偏最小二乘(PartialLeast Square)方法的拟合指标及其在满意度研究中的应用

本文在对顾客满意度模型及PLS方法进行简单介绍的基础上,对PLS的拟合指标,包括共同因子、多元相关平方和冗余,进行了讨论。     

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．     

多元成分数据的对数衬度偏最小二乘通径分析模型

本文研究多元成分数据的路径关联关系的建模问题,提出多元成分数据的对数衬度PLS通径分析模型.将中心化对数比变换与PLS通径分析方法相结合建立模型,其主要优势在于:①PLS通径分析模型对数据没有严格的分布假设要求,特别适于成分数据这类分布复杂的数据建模;②成分数据中心化对数比变换后的变量完全多重相关,PLS方法能够有效解决这一问题;③PLS通径分析模型特别适于多元成分数据这类具有层次关系的数据结构的建模,通过结构模型揭示多元成分数据之间的整体性路径关联关系,通过测量模型揭示成分数据与其成分分量之间的构成关系.更重要的是,本文的方法研究遵循成分数据所特有的代数基本理论,推导出模型的成分数据对数衬度隐变量的表达形式,从理论上证明了该建模方法的科学合理性.最后,将本方法用于北京市三次产业的投资结构、GDP结构、就业结构的路径关联关系的分析中,通过实证研究验证模型的可行性和应用价值.     

基于RFM模型方法的忠诚计划会员顾客价值识别研究

尽管顾客忠诚计划已作为一种关系营销手段在企业中得到了广泛的应用,但却很少有研究关注如何利用忠诚计划收集的顾客交易数据对会员顾客进行价值识别和细分.基于RFM模型及聚类分析方法,提供了一种对忠诚计划会员顾客进行价值识别与细分的方法,并利用一家购物中心的会员顾客交易数据对该方法进行了实证分析.结果表明该方法不仅从统计意义上可以区分开具有差异的会员顾客群体,而且从管理意义上也可找出不同顾客群体间的差异特征,从而为企业针对差异化的顾客实现服务及产品的定制化和差异化提供了理论基础和方法.     

系统的PLS方法在满意度实证研究中的应用

满意度模型实证研究包括系统性方法和非系统性方法.系统性方法更有效地反映因果关系的有机联系,它包括PLS和SEM两种方法.本文在用方程系统表达满意度模型的基础上,说明PLS方法的基本原理,然后对一个具体的满意度模型在SEM方法失效的情况下,运用系统的PLS方法进行实证研究.结果表明,在SEM方法无法得到实证结果的情况下,PLS给出了很有价值的结论.     

ARMA(1,1)需求条件下供应链需求提前承诺的影响效果分析

为了分析供应链需求提前承诺的影响效果,考虑供应链所面临的顾客需求满足ARMA（1,1）过程。首先从理论上建立正常顾客需求与顾客需求提前承诺时零售商订单量波动程度和平均库存的定量描述模型,通过两种情形下的比较分析,得出在顾客需求自回归系数大于零时,顾客需求提前承诺将减小牛鞭效应和平均库存水平;同时得出在顾客需求提前承诺时,如果顾客需求自回归系数大于零,顾客提前承诺的需求比例越高,则牛鞭效应和平均库存水平越低;顾客需求提前承诺的时间跨度越长,则牛鞭效应和平均库存水平也越低。反之亦然。其次运用仿真方法分析了顾客需求提前承诺对零售商平均库存成本的影响,得出在顾客需求自回归系数大于零时,顾客需求提前承诺将有效降低零售商的平均库存成本。     

有优先权顾客带启动时间多重休假的M^1＋M^2/G/1排队系统

研究了带启动时间有顾客优先权多重休假的M^（1）＋M^（2）/G/1排队系统,分别给出了两类顾客的稳态队长的母函数和等待时间分布的LST及其随机分解的结果,推导出忙期、假期和启动期的LST等.     

基于样条变换的PLS回归的非线性结构分析

基于样条变换的:PLS非线性回归模型既吸取了样条函数分段拟合以适应任意曲线连续变化的优点,又借鉴了偏最小二乘回归方法能够有效解决自变量集合高度相关的技术.针对多元加法模型,从理论和仿真试验的角度分别验证了,对于多个独立自变量对单因变量为非线性关系的数据系统,基于样条变换的PLS回归方法不仅能够有效实现自变量对因变量的整体预测,而且能够提取各维自变量对因变量的单独非线性作用特征,从而确定数据系统内部的复杂非线性结构关系,增强了模型的可解释性.     

基于PLS的江苏省房地产价格影响因素的实证研究

通过偏最小二乘(PLS)方法对江苏省2000-2010年9个指标的汇总数据进行研究,并利用变量投影重要性指标(VIP)考察了各影响因素的重要程度.结果表明,城镇人均住房面积、在岗职工平均收入、人均GDP是影响江苏省房价最重要的因素.同时,考虑到江苏省内部发展的差异,又运用PLS法对苏南、苏中、苏北三地区2004-2010年9个指标的面板数据分别进行了分析.结果表明,在岗职工平均收入对三地区的房价均有较大影响.其余影响因素则因经济发展存在差异.     

广义偏最小二乘(PLS)估计类

本文研究了一类含有偏最小二乘（partialleastsquaresPLS）估计的估计类．给出了PLS估计的一般代数形式；讨论了含有PLS估计的广义PPLS估计类的统计性质；给出了该估计类优于最小二乘估计的条件．     

Nonlinear generalized master equations and accounting for initial correlations

We develop a new method based on using a time-dependent operator (generally not a projection operator) converting a distribution function (statistical operator) of a total system into the relevant form that allows deriving new exact nonlinear generalized master equations (GMEs). The derived inhomogeneous nonlinear GME is a generalization of the linear Nakajima-Zwanzig GME and can be viewed as an alternative to the BBGKY chain. It is suitable for obtaining both nonlinear and linear evolution equations. As in the conventional linear GME, there is an inhomogeneous term comprising all multiparticle initial correlations. To include the initial correlations into consideration, we convert the obtained inhomogeneous nonlinear GME into the homogenous form by the previously suggested method. We use no conventional approximation like the random phase approximation (RPA) or the Bogoliubov principle of weakening of initial correlations. The obtained exact homogeneous nonlinear GME describes all evolution stages of the (sub)system of interest and treats initial correlations on an equal footing with collisions via the modified memory kernel. As an application, we obtain a new homogeneous nonlinear equation retaining initial correlations for a one-particle distribution function of the spatially inhomogeneous nonideal gas of classical particles. In contrast to existing approaches, this equation holds for all time scales and takes the influence of pair collisions and initial correlations on the dissipative and nondissipative characteristics of the system into account consistently with the adopted approximation (linear in the gas density). We show that on the kinetic time scale, the time-reversible terms resulting from the initial correlations vanish (if the particle dynamics are endowed with the mixing property) and this equation can be converted into the Vlasov-Landau and Boltzmann equations without any additional commonly used approximations. The entire process of transition can thus be followed from the initial reversible stage of the evolution to the irreversible kinetic stage.     

基于ELM算法的羊肉水分含量的快速无损检测

在近红外光谱900-1700nm的波长范围内采集南疆羊肉的光谱数据,来研究水分含量的快速无损检测.为减弱非目标因素对光谱的影响,采用SNV和去趋势法对光谱数据进行预处理.为降低建模的复杂度,去除共线性的影响,采用连续投影算法和相关系数法相结合选取8个特征波长变量,最后使用PLS和ELM算法分别进行建模.实验表明,与采用全光谱波段建模相比,采用特征波长变量建模,PLS和ELM算法的运行时间都大大缩短,并且在运行时间和预测精度上,ELM算法均优于PLS算法.ELM算法采用8个特征波段变量建模,预测精度达到0.9768,均方误差为4.4291e-04,相关系数为0.7603,运行时间可控制在1e-04s之下,这可为研发羊肉水分含量的便携式检测装置提供理论参考.     

基于广义最大熵原理和遗传算法的多指标权重确定方法研究

本文探讨了多目标评价的实现过程,针对评价过程的权重确定问题,提出了基于广义最大熵原理和遗传算法的赋权方法,该方法把不同赋权方法有机地集成在一起,并可以对各种赋权方法进行优劣比较。最后用实例验证了该方法的准确性、可靠性和有效性。     

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.     

PLS1回归对多变量信息的综合与筛选作用分析

王惠文，ＰＬＳ１回归对多变量信息的综合与筛选作用分析，数理统计与管理，１９９８，１７（４），４６～４９。本文讨论了ＰＬＳ１回归对多变量系统中的信息进行综合与筛选的工作策略。通过例证分析指出，ＰＬＳ１回归方法可以有效地提取对系统解释性最强的综合变量，排除重叠信息或无解释意义的信息干扰，从而较好地克服变量多重相关性在系统建模中的不良作用     

PLS classification of functional data

Partial least squares (PLS) approach is proposed for linear discriminant analysis (LDA) when predictors are data of functional type (curves). Based on the equivalence between LDA and the multiple linear regression (binary response) and LDA and the canonical correlation analysis (more than two groups), the PLS regression on functional data is used to estimate the discriminant coefficient functions. A simulation study as well as an application to kneading data compare the PLS model results with those given by other methods.     

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.     

PLS and dimension reduction for classification

Barker and Rayens (J Chemometrics 17:166–173, 2003) offered convincing arguments that partial least squares (PLS) is to be preferred over principal components analysis (PCA) when discrimination is the goal and dimension reduction is required, since at least with PLS as the dimension reduction tool, information involving group separation is directly involved in the structure extraction. In this paper the basic results in Barker and Rayens (J Chemometrics 17:166–173, 2003) are reviewed and some of their ideas and comparisons are illustrated on a real data set, something which Barker and Rayens did not do. More importantly, new results are introduced, including a formal proof for the superiority of PLS over PCA in the two-group case, as well as new connections between PLS for discrimination and an extended class of PLS-like techniques known as “oriented PLS” (OrPLS). In the latter case, a particularly simple subclass of OrPLS procedures, when used to achieve the dimension reduction, is shown to always produce a lower misclassification rate than when “ordinary” PLS is used for the same purpose.