偏最小二乘通径模型在贸易发展指数中的应用

设计了一套3层综合指数所构成的中国对外贸易发展指数体系,利用偏最小二乘路径模型对中国1999—2009年的相关数据进行了计算和分析,对中国10余年来的贸易发展情况进行总体的把握和描述。经贸易发展指数运算表明,中国自加入WTO以来,对外贸易的贸易流量、贸易结构等各方面水平均有大幅度提高,但是从2009年开始,由于受到国际金融危机的影响,各方面的贸易指数出现下滑并快速反弹的趋势。     

Shrinkage Structure of Partial Least Squares

Partial least squares regression (PLS) is one method to estimate parameters in a linear model when predictor variables are nearly collinear. One way to characterize PLS is in terms of the scaling (shrinkage or expansion) along each eigenvector of the predictor correlation matrix. This characterization is useful in providing a link between PLS and other shrinkage estimators, such as principal components regression (PCR) and ridge regression (RR), thus facilitating a direct comparison of PLS with these methods. This paper gives a detailed analysis of the shrinkage structure of PLS, and several new results are presented regarding the nature and extent of shrinkage.     

Partial least squares estimator for single-index models

The partial least squares (PLS) approach first constructs new explanatory variables, known as factors (or components), which are linear combinations of available predictor variables. A small subset of these factors is then chosen and retained for prediction. We study the performance of PLS in estimating single-index models, especially when the predictor variables exhibit high collinearity. We show that PLS estimates are consistent up to a constant of proportionality. We present three simulation studies that compare the performance of PLS in estimating single-index models with that of sliced inverse regression (SIR). In the first two studies, we find that PLS performs better than SIR when collinearity exists. In the third study, we learn that PLS performs well even when there are multiple dependent variables, the link function is non-linear and the shape of the functional form is not known.     

[HDDA] sparse subspace constrained partial least squares

ABSTRACT

In this paper, we investigate the objective function and deflation process for sparse Partial Least Squares (PLS) regression with multiple components. While many have considered variations on the objective for sparse PLS, the deflation process for sparse PLS has not received as much attention. Our work highlights a flaw in the Statistically Inspired Modification of Partial Least Squares (SIMPLS) deflation method when applied in sparse PLS regression. We also consider the Nonlinear Iterative Partial Least Squares (NIPALS) deflation in sparse PLS regression. To remedy the flaw in the SIMPLS method, we propose a new sparse PLS method wherein the direction vectors are constrained to be sparse and lie in a chosen subspace. We give insight into this new PLS procedure and show through examples and simulation studies that the proposed technique can outperform alternative sparse PLS techniques in coefficient estimation. Moreover, our analysis reveals a simple renormalization step that can be used to improve the estimation of sparse PLS direction vectors generated using any convex relaxation method.     

Study of partial least squares and ridge regression methods

This article considers both Partial Least Squares (PLS) and Ridge Regression (RR) methods to combat multicollinearity problem. A simulation study has been conducted to compare their performances with respect to Ordinary Least Squares (OLS). With varying degrees of multicollinearity, it is found that both, PLS and RR, estimators produce significant reductions in the Mean Square Error (MSE) and Prediction Mean Square Error (PMSE) over OLS. However, from the simulation study it is evident that the RR performs better when the error variance is large and the PLS estimator achieves its best results when the model includes more variables. However, the advantage of the ridge regression method over PLS is that it can provide the 95% confidence interval for the regression coefficients while PLS cannot.     

Partial Least Squares: A First-order Analysis

We compare the partial least squares (PLS) and the principal component analysis (PCA), in a general case in which the existence of a true linear regression is not assumed. We prove under mild conditions that PLS and PCA are equivalent, to within a first-order approximation, hence providing a theoretical explanation for empirical findings reported by other researchers. Next, we assume the existence of a true linear regression equation and obtain asymptotic formulas for the bias and variance of the PLS parameter estimator     

Robustness of partial least-squares method for estimating latent variable quality structures

Latent variable structural models and the partial least-squares (PLS) estimation procedure have found increased interest since being used in the context of customer satisfaction measurement. The well-known property that the estimates of the inner structure model are inconsistent implies biased estimates for finite sample sizes. A simplified version of the structural model that is used for the Swedish Customer Satisfaction Index (SCSI) system has been used to generate simulated data and to study the PLS algorithm in the presence of three inadequacies: (i) skew instead of symmetric distributions for manifest variables; (ii) multi-collinearity within blocks of manifest and between latent variables; and (iii) misspecification of the structural model (omission of regressors). The simulation results show that the PLS method is quite robust against these inadequacies. The bias that is caused by the inconsistency of PLS estimates is substantially increased only for extremely skewed distributions and for the erroneous omission of a highly relevant latent regressor variable. The estimated scores of the latent variables are always in very good agreement with the true values and seem to be unaffected by the inadequacies under investigation.     

Treatments of non-metric variables in partial least squares and principal component analysis

This paper reviews various treatments of non-metric variables in partial least squares (PLS) and principal component analysis (PCA) algorithms. The performance of different treatments is compared in an extensive simulation study under several typical data generating processes and associated recommendations are made. Moreover, we find that PLS-based methods are to prefer in practice, since, independent of the data generating process, PLS performs either as good as PCA or significantly outperforms it. As an application of PLS and PCA algorithms with non-metric variables we consider construction of a wealth index to predict household expenditures. Consistent with our simulation study, we find that a PLS-based wealth index with dummy coding outperforms PCA-based ones.     

Partial least squares Cox regression for genome-wide data

Most methods for survival prediction from high-dimensional genomic data combine the Cox proportional hazards model with some technique of dimension reduction, such as partial least squares regression (PLS). Applying PLS to the Cox model is not entirely straightforward, and multiple approaches have been proposed. The method of Park et al. (Bioinformatics 18(Suppl. 1):S120–S127, 2002) uses a reformulation of the Cox likelihood to a Poisson type likelihood, thereby enabling estimation by iteratively reweighted partial least squares for generalized linear models. We propose a modification of the method of park et al. (2002) such that estimates of the baseline hazard and the gene effects are obtained in separate steps. The resulting method has several advantages over the method of park et al. (2002) and other existing Cox PLS approaches, as it allows for estimation of survival probabilities for new patients, enables a less memory-demanding estimation procedure, and allows for incorporation of lower-dimensional non-genomic variables like disease grade and tumor thickness. We also propose to combine our Cox PLS method with an initial gene selection step in which genes are ordered by their Cox score and only the highest-ranking k% of the genes are retained, obtaining a so-called supervised partial least squares regression method. In simulations, both the unsupervised and the supervised version outperform other Cox PLS methods.     

A comparison of various methods for multivariate regression with highly collinear variables

Regression tends to give very unstable and unreliable regression weights when predictors are highly collinear. Several methods have been proposed to counter this problem. A subset of these do so by finding components that summarize the information in the predictors and the criterion variables. The present paper compares six such methods (two of which are almost completely new) to ordinary regression: Partial least Squares (PLS), Principal Component regression (PCR), Principle covariates regression, reduced rank regression, and two variants of what is called power regression. The comparison is mainly done by means of a series of simulation studies, in which data are constructed in various ways, with different degrees of collinearity and noise, and the methods are compared in terms of their capability of recovering the population regression weights, as well as their prediction quality for the complete population. It turns out that recovery of regression weights in situations with collinearity is often very poor by all methods, unless the regression weights lie in the subspace spanning the first few principal components of the predictor variables. In those cases, typically PLS and PCR give the best recoveries of regression weights. The picture is inconclusive, however, because, especially in the study with more real life like simulated data, PLS and PCR gave the poorest recoveries of regression weights in conditions with relatively low noise and collinearity. It seems that PLS and PCR are particularly indicated in cases with much collinearity, whereas in other cases it is better to use ordinary regression. As far as prediction is concerned: Prediction suffers far less from collinearity than recovery of the regression weights.     

The construction of a partial least-squares biplot

Biplots are useful tools to explore the relationship among variables. In this paper, the specific regression relationship between a set of predictors X and set of response variables Y by means of partial least-squares (PLS) regression is represented. The PLS biplot provides a single graphical representation of the samples together with the predictor and response variables, as well as their interrelationships in terms of the matrix of regression coefficients.     

Implementing partial least squares

Partial least squares (PLS) regression has been proposed as an alternative regression technique to more traditional approaches such as principal components regression and ridge regression. A number of algorithms have appeared in the literature which have been shown to be equivalent. Someone wishing to implement PLS regression in a programming language or within a statistical package must choose which algorithm to use. We investigate the implementation of univariate PLS algorithms within FORTRAN and the Matlab (1993) and Splus (1992) environments, comparing theoretical measures of execution speed based on flop counts with their observed execution times. We also comment on the ease with which the algorithms may be implemented in the different environments. Finally, we investigate the merits of using the orthogonal invariance of PLS regression to improve the algorithms.     

Modified Wynn's Sequential Algorithm for Constructing D-Optimal Designs: Adding Two Points at a Time

Partial least squares (PLS) is a class of methods for modeling relations between sets of observed variables by using the latent components where the predictors are highly collinear. SIMPLS is a commonly used PLS algorithm that calculates the latent components directly as linear combinations of the original variables. However, SIMPLS is known to be very sensible to outliers since it is based on the empirical cross-covariance matrix. RoPLS is a recently proposed iterative method for robust SIMPLS. In this article, the influence function for the RoPLS coefficient estimator is derived. It is demonstrated that under certain conditions, the RoPLS estimator has infinitesimal robustness.     

基于偏最小二乘回归分析的农民收入影响因素研究

文章运用偏最小二乘(PLS)回归方法,分析了转轨以来影响农民增收的12个因素。研究表明,城市化率、农村工业化程度、农户受教育程度以及劳务经济对农民增收作用最为明显。基于以上分析结论,本文认为,加快城市化进程、大力发展乡镇企业以及提高农民文化素质是增加农民收入的根本途径。     

Covariate adjustment in partial least squares (PLS) regression for the extraction of the spatial–temporal pattern from positron emission tomography data

Positron emission tomography (PET) imaging can be used to study the effects of pharmacologic intervention on brain function. Partial least squares (PLS) regression is a standard tool that can be applied to characterize such effects throughout the brain volume and across time. We have extended the PLS regression methodology to adjust for covariate effects that may influence spatial and temporal aspects of the functional image data over the brain volume. The extension involves multi-dimensional latent variables, experimental design variables based upon sequential PET scanning, and covariates. An illustration is provided using a sequential PET data set acquired to study the effect of d-amphetamine on cerebral blood flow in baboons. An iterative algorithm is developed and implemented and validation results are provided through computer simulation studies.     

The additive hazards model with high-dimensional regressors

This paper considers estimation and prediction in the Aalen additive hazards model in the case where the covariate vector is high-dimensional such as gene expression measurements. Some form of dimension reduction of the covariate space is needed to obtain useful statistical analyses. We study the partial least squares regression method. It turns out that it is naturally adapted to this setting via the so-called Krylov sequence. The resulting PLS estimator is shown to be consistent provided that the number of terms included is taken to be equal to the number of relevant components in the regression model. A standard PLS algorithm can also be constructed, but it turns out that the resulting predictor can only be related to the original covariates via time-dependent coefficients. The methods are applied to a breast cancer data set with gene expression recordings and to the well known primary biliary cirrhosis clinical data.     

Comparison of prediction methods for multicollinear data

In this paper we discuss the partial least squares (PLS) prediction method. The method is compared to the predictor based on principal component regression (PCR). Both theoretical considerations and computations on artificial and real data are presented.     

Treating unobserved heterogeneity in PLS path modeling: a comparison of FIMIX-PLS with different data analysis strategies

In the social science disciplines, the assumption that the data stem from a single homogeneous population is often unrealistic in respect of empirical research. When applying a causal modeling approach, such as partial least squares path modeling, segmentation is a key issue in coping with the problem of heterogeneity in the estimated cause–effect relationships. This article uses the novel finite-mixture partial least squares (FIMIX-PLS) method to uncover unobserved heterogeneity in a complex path modeling example in the field of marketing. An evaluation of the results includes a comparison with the outcomes of several data analysis strategies based on a priori information or k-means cluster analysis. The results of this article underpin the effectiveness and the advantageous capabilities of FIMIX-PLS in general PLS path model set-ups by means of empirical data and formative as well as reflective measurement models. Consequently, this research substantiates the general applicability of FIMIX-PLS to path modeling as a standard means of evaluating PLS results by addressing the problem of unobserved heterogeneity.