Generalized Estimating Equations to Binary Probit Model

Inference in generalized linear mixed models with multivariate random effects is often made cumbersome by the high-dimensional intractable integrals involved in the marginal likelihood. This article presents an inferential methodology based on the generalized estimating equations for the probit latent traits models. This method belonging to the broad class of semi parametric approaches involves marginal joint moments of order 1 and 2, which has analytical expression. The different results are illustrated with a simulation study.     

On the BLUEs in Two Linear Models via C. R. Rao's Pandora's Box

We consider the estimation of the parameters in two partitioned linear models, denoted by 𝒜 = {y, X ₁ β ₁ + X ₂ β ₂, V _𝒜} and ? = {y, X ₁ β ₁ + X ₂ β ₂, V _?}, which we call full models. Correspondingly, we define submodels 𝒜₁ = {y, X ₁ β ₁, V _𝒜} and ?₁ = {y, X ₁ β ₁, V _?}. Using the so-called Pandora's Box approach introduced by Rao (1971 Rao , C. R. ( 1971 ). Unified theory of linear estimation . Sankhy?, Ser. A 33 : 371 – 394 . [Corrigendum (1972), 34, p. 194, 477.]  [Google Scholar], we give new necessary and sufficient conditions for the equality between the best linear unbiased estimators (BLUEs) of X ₁ β ₁ under 𝒜₁ and ?₁ as well as under 𝒜 and ?. In our considerations we will utilise the Frisch–Waugh–Lovell theorem which provides a connection between the full model 𝒜 and the reduced model 𝒜 _r  = {M ₂ y, M ₂ X ₁ β ₁, M ₂ V _𝒜 M ₂} with M ₂ being an appropriate orthogonal projector. Moreover, we consider the equality of the BLUEs under the full models assuming that they are equal under the submodels.     

The Role of Posterior Densities in Latent Variable Models for Ordinal Data

In latent variable models, problems related to the integration of the likelihood function arise since analytical solutions do not exist. Laplace and Adaptive Gauss-Hermite (AGH) approximations have been discussed as good approximating methods. Their performance relies on the assumption of normality of the posterior density of the latent variables, but, in small samples, this is not necessarily assured. Here, we analyze how the shape of the posterior densities varies as function of the model parameters, and we investigate its influence on the performance of AGH and of the Laplace approximation.     

“渔”无“鱼”：两个“渔佬儿”的符号释义

从《最后一个渔佬儿》到《铁壳船》,前者根植于“寻根文学”的文化语境,后者根植于中国“城市化进程”的历史境遇,二十余年的时空更迭,他们从“渔”有“鱼”到“渔”无“鱼”的历史终结,两个“渔佬儿”——“柴福奎”和“杨大头”成了一个“互文见义”的人物符号。在人物符号能指的背后,表征出主人公一方面眷恋农业文明,一方面又质疑现代工业文明,折射出的是中国城市化进程中城乡文化冲突、生态隐忧、叙事者文化心态归属等问题。     

On the Loss Robustness of Least-Square Estimators

Abstract

The article revisits univariate and multivariate linear regression models. It is shown that least-square estimators (LSEs) are minimum risk estimators in general class of linear unbiased estimators under some general divergence loss. This amounts to the loss robustness of LSEs.     

当代工笔画中女性服饰的表现研究

描绘女性形象的工笔人物画称之为仕女画，从传统仕女画女性服饰样式着手，尝试通过对不同时期工笔画中女性服饰进行分析和比较，梳理出传统工笔人物画女性服饰概况。通过现当代工笔人物画中女性服饰的表现形式，探求其蕴含的艺术意识。     

Nonlinear mixed‐effects models with misspecified random‐effects distribution

Nonlinear mixed‐effects models are being widely used for the analysis of longitudinal data, especially from pharmaceutical research. They use random effects which are latent and unobservable variables so the random‐effects distribution is subject to misspecification in practice. In this paper, we first study the consequences of misspecifying the random‐effects distribution in nonlinear mixed‐effects models. Our study is focused on Gauss‐Hermite quadrature, which is now the routine method for calculation of the marginal likelihood in mixed models. We then present a formal diagnostic test to check the appropriateness of the assumed random‐effects distribution in nonlinear mixed‐effects models, which is very useful for real data analysis. Our findings show that the estimates of fixed‐effects parameters in nonlinear mixed‐effects models are generally robust to deviations from normality of the random‐effects distribution, but the estimates of variance components are very sensitive to the distributional assumption of random effects. Furthermore, a misspecified random‐effects distribution will either overestimate or underestimate the predictions of random effects. We illustrate the results using a real data application from an intensive pharmacokinetic study.     

电磁场教学中电场的计算

电磁场的求解问题，主要归结为求电场和磁场的问题，其中关于电场的求解主要是求电场强度。不同电场，电场强度的计算方法也不同。以所学电磁场知识为基础，从静态场与动态场两种角度，归纳出几种求解电场强度的方法，并分别给出这些方法的适用范围。     

句子John Saw Peter on the Bus歧义结构的空间域分析

本文拟从空间域分析的角度,并借助于图形背景理论,对句子John saw Peter on the bus的歧义结构进行分析。作者认为歧义的产生来源于动词动作的空间域与地点状语(介词短语)空间域之间的关系。正如对see的空间域和对on the bus的空间域的阐述成功解释了句子John met Peter on the bus和John saw Peter in China没有歧义,通常认为如果前者的空间域大于后者,歧义就有可能产生。