A Bayesian approach for analyzing case 2 interval-censored data under the semiparametric proportional odds model

Analyzing interval-censored data is difficult due to its complex data structure containing left-, interval-, and right-censored observations. An easy-to-implement Bayesian approach is proposed under the proportional odds (PO) model for analyzing such data. The nondecreasing baseline log odds function is modeled with a linear combination of monotone splines. Two efficient Gibbs samplers are developed based on two different data augmentations using the relationship between the PO model and the logistic distribution. In the first data augmentation, the logistic distribution is achieved by the scaled normal mixture with the scale parameter related to the Kolmogorov-Smirnove distribution. In the second data augmentation, the logistic distribution is approximated by a Student’s t distribution up to a scale constant. The proposed methods are evaluated by simulation studies and illustrated with an application of an HIV data set.     

Simple linear approximations to the likelihood equation for combining evidence in multiple 2×2 tables: A critique of conventional procedures

Summary The conventional procedures for a common odds ratio in multiple 2×2 tables are explored and critiqued. Three types of linear approximation to the likelihood equations under some models of common measures of association are used to derive the popular conventional estimators and test statistics. Some of them are derived using the model of the common standardized difference which is an unacceptable measure. The derivation provides us with some characteristics of the procedures. The advantages of procedures based on the conditional and unconditional likelihoods are discussed. The Institute of Statistical Mathematics     

Understanding and interpreting generalized ordered logit models

When outcome variables are ordinal rather than continuous, the ordered logit model, aka the proportional odds model (ologit/po), is a popular analytical method. However, generalized ordered logit/partial proportional odds models (gologit/ppo) are often a superior alternative. Gologit/ppo models can be less restrictive than proportional odds models and more parsimonious than methods that ignore the ordering of categories altogether. However, the use of gologit/ppo models has itself been problematic or at least sub-optimal. Researchers typically note that such models fit better but fail to explain why the ordered logit model was inadequate or the substantive insights gained by using the gologit alternative. This paper uses both hypothetical examples and data from the 2012 European Social Survey to address these shortcomings.     

Bayesian inferences on nonlinear functions of the parameters in linear regression

A variety of statistical problems (e.g. the x-intercept in linear regression, the abscissa of the point of intersection of two simple linear regression lines or the point of extremum in quadratic regression) can be viewed as questions of inference on nonlinear functions of the parameters in the general linear regression model. In this paper inferences on the threshold temperatures and summation constants in crop development will be made. A Bayesian approach for the general formulation of this problem will be developed. By using numerical integration, credibility intervals for individual functions as well as for linear combinations of the functions of the parameters can be obtained. The implementation of an odds ratio procedure is facilitated by placing a proper prior on the ratio of the relevant parameters.Financially supported by the University of the Orange Free State Research Fund.     

Bayesian analysis of definitive screening designs when the response is nonnormal

Definitive screening designs (DSDs) are a class of experimental designs that allow the estimation of linear, quadratic, and interaction effects with little experimental effort if there is effect sparsity. The number of experimental runs is twice the number of factors of interest plus one. Many industrial experiments involve nonnormal responses. Generalized linear models (GLMs) are a useful alternative for analyzing these kind of data. The analysis of GLMs is based on asymptotic theory, something very debatable, for example, in the case of the DSD with only 13 experimental runs. So far, analysis of DSDs considers a normal response. In this work, we show a five‐step strategy that makes use of tools coming from the Bayesian approach to analyze this kind of experiment when the response is nonnormal. We consider the case of binomial, gamma, and Poisson responses without having to resort to asymptotic approximations. We use posterior odds that effects are active and posterior probability intervals for the effects and use them to evaluate the significance of the effects. We also combine the results of the Bayesian procedure with the lasso estimation procedure to enhance the scope of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

基于比例优势模型的上市公司财务困境预测研究

在激烈的市场竞争中,现代企业非常关注风险管理,注重防范与控制风险,而风险管理的关键是预测与控制财务风险。生存分析模型能动态地预测风险事件发生的概率,本文精比例优势模型应用干我国上市公司财务困境预测,根据边际似然与ALASSO变量选择程序,确定了影响财务风险的主要因素,获得模型参数估计,考察了比例优势模型财务困境预测判断能力,比较了Cox模型和比例优势模型这两种生存模型的财务风险预测效果。结果表明,比例优势模型能展现企业财务困境的发展过程,具有较好的财务困境预测能力。     

Evaluating Educational Inequality Within Educational Expansion: A Formal Comparison Between Odds Ratio and the Educational Gini Coefficient

Odds ratio (OR) and the educational Gini coefficient (EGINI) defined on a specific social grouping scheme can both be used to gauge educational inequality. In this study, we systematically review the scholarship that underpins the utilities of OR and EGINI and evaluate their properties across four research scenarios of allocating newly created opportunities under educational expansion. Formal analyses suggest that (1) both OR and EGINI monotonically increase (decrease) if the newly created educational positions are entirely delivered to the upper (lower) class. However, the rate of change differs between OR and EGINI. (2) When educational opportunities within expansion are allocated according to the relative populations of social classes, the probabilities of upper and lower classes to receive better education rise by the same extent, suggesting that all social classes benefit from the proliferation of educational credentials. This would drive down the EGINI, but change in OR is not monotonic. (3) EGINI remains unchanged if the newly created educational opportunities are allocated based on the initial class composition of better educated individuals before educational expansion. However, OR is driven to increase by the “Matthew Effect” where the increment in educational probability for the upper class is larger than that for the lower class. The discrepancy of empirical patterns between OR and EGINI is explained, and the practical implications are discussed using a case study of the educational policy evaluation in Britain.     

Semi- and Nonparametric Modeling of Ordinal Data

Parametric models for categorical ordinal response variables, like the proportional odds model or the continuation ratio model, assume that the predictor is given by a linear form of covariates. In this article the parametric models are extended to include smooth components in a semiparametric or partially parametric fashion. Parts of the covariates are thereby modeled linearly while other covariates are modeled as unspecified but smooth functions. Estimation is based on a combination of local likelihood and profile likelihood and asymptotic properties of the estimates are derived. In a simulation study it is demonstrated that the profile likelihood approach is to be preferred over a backfitting procedure. Two data examples demonstrate the applicability of the models.     

圆筒中炸药装药的爆速估算方法探讨

在圆筒试验中利用光光源药柱激发氩气发光所用时间与圆筒装药中爆轰波传到摄像位的时间之差来估算圆筒中炸药的爆速 ,并计算了两发TNT炸药圆筒中的爆速。结果表明 ,该方法准确程度较高 ,而且测试简便 ,能够应用于实际。     

Computing Estimates in the Proportional Odds Model

The semiparametric proportional odds model for survival data is useful when mortality rates of different groups converge over time. However, fitting the model by maximum likelihood proves computationally cumbersome for large datasets because the number of parameters exceeds the number of uncensored observations. We present here an alternative to the standard Newton-Raphson method of maximum likelihood estimation. Our algorithm, an example of a minorization-maximization (MM) algorithm, is guaranteed to converge to the maximum likelihood estimate whenever it exists. For large problems, both the algorithm and its quasi-Newton accelerated counterpart outperform Newton-Raphson by more than two orders of magnitude.