Random effects regression models for count data with excess zeros in caries research

We extend the family of Poisson and negative binomial models to derive the joint distribution of clustered count outcomes with extra zeros. Two random effects models are formulated. The first model assumes a shared random effects term between the conditional probability of perfect zeros and the conditional mean of the imperfect state. The second formulation relaxes the shared random effects assumption by relating the conditional probability of perfect zeros and the conditional mean of the imperfect state to two different but correlated random effects variables. Under the conditional independence and the missing data at random assumption, a direct optimization of the marginal likelihood and an EM algorithm are proposed to fit the proposed models. Our proposed models are fitted to dental caries counts of children under the age of six in the city of Detroit.     

Evaluating Lightning-Caused Fire Occurrence Using Spatial Generalized Additive Models: A Case Study in Central Spain

It is widely accepted that the relationship between lightning wildfire occurrence and its influencing factors vary depending on the spatial scale of analysis, making the development of models at the regional scale advisable. In this study, we analyze the effects of different biophysical variables and lightning characteristics on lightning-caused forest wildfires in Castilla y León region (Central Spain). The presence/absence of at least one lightning-caused fire in any 4 × 4-km grid cell was used as a dependent variable and vegetation type and structure, terrain, climate, and lightning characteristics were used as possible covariates. Five prediction methods were compared: a generalized linear model (GLM), a random forest model (RFM), a generalized additive model (GAM), a GAM that includes a spatial trend function (GAMs) and a spatial autoregressive model (AUREG). A GAMs with just one covariate, apart from longitude and latitude for each observation included as a combined effect, was considered the most appropriate model in terms of both predictive ability and simplicity. According to our results, the probability of a forest being affected by a lightning-caused fire is positively and nonlinearly associated with the percentage of coniferous woodlands in the landscape, suggesting that occurrence is more closely associated with vegetation type than with topography, climate, or lightning characteristics. The selected GAMs is intended to inform the Regional Government of Castilla y León (the fire and fuel agency in the region) regarding identification of areas at greatest risk so it can design long-term forest fuel and fire management strategies.     

A GEE approach to estimating accuracy and its confidence intervals for correlated data

In this paper, we provide a method for constructing confidence interval for accuracy in correlated observations, where one sample of patients is being rated by two or more diagnostic tests. Confidence intervals for other measures of diagnostic tests, such as sensitivity, specificity, positive predictive value, and negative predictive value, have already been developed for clustered or correlated observations using the generalized estimating equations (GEE) method. Here, we use the GEE and delta‐method to construct confidence intervals for accuracy, the proportion of patients who are correctly classified. Simulation results verify that the estimated confidence intervals exhibit consistent/appropriate coverage rates.     

On the generalized t(GT) distribution

McDonald and Newey [J.B. McDonald and W.K. Newey, Partially adaptive estimation of regression models via the generalized t distribution, Econ. Theor. 4 (1988), pp. 428–457.] introduced the generalized t(GT) distribution. In this paper, several explicit formulas for its cumulative distribution function (cdf) are derived. These formulas will be useful for future developments in the theory and applications of the distribution. One such situation is explained and an application is provided to rainfall data from Orlando, Florida.     

无约束条件下多客户流失挽救最优化决策

对无约束条件下多客户流失挽救的最优方案进行了研究.借助于广义客户终身价值,通过数学建模和分析发现,只有当挽救行动判定值大于1时,对流失客户的挽救才有必要,且存在最优挽救费用,各类客户中的合理挽救次序也存在.     

集值决策信息系统属性约简与规则提取的矩阵算法

在集值决策信息系统中引入了优势矩阵和决策矩阵的概念,进一步建立了集值决策信息系统广义决策约简与规则提取的矩阵算法.算法利用矩阵间的比较提取所有决策规则,并同时得到所有广义决策约简.通过实例分析验证了该算法的有效性,说明了其优点是对数据复杂的决策信息系统也可相对容易地求出所有的广义决策约简与决策规则.     

Singular weighing designs and estimation of total weight

The problem of estimation of total weight of objects using a singular spring balance weighing design has been studied in this paper. A lower bound of the estimated total weight is obtained and some classes of designs attaining the lower bound are studied.     

On the numerical behaviour of ARMA(P,Q) covariance determinants for various sample sizes

An algorithm for the covariance determinant of a stationary autoregressive-moving average model is considered. Some asymptotic properties of this determinant in the stationarity and invertibil-ity region of the process are studied numerically in simple special cases.     

A new variable selection method for uniform designs

As an important class of space-filling designs, uniform designs (UDs) choose a set of points over a certain domain such that these points are uniformly scattered, under a specific discrepancy measure. They have been applied successfully in many industrial and scientific experiments since they appeared in 1980. A noteworthy and practical advantage is their ability to investigate a large number of high-level factors simultaneously with a fairly economical set of experimental runs. As a result, UDs can be properly used as experimental plans that are intended to derive the significant factors from a list of many potential ones. To this end, a new screening procedure is introduced via penalized least squares. A simulation study is conducted to support the proposed method, which reveals that it can be considered quite promising and expedient, as judged in terms of Type I and Type II error rates.     

Confidence sets as programming problems

Optimizing criteria for choosing a confidence set for a parameter are formulated as mathematical programming problems. The two optimizing criteria, probability of coverage and size of set, give rise to a pair of inverse programming problems. Several examples are worked out. The programming problems are then formulated to allow the incorporation of partial information about the parameter. By varying the family of prior distributions, a continuum of problems from the frequency approach to a Bayesian approach is obtained. Some examples are considered in which the family of priors contains more than one but not all prior distributions.