadratic forms in simple residuals, thus yielding straightforward computation. For the case of logistic regression, the resulting estimators are shown to be competitive with the existing robust approaches in terms of both robustness and efficiency, while maintaining affine equivariance. The approach is developed under the case–control sampling scheme, yet is shown to be applicable under prospective sampling logistic regression as well.     

On an application of the diffusion approximation of the generalized birth and death process for stochastic population projection

Assuming that both birth and death rates are density and time dependent, a diffusion approximation of the generalized birth and death process has been considered in this paper to obtain a suitable stochastic population model describing the population size and its moments. A simple method of estimating the parameters of the model Is discussed. The predictions of the expected size of the population, and the variance are made and compared with the corresponding census figures as well as with another deterministic projection series made for the corresponding period.     

The Folded Logistic Distribution

ABSTRACT

Physical measurements like dimensions, including time, and angles in scientific experiments are frequently recorded without their algebraic sign. The directions of those physical quantities measured with respect to a frame of reference in most practical applications are considered to be unimportant and are ignored. As a consequence, the underlying distribution of measurements is replaced by a distribution of absolute measurements. When the underlying distribution is logistic, the resulting distribution is called the “folded logistic distribution”. Here, the properties of the folded logistic distribution will be presented and the techniques for estimating parameters will be given. The advantages of using this folded logistic distribution over the folded normal distribution will be discussed and some examples will be cited.     

Principal point classification: Applications to differentiating drug and placebo responses in longitudinal studies

Principal points are cluster means for theoretical distributions. A discriminant methodology based on principal points is introduced. The principal point classification method is useful in clinical trials where the goal is to distinguish and differentiate between different treatment effects. Particularly, in psychiatric studies where placebo response rates can be very high, the principal point classification is illustrated to distinguish specific drug responders from non-specific placebo responders.     

On the existence of maximum likelihood estimates for weighted logistic regression

The problems of existence and uniqueness of maximum likelihood estimates for logistic regression were completely solved by Silvapulle in 1981 and Albert and Anderson in 1984. In this paper, we extend the well-known results by Silvapulle and by Albert and Anderson to weighted logistic regression. We analytically prove the equivalence between the overlap condition used by Albert and Anderson and that used by Silvapulle. We show that the maximum likelihood estimate of weighted logistic regression does not exist if there is a complete separation or a quasicomplete separation of the data points, and exists and is unique if there is an overlap of data points. Our proofs and results for weighted logistic apply to unweighted logistic regression.     

Two Moments of the Logitnormal Distribution

We display the first two moment functions of the Logitnormal(μ, σ²) family of distributions, conveniently described in terms of the Normal mean, μ, and the Normal signal-to-noise ratio, μ/σ, parameters that generate the family. Long neglected on account of the numerical integrations required to compute them, awareness of these moment functions should aid the sensible interpretation of logistic regression statistics and the specification of “diffuse” prior distributions in hierarchical models, which can be deceiving. We also use numerical integration to compare the correlation between bivariate Logitnormal variables with the correlation between the bivariate Normal variables from which they are transformed.     

基于公司治理信息的财务困境预警实证研究

在分别借助因子分析和单变量检验对公司财务信息和治理信息进行统计处理的基础上,构建并实证检验中国上市公司财务困境预警的两大模型,即仅包含财务信息与融合财务信息和公司治理信息的Logistic回归预警模型。实证结果表明：公司治理信息对公司陷入财务困境具有显著的影响,引入公司治理信息的模型预测能力更强。     

Bayesian Binomial Regression: Predicting Survival at a Trauma Center

Standard methods for analyzing binomial regression data rely on asymptotic inferences. Bayesian methods can be performed using simple computations, and they apply for any sample size. We provide a relatively complete discussion of Bayesian inferences for binomial regression with emphasis on inferences for the probability of “success.” Furthermore, we illustrate diagnostic tools, perform model selection among nonnested models, and examine the sensitivity of the Bayesian methods.     

Efficacy of Statistical Outlier Analysis for Monitoring Quality of Care

Researchers have proposed that hospitals with excessive statistically unexplained mortality rates are more likely to have quality-of-care problems. The U.S. Health Care Financing Administration currently uses this statistical “outlier” approach to screen for poor quality in hospitals. Little is known, however, about the validity of this technique, since direct measures of quality are difficult to obtain. We use Monte Carlo methods to evaluate the performance of the outlier technique as parameters of the true mortality process are varied. Results indicate that the screening ability of the technique may be very sensitive to how widespread quality-related mortality is among hospitals but insensitive to other factors generally thought to be important.     

Logistic与分类树模型变量筛选的比较——基于信用卡邮寄业务响应率分析

基于信用卡邮寄业务响应率分析来讨论Logistic模型和分类树模型在变量选取上的区别,并尝试从几个不同角度去解释两类模型变量筛选差异的原因。笔者认为没有绝对占优势的方法,需要结合具体场景和模型的特点来选择合适的模型。分类树模型在训练集上容易过度拟合,对单个变量的影响很敏感,在进行危险因素分析时结果更能强调危险因素,对孤立点的识别率很高。Logistic模型容易受到解释变量依存关系的影响,加上分类变量的影响容易过多地选入变量或者因子,对孤立点敏感,对噪点不敏感。判别函数的差异是变量筛选差异的关键因素。