Introduction to Partial Least Square: Common Criteria and Practical ...

Advanced Materials Research Vols. 779-780 (2013) pp 1766-1769 © (2013) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.779-780.1766

Introduction to Partial Least Square: Common Criteria and Practical Considerations Ke-Hwa Lee1,a, Shih-Chih Chen2,b,* 1

School of Economics and Management, Beijing Jiaotong University, Beijing, China 2 a

Southern Taiwan University of Science and Technology, Taiwan

[email protected], b [email protected] (Corresponding author) * Corresponding author

Keywords: Partial Least Square (PLS), Structural Equation Modeling (SEM), Covariance-based Structural Equation Modeling (CBSEM)

Abstract. In the social science research area, there are two important statistical methodologies, one is covariance-based structural equation modeling (CBSEM), and the other one is variance-based partial least square (PLS). Compared with CBSEM, PLS lacks comparatively the reference books and full applications. The main purpose of this study is to develop a paradigm to demonstrate how to assess the reliability, convergent validity, discriminant validity, and path analysis in a proposed research model by using Smart PLS. We hope this study’s result can offer some correct steps when using PLS. Introduction In the social science research area, there are two important statistical methodologies, one is covariance-based structural equation modeling (CBSEM), and the other one is variance-based partial least square (PLS). Compared with CBSEM, PLS lacks comparatively the reference books and full applications. According the research results of Urbach & Ahlemann (2010) [1], the amount of publications in Management Information System Quarterly (MISQ) and Information System Research (ISR) which using CBSEM is more than PLS before 1997. However, the amount publications of PLS is more than CBSEM after 1999 (as shown in Figure 1 and Figure 2). The main purpose of this study is to develop a paradigm to demonstrate how to assess the reliability, convergent validity, discriminant validity, and path analysis in a proposed research model by using Smart PLS. We hope this study’s result can offer some correct steps when using PLS. Common Criteria of the Outer Model Generally, the data analysis of PLS was conducted using SmartPLS or PLS-Graph, and followed the two-stage approach for assessing the outer model and the inner model respectively. According the suggestions of Urbach & Ahlemann (2010) [1], this study rearranged the important criteria and processes to estimate the outer and inner model. The first stage, the outer model, likely the functions of measurement model in CBSEM, is often used to assess the reliability and construct validity of measurement items. There are four common criteria to assess the outer model as following:

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(1) Unidimensionality: We can adopt Exploratory Factor Analysis (EFA) with Eigenvalue to understand whether only one dimension in multi-construct empirical studies. (2) Reliability: Reliability mainly is used to assess the internal consistency in a construct and there are two common indexes to fit including Composite Reliability and Cronbach’s Alpha. (3) Convergent validity: It often used to measure the correlation of a dimension’s multiple indicators. convergent validity is acceptable if the following criteria are met [2,3]: (i) the statistical significance of each factor loading is confirmed by a p-value of 0.5, (ii) construct reliability exceeds 0.7, and (iii) average variance extracted (AVE) is greater than 0.5. (4) Discriminant validity: It is often assessed by a construct and its indicators distinct from another construct and its indicators in the outer model. Common Criteria of the Inner Model The second stage, the inner model, likely the functions of structural model in CBSEM, is often used to assess the Goodness-of-fit and research hypotheses in the proposed research framework. According the suggestions of Urbach & Ahlemann (2010) [1], there are five common criteria to assess the outer model as following: (1) Coefficient of determination (R-Square, R2): It is an index to measure each endogenous latent variable’s R-Square. Chin (1998b) [4] suggested that the explanatory power is considered substantial, moderate, and weak if R-square is approximately around 0.67, 0.33 and 0.19 respectively. (2) Global goodness-of-fit (GoF): GoF is an index for the outer and inner model to confirm that the model adequately explains the empirical data (

).

(3) Path coefficient: Observing the direction and significance of path coefficient can understand the research hypotheses whether supported or not in the research proposed model. This test can use a bootstrap procedure in SmartPLS. (4) Effect size (f2): The researcher can evaluate the effect size of each path in the structural equation model by means of f2proposed by Cohen (1988) [5]. (5) Predictive relevance: Q2 as the statistic to examine predictive relevance of inner model that can be evaluated by a nonparametric Stone-Geisser test [6, 7]. This index can apply the blindfolding procedure in SmartPLS. Q2can be applied to examine the extent to which this prediction is successful or not. Discussion & Conclusion The concept of PLS was firstly proposed by Wold (1975) [8] under the name NIPALS (nonlinear iterative partial least squares). In recent years, there are several implementation tools of PLS including SmartPLS, PLS-Graph, Visual PLS, PLS-GUI, LISREL and so on. Like most empirical research of SEM, a PLS model consists of a structural part, which reflects the relationships between the latent constructs, and a measurement indicator, which shows how the latent constructs and their indicators are related; but it also has a third component, the weight relations, which are used to estimate case values for the latent constructs [9, 10].

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Materials, Transportation and Environmental Engineering

When the statistical techniques go ahead, researchers can choose more tools for their data analysis, but the misusing probability of statistical methods is becoming higher. Researchers should understand thoughtfully the advantages and weakness of different innovatively statistical techniques and methods. Therefore, this study mainly proposed and arranged a two-stage approach for PLS, and made a paradigm for PLS applications. We hope this study can fascinate more researchers to develop and revise the PLS approach. In fact, PLS is already applied in many different areas. By research results of this study, we hope more and more breakthrough for improving PLS approach.

Fig. 1: Distribution of research using PLS (Urbach & Ahlemann, 2010) [1]

Fig. 2: Percentage of studies using PLS and CBSEM (Urbach & Ahlemann, 2010) [1]

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Reference [1] N. Urbach and F. Ahlemann (2010). Structural equation modeling in information systems research using partial least squares. Journal of Information Technology Theory and Application, Vol. 11, No. 2, pp. 5-40. [2] J. F. Jr. Hair, W.C. Black, B.J. Babin and R.E. Anderson (2010). Multivariate data analysis: A global perspective (7th ed.). Pearson Education International. [3] C.D. Fornell and F. Larcker (1981). Evaluating structural equation models with unobservable variables and measurement errors. Journal of Marketing Research, Vol. 18, No. 1, pp. 39-50. [4] W.W. Chin (1998). Issues and opinion on structural equation modeling. MIS Quarterly, Vol. 22, No. 1, pp. vii–xvi. [5] J. Cohen (1988). Statistical Power Analysis for the Behavioral Sciences. Hillsdale, NJ: Lawrence Erlbaum Associates. [6] S. Geisser (1975). The predictive sample reuse method with applications. Journal of the American Statistical Association, Vol. 70, pp. 320-328. [7] M. Stone (1974). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, Vol. 36, No. 2, pp.111-133. [8] H. Wold (1975). Path models with latent variables: The NIPALS Approach. In H. M. Blalock, A. Aganbegian, F. M. Borodkin, R. Boudon, V. Capecchi (Ed.s), Quantitative Sociology (pp. 307-359), New York: Academic Press. [9] W.W. Chin and P.R. Newsted (1999). Structural equation modelling analysis with small samples using partial least squares. In R. H. Hoyle (Ed.), Statistical strategies for small sample research (pp. 307-341). Thousand Oaks, CA: Sage. [10] M. Haenlein and A. Kaplan (2004). A beginner’s guide to partial least squares analysis. Understanding Statistics, Vol. 3, No. 4, pp. 283-297.