When to use and how to report the results of PLS-SEM

Joseph F. Hair
Department of Marketing and Quantitative Methods, University of South Alabama, Mobile, Alabama, USA

Jeffrey J. Risher
Department of Marketing, Supply Chain Logistics and Economics, University of West Florida College of Business, Pensacola, Florida, USA and Department of Business, University of Mobile, Mobile, Alabama, USA

Marko Sarstedt
Faculty of Economics and Management, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany and Monash University of Malaysia, Bandar Sunway, Malaysia, and

Christian M. Ringle
Institute of Human Resource Management and Organizations, Hamburg University of Technology (TUHH), Hamburg, Germany and the University of Waikato, Hamilton, New Zealand

Abstract

Purpose – The purpose of this paper is to provide a comprehensive, yet concise, overview of the considerations and metrics required for partial least squares structural equation modeling (PLS-SEM) analysis and result reporting. Preliminary considerations are summarized first, including reasons for choosing PLS-SEM, recommended sample size in selected contexts, distributional assumptions, use of secondary data, statistical power and the need for goodness-of-fit testing.

Next, the metrics as well as the rules of thumb that should be applied to assess the PLS-SEM results are covered. Besides presenting established PLS-SEM evaluation criteria, the overview includes the following new guidelines: PLSpredict (i.e., a novel approach for assessing a model’s out-of-sample prediction), metrics for model comparisons, and several complementary methods for checking the results’ robustness.

Design/methodology/approach – This paper provides an overview of previously and recently proposed metrics as well as rules of thumb for evaluating the research results based on the application of PLS-SEM.

Findings – Most of the previously applied metrics for evaluating PLS-SEM results are still relevant. Nevertheless, scholars need to be knowledgeable about recently proposed metrics (e.g. model comparison criteria) and methods (e.g. endogeneity assessment, latent class analysis and PLSpredict), and when and how to apply them to extend their analyses.

Research limitations/implications – Methodological developments associated with PLS-SEM are rapidly emerging. The metrics reported in this paper are useful for current applications, but must always be up to date with the latest developments in the PLS-SEM method. Originality/value – In light of more recent research and methodological developments in the PLS-SEM domain, guidelines for the method’s use need to be continuously extended and updated. This paper is the most current and comprehensive summary of the PLS-SEM method and the metrics applied to assess its solutions.

目的—本文的目的是對偏最小二乘結構方程式建模 (PLS-SEM) 分析和結果報告所需的考慮和指標提供全面而簡潔的概述。 首先總結了初步考慮因素，包括選擇 PLS-SEM 的原因、選定背景下建議的樣本量、分佈假設、二手數據的使用、統計功效以及擬合優度檢定的需要。
接下來，介紹了用於評估 PLS-SEM 結果的指標和經驗法則。 穩健性.
設計/方法/應用—本文概述了先前和最近提出的指標以及基於 PLS-SEM 應用評估研究結果的經驗法則。
研究結果 – 大多數先前應用的用於評估 PLS-SEM 結果的指標仍然相關。 然而，學者需要了解最近提出的指標（例如模型比較標準）和方法（例如內生性評估、潛在類別分析和 PLS 預測），以及何時以及如何應用它們來擴展他們的分析。
研究局限性/影響——與 PLS-SEM 相關的方法發展正在迅速出現。 本文報告的指標對於目前應用很有用，但必須始終與 PLS-SEM 方法的最新發展保持同步。 原創性/價值—鑑於 PLS-SEM 領域的最新研究和方法學發展，該方法的使用指南需要不斷擴展和更新。 本文是 PLS-SEM 方法以及用於評估其解決方案的指標的最新、最全面的總結。

Keywords

Structural equation modeling, Partial least squares, PLS-SEM, Model comparisons,

Paper type

General review

Even though this article does not use the statistical software SmartPLS (www.smartpls.com), Ringle acknowledges a financial interest in SmartPLS.

Introduction

For many years, covariance-based structural equation modeling (CB-SEM) was the dominant method for analyzing complex interrelationships between observed and latent variables. In fact, until around 2010, there were far more articles published in social science journals that used CB- SEM instead of partial least squares structural equation modeling (PLS-SEM). In recent years, the number of published articles using PLS-SEM increased significantly relative to CB-SEM (Hair et al., 2017b). In fact, PLS-SEM is now widely applied in many social science disciplines, including organizational management (Sosik et al., 2009), international management (Richter et al., 2015), human resource management (Ringle et al., 2019), management information systems (Ringle et al., 2012), operations management (Peng and Lai, 2012), marketing management (Hair et al., 2012b), management accounting (Nitzl, 2016), strategic management (Hair et al., 2012a), hospitality management (Ali et al., 2018b) and supply chain management (Kaufmann and Gaeckler, 2015). Several textbooks (e.g., Garson, 2016; Ramayah et al., 2016), edited volumes (e.g., Avkiran and Ringle, 2018; Ali et al., 2018a), and special issues of scholarly journals (e.g., Rasoolimanesh and Ali, 2018; Shiau et al., 2019) illustrate PLS-SEM or propose methodological extensions.

The PLS-SEM method is very appealing to many researchers as it enables them to estimate complex models with many constructs, indicator variables and structural paths without imposing distributional assumptions on the data. More importantly, however, PLS-SEM is a causal-predictive approach to SEM that emphasizes prediction in estimating statistical models, whose structures are designed to provide causal explanations (Wold, 1982; Sarstedt et al., 2017a). The technique thereby overcomes the apparent dichotomy between explanation – as typically emphasized in academic research – and prediction, which is the basis for developing managerial implications (Hair et al., 2019). Additionally, user-friendly software packages are available that generally require little technical knowledge about the method, such as PLS-Graph (Chin, 2003) and SmartPLS (Ringle et al., 2015; Ringle et al., 2005), while more complex packages for statistical computing software environments, such as R, can also execute PLS-SEM (e.g. semPLS; Monecke and Leisch, 2012). Authors such as Richter et al. (2016), Rigdon (2016) and Sarstedt et al. (2017a) provide more detailed arguments and discussions on when to use and not to use PLS-SEM.

結構方程模型（Structural Equation Modeling, SEM）是一種統計技術，用於檢驗和估計複雜的因果關係。SEM主要分為兩種方法：共變異數結構方程模型（Covariance-Based SEM, CB-SEM）和部分最小平方法結構方程模型（Partial Least Squares SEM, PLS-SEM）。這兩種方法有其各自的特點和適用範圍，以下是它們的異同之處：
共變異數結構方程模型（CB-SEM） 部分最小平方法結構方程模型（PLS-SEM）
目的：
- 主要用於驗證理論模型的適配度，即評估模型與數據的吻合程度。
- 假設資料符合多變量正態分佈。
數據要求：
- 需較大的樣本量，一般建議至少200個以上。
- 資料需符合正態分佈，且變量之間的關係是線性的。
模型適配度：
- 使用多種適配度指標來評估模型的整體適配度（如CFI, TLI, RMSEA, SRMR等）。
變數：
-適合處理反映性（Reflective）測量模型，即觀測變數是由潛在變數引起的。
 目的：
- 主要用於預測和探索性研究，更關注於解釋變量之間的變異。
- 不需要資料符合特定的分佈假設。
數據要求：
- 可處理較小的樣本量（小於200）。
- 對資料的分佈假設較少，可以處理非正態分佈和複雜的變量結構。
模型適配度：
- PLS-SEM主要關注於解釋變量的變異和預測力，適配度指標不像CB-SEM那樣嚴格。
變數：
- 適合處理反映性（Reflective）和形式性（Formative）測量模型，形式性模型是指觀測變數共同構成潛在變數。
異同點總結
相同點：
1.都屬於結構方程模型，旨在分析變數之間的複雜關係。
2.都可以用於處理多變量數據，並且能處理潛在變數和觀測變數之間的關係。
不同點：
1.CB-SEM強調模型的適配度和理論驗證，適合大樣本量和正態分佈資料；而PLS-SEM更強調預測能力和解釋力，適合小樣本量和非正態分佈資料。
2.CB-SEM適用於反映性測量模型，而PLS-SEM適用於反映性和形式性測量模型。
- 總的來說，選擇使用CB-SEM還是PLS-SEM應根據研究目標、數據特性和樣本量來決定。

The objective of this paper is to explain the procedures and metrics that are applied by editors and journal review boards to assess the reporting quality of PLS-SEM findings. We first summarize several initial considerations when choosing to use PLS-SEM and cover aspects such as sample sizes, distributional assumptions and goodness-of-fit testing. Then, we discuss model evaluation, including rules of thumb and introduce important advanced options that can be used. Our discussion also covers PLSpredict, a new method for assessing a model’s out-of-sample predictive power (Shmueli et al., 2016; Shmueli et al., 2019), which researchers should routinely apply, especially when drawing conclusions that affect business practices and have managerial implications. Next, we introduce several complementary methods for assessing the results’ robustness when it comes to measurement model specification, nonlinear structural model effects, endogeneity and unobserved heterogeneity (Hair et al., 2018; Latan, 2018). Figure 1 illustrates the various aspects that we discuss in the following sections.

Figure 1.
Aspects and statistics to consider in a PLS- SEM analysis

Preliminary considerations

The Swedish econometrician Herman O. A. Wold (1975, 1982, 1985) developed the statistical underpinnings of PLS-SEM. The method was initially known and is sometimes still referred to as PLS path modeling (Hair et al., 2011). PLS-SEM estimates partial model structures by combining principal components analysis with ordinary least squares regressions (Mateos- Aparicio, 2011). This method is typically viewed as an alternative to Jöreskog’s (1973) CB-SEM, which has numerous – typically very restrictive – assumptions (Hair et al., 2011).

Jöreskog’s (1973) CB-SEM, which is often executed by software packages such as LISREL or AMOS, uses the covariance matrix of the data and estimates the model parameters by only considering common variance. In contrast, PLS-SEM is referred to as variance-based, as it accounts for the total variance and uses the total variance to estimate parameters (Hair et al., 2017b).

In the past decade, there has been a considerable debate about which situations are more or less appropriate for using PLS-SEM (Goodhue et al., 2012; Marcoulides et al., 2012; Marcoulides and Saunders, 2006; Rigdon, 2014a; Henseler et al., 2014; Khan et al., 2019). In the following sections, we summarize several initial considerations when to use PLS-SEM (Hair et al., 2013). Furthermore, we compare the differences between CB-SEM and PLS-SEM (Marcoulides and Chin, 2013; Rigdon, 2016). In doing so, we note that recent research has moved beyond the CB-SEM versus PLS-SEM debate (Rigdon et al., 2017; Rigdon, 2012), by establishing PLS-SEM as a distinct method for analyzing composite-based path models.

Nevertheless, applied research is still confronted with the choice between the two SEM methods. Researchers should select PLS-SEM:

! when the analysis is concerned with testing a theoretical framework from a prediction perspective;
! when the structural model is complex and includes many constructs, indicators and/ or model relationships;
! when the research objective is to better understand increasing complexity by exploring theoretical extensions of established theories (exploratory research for theory development);
! when the path model includes one or more formatively measured constructs; ! when the research consists of financial ratios or similar types of data artifacts;
! when the research is based on secondary/archival data, which may lack a comprehensive substantiation on the grounds of measurement theory;
! when a small population restricts the sample size (e.g. business-to-business research); but PLS-SEM also works very well with large sample sizes;
! when distribution issues are a concern, such as lack of normality; and
! when research requires latent variable scores for follow-up analyses.

The above list provides an overview of points to consider when deciding whether PLS is an appropriate SEM method for a study.


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