Comparison of Inverse Wishart and Separation-Strategy Priors for Bayesian Estimation of Covariance Parameter Matrix in Growth Curve Analysis

Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due to its proper and conjugate properties. However, many researchers have pointed out that the inverse Wishart prior might not work as expected. The purpose of this study is to investigate the influence of the inverse Wishart prior and compare it with a class of separation-strategy priors on the parameter estimates of growth curve models. In this article, we illustrate the use of different types of priors with 2 real data analyses, and then conduct simulation studies to evaluate and compare these priors in estimating both linear and nonlinear growth curve models. For the linear model, the simulation study shows that both the inverse Wishart and the separation-strategy priors work well for the fixed effects parameters. For the Level 1 residual variance estimate, the separation-strategy prior performs better than the inverse Wishart prior. For the covariance matrix, the results are mixed. Overall, the inverse Wishart prior is suggested if the population correlation coefficient and at least 1 of the 2 marginal variances are large. Otherwise, the separation-strategy prior is preferred. For the nonlinear growth curve model, the separation-strategy priors work better than the inverse Wishart prior.     

加强物理模型教学培养学生创新能力

主要针对目前物理教学实际存在的问题,通过论证物理模型教学与创新思维能力的关系,提出物理模型教学是培养学生创新思维能力的有效途径,并侧重从3个角度论述如何建立物理模型。     

带有时滞的多非线性区间Lurie系统的鲁棒绝对稳定性

讨论了一类带有时滞多非线性区间系统的鲁棒绝对稳定性,通过引入区间矩阵,以及Lyapunov稳定性理论,给出了区间Lurie系统鲁棒绝对稳定性的判别条件,推广了参考文献[5]的结论.     

余数定理和Hamilton—Cayley定理的推广

通过本文的论征,主要推广了余数定理和Hamilton—Cayley定理的结论,同时还揭示了Hamilton—Cayley定理与数α是一元多项式f(x)的根的充要性定理之间的联系,他们都是同一个定理的特殊情形。     

分层各向异性有耗介质的反射和透射系数计算

在广义传播矩阵（CTM）方法分析各向异性分层介质传播特性的基础上，对数值计算进行了研究，克服了有耗介质计算时发散的困难，指出了编程计算时应该注意的问题。在半空间条件下，对分层各向异性有耗介质的反射和透射系数进行了计算，将GTM方法与精确解对比，计算结果一致。     

关于矩阵的二项式定理其应用

类比关于数式的二项式定理，导出关于矩阵的二项式定理，并用数学归纳法予以证明，最后举例说明关于矩阵的二项式定理的应用。     

一种求伴随矩阵的方法

首先证明了如果秩(A)=n-1,则伴随矩阵A*可以通过线性方程组AX=0的基础解系表达,然后给出一种计算n阶伴随矩阵方法。     

在有限域上可逆矩阵的个数和有限域的矩阵表示

本文计数了Galois域GF（q）上可逆矩阵的个数，并讨论了GF(q）中元素的矩阵表示。     

亚次正交矩阵及性质

给出了亚次正交矩阵的定义,并讨论其有关性质.     

线性运算的矩阵模型

线性运算用矩阵表示的两种模型分别对应西方和东方不同的排版格式——横式与竖式,同时也对应两种思维模式,从这两种模型产生两种运算体系,行与列的转置相互对应,两种模型相互对应,两种体系在线性方程组、线性变换、线性表示三个层面上具有等效性.