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.     

VIF-based adaptive matrix perturbation method for heteroskedasticity-robust covariance estimators in the presence of multicollinearity

In this study, we investigate linear regression having both heteroskedasticity and collinearity problems. We discuss the properties related to the perturbation method. Important observations are summarized as theorems. We then prove the main result that states the heteroskedasticity-robust variances can be improved and that the resulting bias is minimized by using the matrix perturbation method. We analyze a practical example for validation of the method.     

浅谈矩阵特征值的估计

矩阵的特征值问题是矩阵计算的一个重要方向,在众多的领域中都得到了应用。在这样的大背景下,有必要深入地研究矩阵的特征值的估计问题。基于此,本文将结合国内外对于矩阵的特征值的估计方面的研究,以及一些具体的应用实例,来深入地探索矩阵的特征值的估计问题。     

为钻头选型的地层模糊聚类研究

本文用模栩聚类分析方法探讨燎合考虑地层多种岩性下的地层分爽.以17种不同地层为例，分析了其模栩相容拒阵的建立方法并给出其聚类圈.讨论了绿合考虑地层多种若性下的钻头选型。