成分数据路径分析模型

路径分析是一种探索和验证系统内部各个因素之间因果关系的多元统计方法.本文针对现实中大量存在的成分数据变量,提出成分数据路径分析模型,给出模型的方程表达形式和图形表达形式.在成分数据多元线性回归的基础上,提出模型的参数估计方法,并利用Bootstrap分析技术,给出路径系数显著性检验办法.在某公司官方网站的用户满意度与推荐意愿影响因素应用研究中,成分数据路径分析建模结果表明,满意度主要受到易用性的影响,而推荐意愿主要受到有用性的影响.这一结论为网站原型设计与营销推广提供了新的启示.     

我国高等教育发展统计特征的PLS通径模型分析

借鉴UNESCO教育指标体系框架,建构我国高等教育发展统计指标体系;采用PLS通径模型这一结构方程建模新技术对建构的指标体系进行验证,并对2006年我国高等教育发展状况进行分析,获得客观统计指标数据特征。     

分工演进、金融发展与经济增长实证研究—基于浙湘1992-2006年数据和PLSR静动态通径模型

根据浙湘1992-2006年的数据,反复设定静态与动态偏最小二乘通径分析模型进行实证估计和检验。分析结果表明多潜变量静态通径模型通径系数估计值绝大多数是统计显著的;双潜变量动态通径模型的即期通径系数估计值和滞后通径系数估计值是统计显著的,显示了潜变量之间的静态与动态作用定量关系。这些分析结果为深入探索中国省区分工演进、金融发展与经济增长的机制提供了经验证据,也为深入探索中国多区域尺度金融发展与经济增长的关系提供了新的方法。     

右半平面上解析的Laplace-Stieltjes变换对数级

本文研究了零级Laplace-Stieltjes变换的增长性问题.利用对数级和对数下级的定义,获得了这类变换具有对数级的特征,即变换的对数级和对数下级与其系数之间的关系,推广了Dirichlet级数的相关结果.     

基于MCMC主成分回归分析方法的经济增长因素研究

将MCMC算法融合到主成分回归分析模型中,提出MCMC主成分回归分析方法.新方法既具有有效避免解释变量之间的多重共线性问题以及简化回归方程结构的主成分回归分析方法的优势,又能够充分利用MCMC算法的融合先验信息、模型信息及样本似然函数的长处.将方法应用于对嘉兴市1997年至201.0年的经济发展指标的数据建模分析,结果表明,方法能有效克服现有分析方法的不足,建立预测精度更高的模型.     

三种统计分析方法在数学建模中的应用

独立成分分析是近十年来兴起的一种新的数据处理方法.它与主成分分析,因子分析都隶属于多元统计分析方法,并且这三种方法都可以用于处理多变量大样本的数据.目前数学建模竞赛越来越受到各大高校的重视,而在数学建模中,大部分赛题都首先需要进行大样本数据的统计预处理.因此将从模型上对这三种方法进行分析与解释,并通过数学建模实例来说明这三种方法在数学建模中的应用.     

幂变换在多元线性回归中的应用

幂变换是多元线性回归分析中数据预处理的有效办法之一.以胰岛素注射治疗糖尿病为例,探讨幂变换实用的条件、研究方法及研究结论,并将幂变换处理后的变量,用于线性回归分析,研究医学问题.具体就是通过对变量数据描述性分析了解数据的特点,相关分析及聚类分析确定胰岛素初始剂量的重要影响因素,幂变换对数据进行预处理,继而进行回归分析,并对比变换前初步回归分析的结果,确定最终以尿蛋白分类标准,RI用量与血糖的对数之间的线性回归模型.     

高维分类数据的关联关系及可压缩性分析

对于高维情形而言,研究变量之间的关联关系及可压缩性是重要和繁琐的.首先,给出了基于对数线性模型和关联图的压缩性定理;然后,讨论了基于条件互信息可压缩性排序的问题,并通过三个不同的实例进行验证分析.研究结果为直观简便地分析高维分类数据的关系及结构提供了方法.     

偏最小二乘建模在R软件中的实现及实证分析

通过介绍偏最小二乘（PLS）的建模和显著性检验原理,解决了小样本多变量且变量间存在多重共线性的回归问题,建立了多变量对多变量的回归模型,并使用R软件（版本为Ri3862．15．1）实现了PLS建模;最后基于葡萄和葡萄酒理化指标数据进行了实证分析．     

散度偏大计数数据回归模型的变量选择与模型比较

讨论了具有散度偏大特征计数数据的建模与拟合问题.针对导致数据散度偏大的原因和常用的几类候选模型的结构,分别给出了关于嵌套模型的模型与变量同时选择的Bayes方法和关于非嵌套模型的模型检验与比较方法,并在此基础上进一步完善,提出了较为系统完整的模型与变量选择方法.实际例子说明了方法的具体实现过程和有效性.     

Goodness-of-fit indices for partial least squares path modeling

This paper discusses a recent development in partial least squares (PLS) path modeling, namely goodness-of-fit indices. In order to illustrate the behavior of the goodness-of-fit index (GoF) and the relative goodness-of-fit index (GoF_rel), we estimate PLS path models with simulated data, and contrast their values with fit indices commonly used in covariance-based structural equation modeling. The simulation shows that the GoF and the GoF_rel are not suitable for model validation. However, the GoF can be useful to assess how well a PLS path model can explain different sets of data.     

On the convergence of the partial least squares path modeling algorithm

This paper adds to an important aspect of Partial Least Squares (PLS) path modeling, namely the convergence of the iterative PLS path modeling algorithm. Whilst conventional wisdom says that PLS always converges in practice, there is no formal proof for path models with more than two blocks of manifest variables. This paper presents six cases of non-convergence of the PLS path modeling algorithm. These cases were estimated using Mode A combined with the factorial scheme or the path weighting scheme, which are two popular options of the algorithm. As a conclusion, efforts to come to a proof of convergence under these schemes can be abandoned, and users of PLS should triangulate their estimation results.     

A hyperspherical transformation forecasting model for compositional data

Although Aitchison’s [Aitchison, J., 1986. The Statistical Analysis of Compositional Data, Chapman and Hall, London] method of logratio transformation of compositional data is widely used in various domains, it is limited by the assumption of a strict non-negativity of the components and the requirement of special treatments in practice of the zero components. We propose a dimension-reduction approach through a hyperspherical transformation that is capable of resolving the difficulty in maintaining non-negativity and unit-sum in forecasting compositional data over time. Applying the proposed model to a numerical simulation with a 4D compositional data embedded with zero components and forecasting the three production sectors in the Chinese economy both demonstrate the usefulness and validity of the new approach.     

Non-symmetrical composite-based path modeling

Partial least squares path modeling presents some inconsistencies in terms of coherence with the predictive directions specified in the inner model (i.e. the path directions), because the directions of the links in the inner model are not taken into account in the iterative algorithm. In fact, the procedure amplifies interdependence among blocks and fails to distinguish between dependent and explanatory blocks. The method proposed in this paper takes into account and respects the specified path directions, with the aim of improving the predictive ability of the model and to maintain the hypothesized theoretical inner model. To highlight its properties, the proposed method is compared to the classical PLS path modeling in terms of explained variability, predictive relevance and interpretation using artificial data through a real data application. A further development of the method allows to treat multi-dimensional blocks in composite-based path modeling.     

Rapidly computing robust minimum capacity s-t cuts: a case study in solving a sequence of maximum flow problems

Near infrared (NIR) spectroscopy is a rapid, non-destructive technology to predict a variety of wood properties and provides great opportunities to optimize manufacturing processes through the realization of in-line assessment of forest products. In this paper, a novel multivariate regression procedure, the hybrid model of principal component regression (PCR) and partial least squares (PLS), is proposed to develop more accurate prediction models for high-dimensional NIR spectral data. To integrate the merits of PCR and PLS, both principal components defined in PCR and latent variables in PLS are utilized in hybrid models by a common iterative procedure under the constraint that they should keep orthogonal to each other. In addition, we propose the modified sequential forward floating search method, originated in feature selection for classification problems, in order to overcome difficulties of searching the vast number of possible hybrid models. The effectiveness and efficiency of hybrid models are substantiated by experiments with three real-life datasets of forest products. The proposed hybrid approach can be applied in a wide range of applications with high-dimensional spectral data.     

Properties of graphical regression models for multidimensional categorical data

We propose a two-component graphical chain model, the discrete regression distribution, where a set of discrete random variables is modeled as a response to a set of categorical and continuous covariates. The proposed model is useful for modeling a set of discrete variables measured at multiple sites along with a set of continuous and/or discrete covariates. The proposed model allows for joint examination of the dependence structure of the discrete response and observed covariates and also accommodates site-to-site variability. We develop the graphical model properties and theoretical justifications of this model. Our model has several advantages over the traditional logistic normal model used to analyze similar compositional data, including site-specific random effect terms and the incorporation of discrete and continuous covariates.     

一类小样本的统计方法建模及其可视化

针对一类高维小样本数据,利用统计方法的非参数检验与偏最小二乘回归(PLS)构造小样本预测模型,实现基于Wilcoxon秩和检验的变量选择与基于PLS的变量压缩降维.并通过DNA序列分类问题实现基于统计方法的小样本数据建模与可视化,计算结果表明方法对小样本具有可行性、有效性.     

On the exploration of linear latent effect for multivariate modeling

A data analysis method is proposed to derive a latent structure matrix from a sample covariance matrix. The matrix can be used to explore the linear latent effect between two sets of observed variables. Procedures with which to estimate a set of dependent variables from a set of explanatory variables by using latent structure matrix are also proposed. The proposed method can assist the researchers in improving the effectiveness of the SEM models by exploring the latent structure between two sets of variables. In addition, a structure residual matrix can also be derived as a by-product of the proposed method, with which researchers can conduct experimental procedures for variables combinations and selections to build various models for hypotheses testing. These capabilities of data analysis method can improve the effectiveness of traditional SEM methods in data property characterization and models hypotheses testing. Case studies are provided to demonstrate the procedure of deriving latent structure matrix step by step, and the latent structure estimation results are quite close to the results of PLS regression. A structure coefficient index is suggested to explore the relationships among various combinations of variables and their effects on the variance of the latent structure.     

基于Pairwise惩罚方法的面板数据模型结构变点估计

面板数据模型在经济、生物、统计等领域有着广泛的应用。经典的面板数据模型假设解释变量系数不随时间变化。然而在现实中,解释变量系数可能会因多种因素的影响而存在多重未知的结构变点。本文假设交互固定效应面板数据模型中含有多重未知的结构变点。研究发现通过Pairwise惩罚的参数估计方法在目标函数中增加对相邻时间解释变量系数的惩罚项,能够同时进行参数估计和结构变点诊断。蒙特卡洛模拟结果显示,不管是否存在同方差假设,该方法估计的解释变量系数均偏差较小且结构变点诊断错误率低。     

A complex multi-attribute large-group PLS decision-making method in the interval-valued intuitionistic fuzzy environment

In the complex multi-attribute large-group decision-making (CMALGDM) problems in interval-valued intuitionistic fuzzy (IVIF) environment, attributes of the alternatives are often stratified and correlated. This paper proposes a decision-making method for these problems based on partial least squares (PLS) path modelling, which not only fully exploits the decision information of decision makers (DMs), but also effectively addresses the relativity problem in the decision attributes and objectively assigned weights to the primary decision attributes (i.e., “latent variables for decision making”). The method can be outlined in three steps. First, a two-stage method is proposed to transform the interval-valued intuitionistic fuzzy number (IVIFN) samples into single-valued samples. In this step, an improved C-OWA operator is first given to transform the IVIFN samples into intuitionistic fuzzy number (IFN) samples, which makes the preference information of the DMs more objectively aggregated. Then a proposed membership-based method is applied to reduce the information loss and transform the IFN samples into single-valued samples. Second, the estimated values and weights of the “latent variables for decision-making” are obtained by means of the PLS path modelling algorithm. Finally, a multi-alternative sorting method is devised in accordance with the estimated values and weights. An example is provided to illustrate the proposed technique and evaluate its feasibility and validity.