Minimum Sample Size Estimation in PLS-SEM: The Inverse Square Root and Gamma-Exponential Methods

Jul 3, 2026

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Partial least squares-based structural equation modelling (PLS-SEM) is widely used in information systems and other multivariate settings. A key problem in PLS-SEM is estimating the minimum required sample size. While the simple “10-times rule” is popular, it can produce imprecise results. Two equation-based alternatives are proposed: the inverse square root method and the gamma-exponential method. Monte Carlo simulations show both approaches are fairly accurate, with the inverse square root method especially straightforward to apply.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages35

Reading Time1 h 28 min

AccessFree to download

Introduction

Minimum sample size estimation in PLS-SEM

Proposed methods

Inverse square root method

Gamma-exponential method

Heuristic use in research design

Illustrative IS study: MBLC

doi: 10.1111/isj.12131 Info Systems J (2016) Minimum sample size estimation in PLS-SEM: The inverse square root and gamma-exponential methods Ned Kock* & Pierre Hadaya† *Division of International Business and Technology Studies, Texas A&M International University, 5201 University Boulevard, Laredo, TX 78041, USA, email: [nedkock@tamiu.com](nedkock@tamiu.com) , and †Department of Management and Technology, École des Sciences de la Gestion, Université du Québec à Montréal, PO Box 8888, Downtown Station, Montreal, Quebec H3C 3P8, Canada Abstract. Partial least squares-based structural equation modelling (PLS-SEM) is extensively used in the ﬁeld of information systems, as well as in many other ﬁelds where multivariate statistical methods are used. One of the most fundamental issues in PLS-SEM is that of minimum sample size estimation. The ‘ 10-times rule ’has been a favourite because of its simplicity of application, even though it tends to yield imprecise estimates. We propose two related methods, based on mathematical equations, as alternatives for minimum sample size estimation in PLS-SEM: the inverse square root method, and the gamma-exponential method. Based on three Monte Carlo experiments, we demonstrate that both methods are fairly accurate. The inverse square root method is particularly attractive in terms of its simplicity of application. © 2016 John Wiley & Sons Ltd Keywords: information systems, partial least squares, structural equation modelling, statistical power, Monte Carlo simulation INTRODUCTION The ﬁeld of information systems (IS) is closely linked with the development, software implementation and use of the partial least squares (PLS) technique (Chin, 1998; Chin et al. , 2003; Kock, 2010; Wold, 1980) . This technique has been extensively used in IS (Bradley et al. , 2012; Goodhue et al. , 2012), a practice that has extended to other ﬁelds over the years, to analyse path models with variables that are measured indirectly through other variables (Chin, 1998; Hair et al. , 2011; 2014; Lohmöller, 1989) . These indirectly measured variables are generally known as latent variables (Kline, 1998; Kock & Lynn, 2012) . The approach to analysing path models with latent variables is broadly known as structural equation modelling (SEM) . Thus, the acronym ‘PLS-SEM’ is used here to refer to SEM using PLS. © 2016 John Wiley & Sons Ltd N Kock & P Hadaya One of the most fundamental issues in PLS-SEM is that of minimum sample size estimation. A widely used minimum sample size estimation method in PLS-SEM is the ‘ 10-times rule’method (Hair et al., 2011), which builds on the assumption that the sample size should be greater than 10 times the maximum number of inner or outer model links pointing at any latent variable in the model. While this method’s simplicity of application makes it a favourite among PLS-SEM users, it has been shown in the past to lead to inaccurate estimates (Goodhue et al. , 2012) . We propose two related methods, based on mathematical equations, for minimum sample size estimation in PLS-SEM. The ﬁrst method is called the inverse square root method, because it uses the inverse square root of a sample’s size for standard error estimation – an important step in minimum sample size estimation. The second method is called the gamma-exponential method, because it relies on gamma and exponential smoothing function corrections applied to the ﬁrst method. Based on Monte Carlo experiments, we show that both methods are fairly accurate, with the ﬁrst method being also particularly attractive in terms of its simplicity of application. The methods we propose here should be seen as heuristic methods; that is, as practical methods that are not guaranteed to yield optimal estimates. We believe that they are valuable time-saving tools to be used in the early cyclical phases of research design, and that can be signiﬁcantly more precise than comparable early-stage research heuristics currently used b

FAQs

What is the main issue addressed in the paper about PLS-SEM?

The paper focuses on minimum sample size estimation in PLS-SEM, an essential yet difficult design problem.

Why is the “10-times rule” criticized?

Although easy to apply, prior work shows it can lead to inaccurate or imprecise minimum sample size estimates.

What are the two proposed minimum sample size estimation methods?

The paper proposes the inverse square root method and the gamma-exponential method, both based on mathematical equations and validated through Monte Carlo experiments.

Jul 3, 2026

131

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