The Multilevel Approach to Repeated Measures for Complete and Incomplete Data

Repeated measurements often are analyzed by multivariate analysis of variance (MANOVA). An alternative approach is provided by multilevel analysis, also called the hierarchical linear model (HLM), which makes use of random coefficient models. This paper is a tutorial which indicates that the HLM can be specified in many different ways, corresponding to different sets of assumptions about the covariance matrix of the repeated measurements. The possible assumptions range from the very restrictive compound symmetry model to the unrestricted multivariate model. Thus, the HLM can be used to steer a useful middle road between the two traditional methods for analyzing repeated measurements. Another important advantage of the multilevel approach to analyzing repeated measures is the fact that it can be easily used also if the data are incomplete. Thus it provides a way to achieve a fully multivariate analysis of repeated measures with incomplete data. This revised version was published online in June 2006 with corrections to the Cover Date.     

上市公司审计收费影响因素的实证研究

本文利用我国深沪两市A股上市公司2003年年报中披露的数据,对可能影响我国上市公司年度审计费用的主要因素,运用多元线性回归进行实证分析。研究结果发现,上市公司资产总额、纳入合并报表的控股子公司数目、其他应收款占总资产的比例、公司和事务所是否位于经济发达地区和董事会规模与年度审计费用显著正相关,而独立董事人数与年度审计费用显著负相关;应收账款占总资产的比例、存货占总资产的比例、审计意见、当年和前一年度的盈利状况等因素对年度审计费用的影响并不显著。因此,我国上市公司审计费用主要由审计的产品费用所决定,从而会计师事务所的审计收费主要反映了现实的审计成本,而审计风险等潜在风险成本并没有在审计收费中体现出来。     

基于线性概率序列的报童模型模拟分析

经典的报童模型能很好地解决需求分布确定情形下对最优订购量的求解,但并不适用于需求分布不确定的情况。从实际情况出发,提出需求为线性正态分布序列的报童模型,采用线性回归的方式来确定模型参数,得出了线性正态分布序列下报童模型的解是一个随时间变化的线性序列的结论,并用计算机模拟的办法检验了此思路的可行性。     

Labor market analysis through transformations and robust multivariate models

The work presents a robust approach to labor share analysis. The estimate of labor share presents various complexities related to the nature of the data sets to be analyzed. Typically, labor share is evaluated by using discriminant analysis and linear or generalized linear models, that do not take into account the presence of possible outliers. Moreover, the variables to be considered are often characterized by a high dimensional structure. The proposed approach has the objective of improving the estimation of the model using robust multivariate regression techniques and data transformation.     

单层网壳极限承载力分析

文章采用线性屈曲、几何非线性及材料非线性和几何非线性耦合的分析方法,对某大跨度单层球面网壳进行极限承载力分析。分析表明,材料非线性对网壳结构的承载力均有较大的影响,采用线性屈曲、几何非线性分析方法均高估网壳结构的极限承载力,因此,要准确评估出网壳结构的极限承载力,就必须全面考虑网壳结构的几何非线性及材料非线性的影响。     

上市公司股权结构与股利政策相关性实证分析——西北五省区的数据

本文以2002年~2004年西北五省区有股利分配的上市公司作为样本,采用多元回归分析方法,验证股权结构自变量与股利之间的线性关系,用非线性回归方法检验未通过线性关系检验的自变量与股利之间的关系。结果发现,西北五省区股利偏低,股东对现金股利有不同偏好。     

Application of Multilevel Models to Structured Repeated Measurements

The linear mixed-effects model has been widely used for the analysis of continuous longitudinal data. This paper demonstrates that the linear mixed model can be adapted and used for the analysis of structured repeated measurements. A computational advantage of the proposed methodology is that there is no extra burden on the analyst since any software for linear mixed-effects models can be used to fit the proposed models. Two data sets from clinical psychology are used as motivating examples and to illustrate the methods.     

Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model

Assessing regional population compositions is an important task in many research fields. Small area estimation with generalized linear mixed models marks a powerful tool for this purpose. However, the method has limitations in practice. When the data are subject to measurement errors, small area models produce inefficient or biased results since they cannot account for data uncertainty. This is particularly problematic for composition prediction, since generalized linear mixed models often rely on approximate likelihood inference. Obtained predictions are not reliable. We propose a robust multivariate Fay–Herriot model to solve these issues. It combines compositional data analysis with robust optimization theory. The nonlinear estimation of compositions is restated as a linear problem through isometric logratio transformations. Robust model parameter estimation is performed via penalized maximum likelihood. A robust best predictor is derived. Simulations are conducted to demonstrate the effectiveness of the approach. An application to alcohol consumption in Germany is provided.     

供水管网模糊优化设计数学模型研究

供水管网优化设计通常具有模糊性，即影响管网优化设计的某些因素难以准确确定。针对这一特点，建立了供水管网模糊优化设计数学模型。通过变换，将模糊线性规划问题转化成一般线性规划问题，用单纯形法求解。根据所建立的管网模糊优化设计模型，可确定模糊环境下供水管网优化设计方案，与普通线性规划问题相比，该方法使设计结果更为经济合理。     

多目标线性规划在广深城际列车组合中的应用

利用多目标线性规划的方法,以广深城际列车组合产品为研究对象。经过建立数学模型并采用LINGO软件分析,可以达到对多目标线性规划问题较易求解的目标,从而较好的利用多目标线性规划解决实际问题。     

Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study

Functional data analysis is a field of growing importance in Statistics. In particular, the functional linear model with scalar response is surely the model that has attracted more attention in both theoretical and applied research. Two of the most important methodologies used to estimate the parameters of the functional linear model with scalar response are functional principal component regression and functional partial least‐squares regression. We provide an overview of estimation methods based on these methodologies and discuss their advantages and disadvantages. We emphasise that the role played by the functional principal components and by the functional partial least‐squares components that are used in estimation appears to be very important to estimate the functional slope of the model. A functional version of the best subset selection strategy usual in multiple linear regression is also analysed. Finally, we present an extensive comparative simulation study to compare the performance of all the considered methodologies that may help practitioners in the use of the functional linear model with scalar response.     

Methods for Scalar‐on‐Function Regression

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images and so on are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorising the basic model types as linear, non‐linear and non‐parametric. We discuss publicly available software packages and illustrate some of the procedures by application to a functional magnetic resonance imaging data set.     

Modelling Strategies for Repeated Multiple Response Data

This article discusses modelling strategies for repeated measurements of multiple response variables. Such data arise in the context of categorical variables where one can select more than one of the categories as the response. We consider each of the multiple responses as a binary outcome and use a marginal (or population‐averaged) modelling approach to analyse its means. Generalized estimating equations are used to account for different correlation structures, both over time and between items. We also discuss an alternative approach using a generalized linear mixed model with conditional interpretations. We illustrate the methods using data from a panel study in Australia called the Household, Income, and Labour Dynamics Survey.     

An Overview of Normal Theory Structural Measurement Error Models

This paper gives an introduction and overview to the often under‐used measurement error model. The purpose is to provide a simple summary of problems that arise from measurement error and of the solutions that have been proposed. We start by describing how measurement error models occur in real‐world situations. Then we proceed with defining the measurement error model, initially introducing the multivariate form of the model, and then, starting with the simplest form of the model thoroughly discuss its features and solutions to the problems introduced due to measurement error. We discuss higher‐dimensional and more advanced forms of the model and give a brief numerical illustration.     

Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

A simultaneous confidence band provides a variety of inferences on the unknown components of a regression model. There are several recent papers using confidence bands for various inferential purposes; see for example, Sun et al. (1999) , Spurrier (1999) , Al‐Saidy et al. (2003) , Liu et al. (2004) , Bhargava & Spurrier (2004) , Piegorsch et al. (2005) and Liu et al. (2007) . Construction of simultaneous confidence bands for a simple linear regression model has a rich history, going back to the work of Working & Hotelling (1929) . The purpose of this article is to consolidate the disparate modern literature on simultaneous confidence bands in linear regression, and to provide expressions for the construction of exact 1 ?α level simultaneous confidence bands for a simple linear regression model of either one‐sided or two‐sided form. We center attention on the three most recognized shapes: hyperbolic, two‐segment, and three‐segment (which is also referred to as a trapezoidal shape and includes a constant‐width band as a special case). Some of these expressions have already appeared in the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation.     

Constrained Kalman Filtering: Additional Results

This paper deals with linear state space modelling subject to general linear constraints on the state vector. The discussion concentrates on four topics: the constrained Kalman filtering versus the recursive restricted least squares estimator; a new proof of the constrained Kalman filtering under a conditional expectation framework; linear constraints under a reduced state space modelling; and state vector prediction under linear constraints. The techniques proposed are illustrated in two real problems. The first problem is related to investment analysis under a dynamic factor model, whereas the second is about making constrained predictions within a GDP benchmarking estimation.     

Copula-based multivariate GARCH model with uncorrelated dependent errors

Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests a conventional MGARCH model as a special case. The aim of this paper is to model MGARCH for non-normal multivariate distributions using copulas. We model the conditional correlation (by MGARCH) and the remaining dependence (by a copula) separately and simultaneously. We apply this idea to three MGARCH models, namely, the dynamic conditional correlation (DCC) model of Engle [Engle, R.F., 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20, 339–350], the varying correlation (VC) model of Tse and Tsui [Tse, Y.K., Tsui, A.K., 2002. A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20, 351–362], and the BEKK model of Engle and Kroner [Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122–150]. Empirical analysis with three foreign exchange rates indicates that the C-MGARCH models outperform DCC, VC, and BEKK in terms of in-sample model selection and out-of-sample multivariate density forecast, and in terms of these criteria the choice of copula functions is more important than the choice of the volatility models.     

Stable mixture GARCH models

A new model class for univariate asset returns is proposed which involves the use of mixtures of stable Paretian distributions, and readily lends itself to use in a multivariate context for portfolio selection. The model nests numerous ones currently in use, and is shown to outperform all its special cases. In particular, an extensive out-of-sample risk forecasting exercise for seven major FX and equity indices confirms the superiority of the general model compared to its special cases and other competitors. Estimation issues related to problems associated with mixture models are discussed, and a new, general, method is proposed to successfully circumvent these. The model is straightforwardly extended to the multivariate setting by using an independent component analysis framework. The tractability of the relevant characteristic function then facilitates portfolio optimization using expected shortfall as the downside risk measure.     

运用MATLAB软件求解物流运输问题

在引入物流运输问题的优化模型的基础上使用MATLAB软件中的linprog函数来求解线性规划问题,并结合实例显示了MATLAB软件在物流运输定量分析过程中的优越性。     

线性规划在假设开发法中的应用研究

本文尝试运用运筹学中线性规划理论的数学模型,结合SWOT分析决策房地产开发最高最佳使用方式,为开发商或土地估价师提供一条可供参考的技术路线。