偏最小二乘路径建模与R语言实践

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"PLS_Path_Modeling_with_R.pdf - 偏最小二乘路径建模在R中的应用，由Gaston Sanchez撰写，并采用CCBY-NC-SA3.0许可协议，旨在非营利教学中分享和修改内容。" 偏最小二乘路径建模(PLS-Path Modeling)，也称为部分最小二乘路径建模（PLSPM），是一种统计分析方法，主要用于处理具有多重共线性和高维数据的复杂结构关系。这种方法特别适用于预测变量（X）的数量超过观测变量（Y）或X变量之间存在高度相关性的场景。在PLS中，目标是寻找X向量集的最佳线性组合，这些组合能够最大化解释Y向量集的方差，从而建立一个有效的预测模型。 R语言是一个广泛应用于统计计算和图形生成的开源环境，它提供了多种包来实现PLS建模，如`plsr`、`caret`和`semPLS`等。Gaston Sanchez的这本书《PLS Path Modeling with R》深入探讨了如何在R中进行PLS路径建模，包括概念解释、步骤演示以及实际应用案例。在PLS-Path Modeling中，模型通常被分解为两个主要步骤：成分（Component）提取和路径（Path）分析。首先，成分提取阶段通过最大化X和Y之间的相关性来寻找新空间的投影，这被称为因子得分。然后，在路径分析阶段，通过建立这些因子得分与因变量之间的结构方程来揭示变量间的因果关系。该书可能涵盖了以下内容： 1. PLS方法的基本原理和数学基础。 2. 如何在R中安装和使用相关包进行PLS建模。 3. 数据预处理的重要性，包括缺失值处理和标准化。 4. 如何选择合适的组件（Components）数量。 5. 模型验证技术，如交叉验证和预测能力评估。 6. 结果解释，包括因子载荷、路径系数和模型的统计显著性测试。 7. 案例研究，展示在不同领域的实际应用，如社会科学、市场营销和生物医学研究。 8. 如何处理非线性关系和非正态分布的数据。 9. 对比其他回归方法，如普通最小二乘法（OLS）和结构方程模型（SEM）。 Gaston Sanchez强调了学习编程和计算技能的重要性，这是他个人经验的反思，他认为这些技能对于现代科学研究至关重要，尤其是在数据驱动的决策环境中。这本书不仅是对PLS方法的全面介绍，还提供了实用的R代码示例，使得读者能够自行实现和理解PLS路径建模的过程。对于那些想要在R中应用PLS进行复杂数据建模的研究者来说，这本书是一个宝贵的资源。

Chapter 1

Introduction

This book provides a hands-on introduction to Partial Least Squares Path Modeling using

the R package plspm. Although there are a few texts that cover the theoretical aspects of

PLS Path Modeling (PLS-PM) with some applications to real data, there are virtually no

textbooks that teach how to use PLS Path Modeling and how to handle its broad range of

applications with the existing PLS-PM software. The goal of this book is to introduce you to

the world of PLS-PM using plspm and R through practical examples; teach you the basics

so that you can analyze your own data; and even turn you into a conﬁdent PLS-PM user

who can try out diﬀerent analysis options.

1.1 PLS Path Modeling

Let’s face it once and for all: Partial Least Squares Path Modeling is a name that does not

provide many clues about what it is or what it can do. Simply put, Partial Least Squares

Path Modeling is a statistical data analysis methodology that exists at the intersection of

Regression Models, Structural Equation Models, and Multiple Table Analysis methods. If

you were to review the extensive literature about PLS Path Modeling, chances are that you

would ﬁnd some variation of the following descriptions:

• PLS-PM is the Partial Least Squares approach to Structural Equation Modeling.

• PLS-PM is a statistical method for studying complex multivariate relationships among

observed and latent variables.

• PLS-PM is a data analysis approach for studying a set of blocks of observed variables

in which each block can be summarized by a latent variable and that linear relations

exist between latent variables.

The ﬁrst description above is the most common on PLS Path Modeling. In most cases, PLS

Path Modeling is usually referred to as the PLS approach to Structural Equation Modeling

(SEM). However, around the small but growing PLS community, the term Path Modeling

is preferred over Structural Equation Modeling, although both terms are often used inter-

changeably. My preferred description is the one that views PLS-PM from a broader con-

ceptual perspective for analyzing multiple relationships between blocks of variables. Under

this framework, we establish the relationships among the blocks by taking into account some

previous knowledge (e.g. theory) of the phenomenon under analysis. In addition, we assume

that each block of variables plays the role of a theoretical concept represented in the form of

a latent (unobserved) variable.

Personally, I try to avoid using the term SEM for two main reasons. The ﬁrst reason has to do

with the connotations behind Structural Equation Modeling where the dominating approach

is based on Covariance Structure Analysis (sometimes also referred to as LISREL). Because of

the overwhelming market share of LISREL, PLS-PM occupies a small niche within the SEM

community. For the same reason, CSA purists perceive PLS-PM as an awkward methodology

that distorts the SEM ideals (for the record, I have nothing against the CSA community and

the Lisrelites). The second reason has to do with the broad range of applications outside the

SEM spectrum that can be targeted with the ﬂexible PLS-PM standpoint.

Though I don’t use SEM often, I sometimes may use the term SEM-PLS because it helps

people to have some reference that allows them to get a better idea of the method. What I

prefer to use is the term PLS Path Modeling to give the methodology its own territory.

Yes, you can apply PLS for SEM applications, but there are also many other types of problems

that can be treated via PLS-PM that don’t ﬁt within the SEM framework.

The Network Analogy

It is not easy to explain PLS Path Modeling in simple terms to newcomers but I’ll give my

best shot. First, imagine that you have a network of variables. Usually, the connections in

the network are assumed to represent some cause-eﬀect process. But you can think of it as

a ﬂow chart where the process ﬂows in one direction (no loops allowed). Having deﬁned the

network, one of the goals is to quantify the connections or relationships among the variables.

The interesting part comes with the subtlety that each of the connected variables are obtained

by combining a set of other variables. Although this is the interesting part it is also the tricky

part, but the main idea to keep in mind is the network of connected variables. PLS Path

Modeling quantiﬁes the relationships by considering the network as a system of multiple

interconnected linear regressions. Still don’t get it? That’s why I wrote this book as my bold

yet humble attempt to help people not only understand Partial Least Squares Path Modeling

but also to show them how to apply it in R.

CC BY-NC-SA 3.0 Gaston Sanchez PLS Path Modeling with R

1.2 R package plspm

R is a free open source software for data analysis, statistical computing, and graphics. In

turn, plspm is an R package dedicated to Partial Least Squares Path Modeling analysis. The

plspm project timidly began in the fall of 2005 as part of my PhD work. One of the initial

goals was to create a package to estimate PLS path models in R. Almost four years later, the

ﬁrst R package for PLS-PM was created and the ﬁrst version was released on April, 2009.

Two months later, with the collaboration of Laura Trinchera, REBUS-PLS for detecting

classes was added to plspm. Since then, various features and new capabilities have been

implemented in the package, and its development continues every year.

There are a number of other softwares for PLS Path Modeling: perhaps the most well known

are SmartPLS (by Christian Ringle, Sven Wende and Alexander Will) and the PLSPM

module from XLSTAT (by Addinsoft). In addition, there’s also semPLS which is another R

package (by Armin Monecke).

One of the main diﬀerences of plspm to other PLS-PM software is the lack of a graphical

interface to draw path diagrams. This may be a surprise for readers that are used to working

with other programs in which you are able to deﬁne a model with a combination of mouse

clicks and dragging objects. While plspm might not be the optimal choice if what you’re

looking for is using a mouse to deﬁne the models, it does not mean that it is less advantegeous.

On the contrary, you will be surprised by how fast it is to deﬁne a model and run a PLS-PM

analysis with plspm. The other major diﬀerence is that you need to know a little bit about

R and feel comfortable typing commands. But this is precisely what makes plspm stronger

by taking full advantage of the data analysis options and programming capabilities of R.

1.2.1 Why R?

The main reason for choosing R is that it is an extremely powerful program for manipulat-

ing and analyzing data. R’s unstoppable popularity has made it the software for statistics

and analytics in many disciplines, and it is increasingly taught at many universities. The

second major reason for selecting R is that it’s platform independent —you can use it under

Windows, Mac or Unix— And is free. You don’t have to spend a cent in licenses, renew

contracts, negotiate upgrades, or pay for maintenance. Commercial software vendors may

provide support and oﬀer some type of guarantee, but that’s secondary. You just can’t beat

the price and functionality of R.

R is enriched by the fact that many people (me among them) from all over the world con-

tribute and share their own work in the form of packages for almost whatever method you

can think of. No other commercial software has that advantage of oﬀering the latest state-of-

the-art methods. Likewise, R has unrivaled help resources, both online and physical. There

are many online forums, email lists, interest groups, forums, blogs, and websites full of rich

CC BY-NC-SA 3.0 Gaston Sanchez PLS Path Modeling with R

information about R. In addition, many R books of excellent quality are increasingly pub-

lished every year. What I really value about R is that it is open source: you can see the guts

of the code. It’s not a black box, so you can actually see what’s behind the functions you

are using. In addition, being a free software, R has no rival for reaching the marginalized

academic places of the world. Just think about those students, professors and researchers

from developing countries that would be left further behind without resources such as R.

As the Spanish say, bueno, bonito y barato, which means “good, beautiful and inexpensive”,

Why use anything else?

1.3 About Partial Least Squares

You have probably heard the term Partial Least Squares a few times before reading this

book. If you are like me, those three words might be intimidating the ﬁrst time you hear

them. You are probably familiar with least squares, but what about the partial? Partial

Least Squares even sounds like a spell out of Harry Potter’s world.

So, what exactly is Partial Least Squares? Well, it depends on who you talk to. Perhaps the

most popular answer is to equate PLS as a regression analysis technique. This is too narrow

and somewhat misleading, especially because there are so many methods, techniques, and

algorithms that share this brand. It is true that PLS has to do with regression analysis but it

is much more than that. From the broadest point of view, PLS is a family —I would say a big

family— of data analysis methods. However, this is perhaps the main obstacle to deﬁning

what PLS is. These methods are designed for dealing with a wide range of data analysis

tasks such as exploration, visualization, explanation, prediction, classiﬁcation, and study of

structural systems. In its purest data analysis sense, PLS can be viewed as a set of methods

for analyzing multiple relationships between various blocks of variables (or tables of data).

If we consider a block of variables as a data table, the diﬀerence between the various PLS

methods depends on the number of tables and the type of relationships between variables.

The perception of PLS methods is not exempt of misconceptions, misunderstandings, and

misinterpretations. One initial obstacle has to do with the terminology and jargon: latent

structures, projections, component-based, soft modeling, scores, loadings, path coeﬃcients,

path diagrams, just to mention a few terms. There is also a widespread use of acronyms:

PLS, PLSR, PLSPM, NIPALS, and many more. However, once you have surpassed the

initial phase of adaptation, PLS methods open a new way of dealing with many statistical

problems. Think of PLS like a set of tools that you can use for diﬀerent purposes. Well

applied, PLS can be a very handy and useful set of tools. However, you have to keep in mind

that there is no single best approach to analyze data, and there is also no single method that

works for all problems. PLS is not the exception. In this sense, PLS data analysis is both

an art and a science that require not only mathematical principles, but it also requires some

intuition and skills that are developed over time with practice.

CC BY-NC-SA 3.0 Gaston Sanchez PLS Path Modeling with R

1.3.1 Short tale of PLS

I have dedicated an entire appendix at the end of the book to the historical overview of PLS

Path Modeling. However, let me oﬀer you a brief summary to start making things a bit

more clear. The development of PLS methods as we know them took place over a period

of approximately 20 years. Its origins can be traced back to the mid 1960s where the ﬁrst

PLS analytical tools were developed by Herman Wold at the Uppsala University, Sweden.

Throughout the 1970s, Wold’s team reﬁned and polished diﬀerent techniques that gave rise to

a series of methods more or less uniﬁed under a common umbrella: a set of approaches whose

estimation was based on iterative algorithms of least squares regressions. Brieﬂy, Herman

Wold and his group developed PLS as a multi-tool to handle diﬀerent types of problems that

could be solved by applying least squares. In other words, rather than a single technique,

the set of PLS methods was developed as a toolkit to tackle several data analysis problems

and solving them by applying a number of adapted least squares procedures.

In the 1980s, the evolution of the PLS methods experienced an interesting metamorphosis

led by Svante Wold (son of Herman Wold) with the application of the PLS principles to the

analysis of chemical data. Prior to this event, the application of PLS methods was focused on

economics and social sciences without really catching the attention of social researchers and

related practitioners. However, the application to chemical data opened an unexplored venue

for some of the PLS tools and were quickly accepted with great success. This developmental

branch took the shape of the techniques associated to what is known as PLS Regression.

Not all of the PLS tools shared the same luck as the PLS Regression techniques. During the

1990s, the less successful PLS Path Modeling (PLS-PM) approach remained in an almost

complete oblivion. Fortunately, PLS-PM was kept active by a handful of practitioners,

mainly in the USA, saving it from extinction. Then, in the late 1990s, PLS Path Modeling

caught the attention of a group of european statisticians and analysts under guidance of

Michel Tenenhaus. With an authentic curatorial task, they slowly repositioned the general

framework of PLS methods on the data analysis map.

In the last decade (2000-2010), the PLS analysis methods were subjected to a great eﬀort of

international diﬀusion which continues today. As a result, new proposals and developments

have been appearing in all the diﬀerent PLS areas. In addition, several programs and multiple

software have been released that allow users to apply the variety of PLS related methods.

This reﬂects their great modeling potential, versatility, and analytical capabilities.

1.3.2 Regressionists and Path-modelists

Nowadays, there are two main populations within the PLS world. PLS users can be roughly

separated in two populations, let me call them: the regressionists and the path-modelists.

The regressionists are comprised by users of PLS regression methods. The path-modelists

CC BY-NC-SA 3.0 Gaston Sanchez PLS Path Modeling with R

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偏最小二乘路径建模与R语言实践

PyPI 官网下载 | plspm-0.2.1.tar.gz

路径模型和PLSppt

基于内部非线性映射模型PLS算法的比较研究_宋斯男

解释每一句# 读取训练好的模型 import paddle from ppcls.modeling.architectures.se_resnet_vd import SE_ResNet50_vd model = SE_ResNet50_vd(class_dim=16) model.set_state_dict(paddle.load('./output/SE_ResNet50_vd/best_model/ppcls.pdparams'))

No module named 'paddlehub.module.modeling_ernie'

No module named 'transformers.modeling_bert'

Sybase.Modeling.NMap.Runtime

paddlenlp.transformers.xlnet.modeling.XLNetPretrainedModel 模块主要功能是什么，请代码展示

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