A Comparison of Correlation Structure Selection Penalties for Generalized Estimating Equations

Correlated data are commonly analyzed using models constructed using population-averaged generalized estimating equations (GEEs). The specification of a population-averaged GEE model includes selection of a structure describing the correlation of repeated measures. Accurate specification of this structure can improve efficiency, whereas the finite-sample estimation of nuisance correlation parameters can inflate the variances of regression parameter estimates. Therefore, correlation structure selection criteria should penalize, or account for, correlation parameter estimation. In this article, we compare recently proposed penalties in terms of their impacts on correlation structure selection and regression parameter estimation, and give practical considerations for data analysts. Supplementary materials for this article are available online.     

Continuity of f-projections and applications to the iterative proportional fitting procedure*

This paper proves continuity of f-projections and the continuous dependence of the limit matrix of the iterative proportional fitting procedure (IPF procedure) on the given matrix as well as the given marginals under certain regularity constraints. For finite spaces, the concept of f-projections of finite measures on a compact and convex set is introduced and continuity of f-projections is proven. This result is applied to the IPF procedure. Given a nonnegative matrix as well as row and column marginals the IPF procedure generates a sequence of matrices, called the IPF sequence, by alternately fitting rows and columns to match their respective marginals. The procedure is equivalent to cyclic f-projections. If the IPF sequence converges, the application of the continuity of f-projections yields the continuous dependence of the limit matrix on the given matrix. By generalized convex programming and under some constraints, it is shown that the limit matrix of the IPF sequence continuously depends not only on the given matrix but also on the marginals.     

Joint GEEs for multivariate correlated data with incomplete binary outcomes

This study considers a fully-parametric but uncongenial multiple imputation (MI) inference to jointly analyze incomplete binary response variables observed in a correlated data settings. Multiple imputation model is specified as a fully-parametric model based on a multivariate extension of mixed-effects models. Dichotomized imputed datasets are then analyzed using joint GEE models where covariates are associated with the marginal mean of responses with response-specific regression coefficients and a Kronecker product is accommodated for cluster-specific correlation structure for a given response variable and correlation structure between multiple response variables. The validity of the proposed MI-based JGEE (MI-JGEE) approach is assessed through a Monte Carlo simulation study under different scenarios. The simulation results, which are evaluated in terms of bias, mean-squared error, and coverage rate, show that MI-JGEE has promising inferential properties even when the underlying multiple imputation is misspecified. Finally, Adolescent Alcohol Prevention Trial data are used for illustration.     

Combined asymmetric spatial weights matrix with application to housing prices

In this study, a combined asymmetric spatial weights matrix is proposed for capturing the unequal spatial dependence of housing prices, where the advantage of this matrix was demonstrated by a non-nested hypothesis test. To explore the heterogeneous spatial impacts of urban essential characteristics on housing prices over the eastern, central, and western regions of China, after the Lagrange multiplier and likelihood ratio tests, the spatial Durbin model using the proposed weights matrix was applied to each region. The estimation results showed that the direct impacts of college and new employment were significantly negative in the eastern region, but not significant in the central and western regions. By contrast, the direct impacts of hospitals and scenic spots were significantly positive in eastern China, but not significant in central and western China. In addition, the indirect impacts of the four variables were not significant in the three regions. These results suggest that in eastern China, the government may increase the requirements for using medical resources and close tourist attractions in a single city to cool down the skyrocketing housing prices in this area.     

More on the restricted Liu estimator in the logistic regression model

?iray et al. proposed a restricted Liu estimator to overcome multicollinearity in the logistic regression model. They also used a Monte Carlo simulation to study the properties of the restricted Liu estimator. However, they did not present the theoretical result about the mean squared error properties of the restricted estimator compared to MLE, restricted maximum likelihood estimator (RMLE) and Liu estimator. In this article, we compare the restricted Liu estimator with MLE, RMLE and Liu estimator in the mean squared error sense and we also present a method to choose a biasing parameter. Finally, a real data example and a Monte Carlo simulation are conducted to illustrate the benefits of the restricted Liu estimator.     

Haddon矩阵模型在技巧啦啦队训练损伤防范中的运用

本文应用Haddon矩阵模型理论对技巧啦啦队训练伤害的防范进行研究。试图以新的视角寻找损伤防范的规律,建立新的啦啦队训练赛事精准分析矩阵模型,将弥补技巧啦啦队训练伤害防范中的理论空白。并依据新矩阵模型,研究从运动者、物理环境、社会环境以及媒介四个方面提出减少训练损伤的方法。     

基于区间数大小不能直接判定的灰矩阵博弈的策略优超及其最优解研究

对于区间灰数大小不能直接判定的灰矩阵博弈G(⊗)={S₁,S₂,A(⊗)}问题,其策略优超和纯策略求解问题的关键在于A(⊗)中区间灰数大小判定准则的设定与判定方法的设计。本文运用灰色系统思想和系统工程的理论,揭示了人们在灰信息条件下的博弈心理与博弈决策规则,根据区间灰数势关系的判定规则,提出了灰数势意义下的策略优超法则,定义了纯策略解。最后,以商业银行贷款动态损失准备金计提为案例,对其灰势意义下的策略优超和纯策略解问题进行了研究。     

一种基于区间数判断矩阵的群决策新方法

针对基于区间数判断矩阵的群决策问题,提出了一种群决策新方法.借助于集值统计原理,构造了与区间数判断矩阵群信息等价的具有一定可靠度的确定数判断矩阵,建立了计算这类群信息集结值可靠度的模型,运用和积法对所得新判断矩阵进行处理,得到了一种简便的方案排序方法.最后,通过一个算例验证了该方法的有效性和实用性.