Modified likelihood ratio statistics for inflated beta regressions

The class of inflated beta regression models generalizes that of beta regressions [S.L.P. Ferrari and F. Cribari-Neto, Beta regression for modelling rates and proportions, J. Appl. Stat. 31 (2004), pp. 799–815] by incorporating a discrete component that allows practitioners to model data on rates and proportions with observations that equal an interval limit. For instance, one can model responses that assume values in (0, 1]. The likelihood ratio test tends to be quite oversized (liberal, anticonservative) in inflated beta regressions estimated with a small number of observations. Indeed, our numerical results show that its null rejection rate can be almost twice the nominal level. It is thus important to develop alternative testing strategies. This paper develops small-sample adjustments to the likelihood ratio and signed likelihood ratio test statistics in inflated beta regression models. The adjustments do not require orthogonality between the parameters of interest and the nuisance parameters and are fairly simple since they only require first- and second-order log-likelihood cumulants. Simulation results show that the modified likelihood ratio tests deliver much accurate inference in small samples. An empirical application is presented and discussed.     

A Matching Prior for the Shape Parameter of the Skew‐Normal Distribution

Abstract. This paper deals with the issue of performing a default Bayesian analysis on the shape parameter of the skew‐normal distribution. Our approach is based on a suitable pseudo‐likelihood function and a matching prior distribution for this parameter, when location (or regression) and scale parameters are unknown. This approach is important for both theoretical and practical reasons. From a theoretical perspective, it is shown that the proposed matching prior is proper thus inducing a proper posterior distribution for the shape parameter, also when the likelihood is monotone. From the practical perspective, the proposed approach has the advantages of avoiding the elicitation on the nuisance parameters and the computation of multidimensional integrals.     

Estimating a Single Shelf‐Life for Multiple Batches

Pharmaceutical companies and manufacturers of food products are legally required to label the product's shelf‐life on the packaging. For pharmaceutical products the requirements for how to determine the shelf‐life are highly regulated. However, the regulatory documents do not specifically define the shelf‐life. Instead, the definition is implied through the estimation procedure. In this paper, the focus is on the situation where multiple batches are used to determine a label shelf‐life that is applicable to all future batches. Consequently, the short‐comings of existing estimation approaches are discussed. These are then addressed by proposing a new definition of shelf‐life and label shelf‐life, where greater emphasis is placed on within and between batch variability. Furthermore, an estimation approach is developed and the properties of this approach are illustrated using a simulation study. Finally, the approach is applied to real data.     

清代举子中式的平均年龄研究

从《清代卷集成》考生的履历计算举子中式贡生、举人、贡士(进士)的平均年龄。根据年龄与人们的智力和能力之间的关系,得出科举考试包含着一种考查人们智力的成分,并非全靠死记硬背就能奏效的新认识。     

利润分享机制下经理行动组合的探讨

本文对提高经理工作努力和减少经理机会主义行为的问题进行了探讨。首先,认为经理不但有机会主义行为的动机而且还有实施机会主义行为的条件,因此,认为经理机会主义行为的发生是完全可能的。然后,把问题模型化并进行了分析。通过分析指出:简单委托—代理模型分析得到的利润分享系数偏低。提高利润的分享系数不但会增加经理的工作努力而且能够抑制经理的机会主义行为。在契约生效后,所有者还可以用一些方法来提高经理的工作努力或者抑制经理的机会主义行为。     

A weighted Poisson distribution and its application to cure rate models

The family of weighted Poisson distributions offers great flexibility in modeling discrete data due to its potential to capture over/under-dispersion by an appropriate selection of the weight function. In this paper, we introduce a flexible weighted Poisson distribution and further study its properties by using it in the context of cure rate modeling under a competing cause scenario. A special case of the new distribution is the COM-Poisson distribution which in turn encompasses the Bernoulli, Poisson, and geometric distributions; hence, many of the well-studied cure rate models may be seen as special cases of the proposed model. We focus on the estimation, through the maximum likelihood method, of the cured proportion and the properties of the failure time of the susceptibles/non cured individuals; a profile likelihood approach is also adopted for estimating the parameters of the weighted Poisson distribution. A Monte Carlo simulation study demonstrates the accuracy of the proposed inferential method. Finally, as an illustration, we fit the proposed model to a cutaneous melanoma data set.     

Estimating the variance for heterogeneity in arm‐based network meta‐analysis

Network meta‐analysis can be implemented by using arm‐based or contrast‐based models. Here we focus on arm‐based models and fit them using generalized linear mixed model procedures. Full maximum likelihood (ML) estimation leads to biased trial‐by‐treatment interaction variance estimates for heterogeneity. Thus, our objective is to investigate alternative approaches to variance estimation that reduce bias compared with full ML. Specifically, we use penalized quasi‐likelihood/pseudo‐likelihood and hierarchical (h) likelihood approaches. In addition, we consider a novel model modification that yields estimators akin to the residual maximum likelihood estimator for linear mixed models. The proposed methods are compared by simulation, and 2 real datasets are used for illustration. Simulations show that penalized quasi‐likelihood/pseudo‐likelihood and h‐likelihood reduce bias and yield satisfactory coverage rates. Sum‐to‐zero restriction and baseline contrasts for random trial‐by‐treatment interaction effects, as well as a residual ML‐like adjustment, also reduce bias compared with an unconstrained model when ML is used, but coverage rates are not quite as good. Penalized quasi‐likelihood/pseudo‐likelihood and h‐likelihood are therefore recommended.     

Efficiently weighted estimating equations with application to proportional excess hazards

A general approach to estimation, that can lead to efficient estimation in two stages, is presented. The method will not always be available, but sufficient conditions for efficiency are provided together with four examples of its use: (1) estimation of the odds ratio in 1:M matched case-control studies with a dichotomous exposure variable; (2) estimation of the relative hazard in a two-sample survival setting; (3) estimation of the regression parameters in the proportional excess hazards model; and (4) estimation in a partly linear parametric additive hazards model. The method depends upon finding a family of weighted estimating equations, which includes a simple initial equation yielding a consistent estimate and also an equation that yields an efficient estimate, provided the optiomal weights are used.     

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.     

PISCES对具有场限环的平面结二极管电场分布的模拟

将二维(2D)电势表达式和新判据引入到 Stanford 大学的器件模拟器 PISCES-IIB中,使之能在零载流子工作模式下便能迅速、正确地对具有浮空场限环(FFLR's)的平面结二极管的表面电场进行二维数值模拟。