A likelihood ratio test of quasi-independence for sparse two-way contingency tables

We consider a likelihood ratio test of independence for large two-way contingency tables having both structural (non-random) and sampling (random) zeros in many cells. The solution of this problem is not available using standard likelihood ratio tests. One way to bypass this problem is to remove the structural zeroes from the table and implement a test on the remaining cells which incorporate the randomness in the sampling zeros; the resulting test is a test of quasi-independence of the two categorical variables. This test is based only on the positive counts in the contingency table and is valid when there is at least one sampling (random) zero. The proposed (likelihood ratio) test is an alternative to the commonly used ad hoc procedures of converting the zero cells to positive ones by adding a small constant. One practical advantage of our procedure is that there is no need to know if a zero cell is structural zero or a sampling zero. We model the positive counts using a truncated multinomial distribution. In fact, we have two truncated multinomial distributions; one for the null hypothesis of independence and the other for the unrestricted parameter space. We use Monte Carlo methods to obtain the maximum likelihood estimators of the parameters and also the p-value of our proposed test. To obtain the sampling distribution of the likelihood ratio test statistic, we use bootstrap methods. We discuss many examples, and also empirically compare the power function of the likelihood ratio test relative to those of some well-known test statistics.     

Marginal Nested Interactions for Contingency Tables

We introduce a new definition of generalized marginal interactions, called marginal nested interactions, which includes baseline, local, continuation and reverse continuation logits and odds ratios as special cases. The significant aspect of this definition is the inclusion of new types of logits and odds ratios that can handle non-ordinal, ordinal and partially ordered categorical variables in a flexible and appropriate way. It is proved also that the marginal nested interactions define a saturated model of a multi-way contingency table.     

Space-time estimation of a particle system model

Let X be a discrete time contact process (CP) on ?², as defined by Durrett and Levin (1994, Stochastic spatial models: a user's guide to ecological applications. Philosophical Transactions of the Royal Society of London Series B, 343, 329–350). We study the estimation of the model based on space-time evolution of X, that is, T + 1 successive observations of X on a finite subset S of sites. We consider the maximum marginal pseudo-likelihood (MPL) estimator and show that, when T→∞, this estimator is consistent and asymptotically normal for a non-vanishing supercritical CP. Numerical studies confirm these theoretical ones.     

Beta approximation of ratio distribution and its application to next generation sequencing read counts

Paired sequencing data are commonly collected in genomic studies to control biological variation. However, existing data processing strategies suffer at low coverage regions, which are unavoidable due to the limitation of current sequencing technology. Furthermore, information contained in the absolute values of the read counts is commonly ignored. We propose a read count ratio processing/modification method, to not only incorporate information contained in the absolute values of paired counts into one variable, but also mitigate the discrete artifact, especially when both counts are small. Simulation shows that the processed variable fits well with a Beta distribution, thus providing an easy tool for down-stream inference analysis.     

Parameter change test for zero-inflated generalized Poisson autoregressive models

In this paper, we consider the problem of testing for parameter change in zero-inflated generalized Poisson (ZIGP) autoregressive models. We verify that the ZIGP process is stationary and ergodic and that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal. Based on these results, we construct CMLE- and residual-based cumulative sum tests and show that their limiting null distributions are a function of independent Brownian bridges. The simulation results are provided for illustration. A real data analysis is performed on some crime data of Australia.     

Bivariate zero-inflated negative binomial regression model with applications

Count data often display excessive number of zero outcomes than are expected in the Poisson regression model. The zero-inflated Poisson regression model has been suggested to handle zero-inflated data, whereas the zero-inflated negative binomial (ZINB) regression model has been fitted for zero-inflated data with additional overdispersion. For bivariate and zero-inflated cases, several regression models such as the bivariate zero-inflated Poisson (BZIP) and bivariate zero-inflated negative binomial (BZINB) have been considered. This paper introduces several forms of nested BZINB regression model which can be fitted to bivariate and zero-inflated count data. The mean–variance approach is used for comparing the BZIP and our forms of BZINB regression model in this study. A similar approach was also used by past researchers for defining several negative binomial and zero-inflated negative binomial regression models based on the appearance of linear and quadratic terms of the variance function. The nested BZINB regression models proposed in this study have several advantages; the likelihood ratio tests can be performed for choosing the best model, the models have flexible forms of marginal mean–variance relationship, the models can be fitted to bivariate zero-inflated count data with positive or negative correlations, and the models allow additional overdispersion of the two dependent variables.     

近代江湖文化研究论纲

江湖社会具有独特的江湖文化内涵。江湖文化就是指存在于江湖人、江湖社会中的各种文化现象的总和。江湖文化伴随传统社会的发展而产生。古代的巫、医、百戏实为江湖文化的源头,明清以来,传统江湖社会逐渐成型,演至近代,江湖文化有所增益变化,但基本内容没有改变。江湖人物,谓之"三教九流",江湖行当,称作"五花八门",江湖社会包含了诸多独特的文化内容。延续至近代的江湖文化具有流动性、欺骗性、秘密性、一定的反社会性等特征。以"近代江湖文化"为对象展开研究,具有拓展历史学、社会学研究的学术意义,以及为当今社会治理江湖问题提供借鉴的现实意义。     

五品联动模式下品位决策问题建模与优化

矿冶工程中,地质品位、采出品位、入选品位、精矿品位、入炉品位是互为条件、相互联系的,对其进行实时动态优化是“五品联动”矿冶工程管理模式的基础。本文通过考察开采、配矿、选矿和冶炼过程中的品位与产量关系,推导出各阶段的品位与成本的关系模型,并在该模型的基础上进行边际分析,得出各阶段的品位-成本边际模型。建立了相应的品位-链接成本关系模型,并此基础上提出了品位-成本边际指数。最后,提出了五品联动的品位优化方法并给出具体步骤。文中还应用鞍钢矿业的实际数据进行了公式计算,结果和实际生产的情况吻合。     

Decision support for lead time and demand variability reduction

Companies undertaking operations improvement in supply chains face many alternatives. This work seeks to assist practitioners to prioritize improvement actions by developing analytical expressions for the marginal values of three parameters – (i) lead time mean, (ii) lead time variance, and (iii) demand variance – which measure the marginal cost of an incremental change in a parameter. The relative effectiveness of reducing lead time mean versus lead time variance is captured by the ratio of the marginal value of lead time mean to that of lead time variance. We find that this ratio strongly depends on whether the lead time mean and variance are independent or correlated. We illustrate the application of the results with a numerical example from an industrial setting. The insights can help managers determine the optimal investment decision to modify demand and supply characteristics in their supply chain, e.g., by switching suppliers, factory layout, or investing in information systems.     

“Locals” and “Cosmopolitans”

An analysis is provided of the results of a study of the scholarly productivity of Russian doctors of science in the middle generation who work within the Russian Academy of Sciences system. We show that the scholars’ achievements on the international versus domestic Russian arenas are not only different, but are also only weakly related. This gives reason to conclude that the competencies and social capital of scholars that facilitate their achievements inside the country and abroad are different, and sometimes even alternatives to each other. We also reveal that scholarly citation indexes are insufficient to evaluate domestic Russian achievements by scholars, while the evaluation of their international achievements is much more accurate.