The Use and Misuse of Structural Equation Modeling (SEM) in Social Science Researches Prof. Dr Zainudin Awang Faculty of Economics and Management Sciences University Sultan Zainal Abidin (UniSZA) 21300 Kuala Terengganu, Terengganu 09-6688267/019-9595700

The Coverage of Presentation 1.What Is Structural Equation Modeling (SEM)?? 2.Types of SEM (Difference between SEM and PLS-SEM) 3.The Use of SEM and PLS-SEM 4.The Misuse of SEM: Violating the Required Parametric Assumptions (Independently, Identically, Normally Distributed data) Mistakes – Using Wrong Data Scales, Wrong Sampling Method, Heterogeneous Target Population, Biased Sampling (Non Probability) Problems – Data Not Normally Distributed, CFA Procedure Failed, Items Redundancy, Constructs Redundancy, Fitness Indexes Not Achieved Solution to all mistakes – Use PLS-SEM (The Misuse of SEM) 5. Q & A

What Is Structural Equation Modeling?? SEM is among the most advanced statistical analysis techniques that emerged in recent decades (Hair et al., 2013) SEM is a class of multivariate techniques that combine aspects of factor analysis and regression, enabling the researchers to simultaneously examine relationships among latent constructs. Considering the importance of analyzing latent constructs such as Consumer Perceptions, Attitudes, or Intentions and their influence on Organizational Performance measures (stock market price, profit, turnover, market share), SEM is one of the most prominent statistical analysis techniques today (Hair et al., 2013)

The SEM is a powerful statistical method to solve the following analyses: To analyse the model with latent constructs To run the Confirmatory Factor Analysis (CFA) To analyse multiple equations simultaneously To analyse regressions with multi-collinearity problems To analyze the path analysis with multiple dependents To estimate the correlation and covariance in a model To model inter-relationships simultaneously in a model To model and test the mediating variables in a model To analyse and test the moderating variables in a model

Types of Structural Equation Modeling: There are two approaches to estimate the relationships in a structural equation models namely PLS-SEM and SEM (Hair et al., 2010; Hair et al., 2011; Hair et al., 2012a; Hair et al., 2013) Each is appropriate for a different research objective, and researchers need to understand in order to apply the correct method Researchers should focus on the characteristics and objectives that distinguish the two methods In situations where theory is less developed, researchers should consider the use of PLS-SEM as an alternative to SEM. Once PLS-SEM is employed, the study is considered exploratory The estimation procedure in PLS-SEM is OLS (Ordinary Least Squares) regression-based method rather than the MLE (Maximum Likelihood Estimates) for SEM

HISTORY OF MULTIVARIATE ANALYSIS METHOD Type of Statistical Analysis SEM or PLS-SEM?? HISTORY OF MULTIVARIATE ANALYSIS METHOD Time Period Type of Statistical Analysis   1st Generation (1900-1990) Exploratory Confirmatory Exploratory Factor Analysis (EFA) Cluster Analysis Multidimensional Scaling ANOVA Logistic Regression Multiple Regression  2nd Generation (1990-Now) PLS-SEM (VB-SEM) SEM (CB-SEM) The Software Smart PLS Warp PLS Visual PLS Spad PLS PLS Graph PLS Gui AMOS (SPSS) LISREL SAS EQS, MPLUS SIMPLIS, PRELIS SePATH

History of Multivariate Statistical Analysis   History of Multivariate Statistical Analysis 1. Ordinary Least Square (OLS) Regression Galileo (1805) 2. Partial Least Square SEM PLS-SEM (PLS-Regression) Herman Wold (1963, 1975, 1982) 3. Structural Equation Modeling (SEM) Karl Joreskog (1966, 1967, 1969, 1970, 1973,1979), Wiley (1973), Joreskog & Sorbom (1982) Software comparison between SEM (SPSS-AMOS) and PLS- SEM (Smart-PLS)   1. AMOS – Jim Arbuckle (1995) available in IBM-SPSS Version 20.0 and above as one of its analysis option 2. Smart-PLS – Ringle et al. (2005) available in webpage www.smartpls.com - free download Version 1.0, 2.0 – BUT Version 3.0 (400 Euro for one year)

The Comparison between Amos and Smart PLS in Hair et al.(2013)   Estimator Used Research Objective Statistical Approach Model Assessment SEM MLE Maximum Likelihood Confirmatory Theory Testing Theory Comparison Theory Confirmation Parametric Regression ANOVA t-Test F-Test Fitness Indexes Reflect the fitness of the model (Table 1, 2) PLS_SEM OLS Ordinary Least Square Exploratory Prediction Development Exploring Non Parametric Wilcoxon Mann-Whitney Kruskal Wallis No fitness Indexes

Fitness Indexes Name of category Name of index Level of acceptance Comments Absolute_Fit Index Chisq P > 0.05 Sensitive to sample size >200 RMSEA RMSEA < 0.08 Range 0.05 to 0.10 is acceptable GFI GFI > 0.90 GFI = 0.95 is a good fit Incremental Fit Index AGFI AGFI > 0.90 AGFI = 0.95 is a good fit CFI CFI > 0.90 CFI = 0.95 is a good fit TLI TLI > 0.90 TLI = 0.95 is a good fit NFI NFI > 0.90 NFI = 0.95 is a good fit Parsimonious Fit Index Chisq/df Chi square/ df < 3.0 The value less than 3.0 is considered good fit.

The literature support for the respective fitness indexes Name of category Name of index Index full name Literature Absolute Fit Index Chisq Discrepancy Chi Square Wheaton et al. (1977) RMSEA Root Mean Square of Error Approximation Browne and Cudeck (1993) GFI Goodness of Fit Index Joreskog and Sorbom (1984) Incremental Fit Index AGFI Adjusted Goodness of Fit Tanaka and Huba (1985) CFI Comparative Fit Index Bentler (1990) TLI Tucker-Lewis Index Bentler and Bonett (1980) NFI Normed Fit Index Bollen (1989b) Parsimonious Fit Index Chisq/df Normed Chi-Square Marsh and Hocevar (1985)

Caution: Many researchers apply the statistical procedure without a comprehensive understanding of its basic foundations and principles. Researchers often fail in understanding of: Conceptual background of the research problem under study, which should be grounded in theory and applied in management Indicator-Construct misspecification design (Chin 1998; Jarvis et al., 2003; Mckanzie, 2001; Mckenzie et al., 2005) An inappropriate use of the necessary measurement steps, which is evident in the application of CB-SEM Inaccurate use of sample size and population under study (Baumgartner and Homburg, 1996)

The Role of Theory in Academic Research Academic research is grounded in theory, which should be confirmed or rejected, or need further research. A model should not be developed without some underlying theory (Hair et al., 2010) SEM is strictly theory driven because of the exact construct specification in measurement and structural model as well as necessary modification of the models during the estimating procedure (Hair et al., 2010) PLS-SEM is also based on some theoretical foundations, but its goal is to predict the behaviour of the relationship among constructs and to explore the underlying theoretical concept.

Limitation of PLS-SEM The use for theory testing and theory confirmation is limited since it has no global fitness indexes to confirm PLS-SEM parameter estimates are not optimal regarding bias and consistency (PLS-SEM Bias) PLS-SEM is not recommended as a universal alternative to SEM Researchers need to apply the SEM technique that best suit their research objectives, data characteristics, and model set-up (Hair et al., 2013) – (repeated again and again in the textbook)

The Misuse of SEM Data Characteristics Data characteristics such as minimum sample size, non-normal data, and scale of measurement are among the most often stated reasons for applying PLS-SEM (Hair et al., 2012b; Henseler et al., 2009). While some of the arguments are consistent with the method’s capabilities, others are not. For example small sample size is the most often abused argument associated with the use of PLS-SEM (Goodhue et al., 2012; Marcoulides and Saunders, 2006). The result of these misrepresentations has been scepticism in general about the use of PLS-SEM (Hair et al., 2013) Sample size in PLS-SEM is essentially build on the properties of OLS regression, researchers should revert to more differentiated rule of thumb provided by Cohen (1992) in his statistical power analysis provided that the measurement models have an acceptable quality in terms outer loadings (loadings should be above 0.7) Alternatively, researchers can use programs such as G*Power (www.psycho.uni- duesseldorf.de/aap/project/gpower/) to carry out power analyses specific to the model setups. So there is no rule of the thumb as 20, 30, etc.

Validating the Measurement Model

After Deleting Poor Loading Items

Modification Indices: Modify the Model

Standardized Regression Weight

Path Coefficients (Regression Weight)

Output SEM (Amos) D <--- A .134 .082 1.625 .104 Not Significant C Latent Constructs Estimate S.E. C.R. P Result D <--- A .134 .082 1.625 .104 Not Significant C .513 .102 5.058 *** Significant B .155 .124 1.258 .208

Measurement Model using PLS-SEM

Reliability and Validity of PLS-SEM   AVE CR R Square Cronbachs Alpha Communality Redundancy A 0.6894 0.8986 0.8493 B 0.6039 0.8840 0.8386 C 0.6946 0.9190 0.8893 D 0.5249 0.8632 0.567 0.8092 0.0922 Discriminant Validity   A B C D 0.8303 0.5227 0.7771 0.5498 0.5882 0.8334 0.5623 0.6023 0.6991 0.7245

Structural Model after Bootstrapping

Standard Error (STERR) t-Statistics (|O/STERR|) Output PLS-SEM Original Sample (O) Sample Mean (M) Standard Error (STERR) t-Statistics (|O/STERR|) Results A -> D 0.1880 0.2010 0.0908 2.0708 Significant B -> D 0.2349 0.2338 0.1284 1.8303 Not Significant C -> D 0.4575 0.4629 0.0911 5.0239 Output SEM (Amos) Latent Constructs Estimate S.E. C.R. P Result D <--- A 0.134 0.082 1.625 .104 Not Significant C 0.513 0.102 5.058 *** Significant B 0.155 0.124 1.258 .208

The Skewed Data – Parametric Assumption Failed Descriptive Statistics   N Std. Deviation Skewness Statistic Std. Error B1 452 .826 -1.026 .115 B2 1.030 -.738 B3 .781 -1.038 B4 .774 -1.231 B5 .743 -1.121 B6 .754 -1.343 B7 .762 -1.245 B8 .973 -1.593 B9 .939 -1.067 B10 .849 -1.295 M1 .867 -1.669 M2 .782 -1.043 M3 .855 -.910 M4 .913 -.899 M5 .829 -1.098 M6 .772 -1.163 M7 .937 -.931 M8 .882 -.865 M9 1.088 -.331 M10 .821 -.970

Run Using PLS Algorithm

Reliability and Validity   AVE Composite Reliability R Square Cronbachs Alpha A 0.644213 0.900154 0.862023 B 0.666972 0.909054 0.874587 C 0.69590 0.901412 0.868195 D 0.65140 0.929972 0.725152 0.914660 Discriminant Validity   A B C D 0.80263 0.785486 0.81668 0.749430 0.684700 0.83421 0.676266 0.614062 0.80110 0.81326

The Output of the Model

Output PLS-SEM for Non-Normal Data Path Coefficients (Mean, STDEV, T-Values) Output PLS-SEM for Non-Normal Data   Original Sample (O) Sample Mean (M) Standard Error (STERR) t-Statistics (|O/STERR|) A -> D 0.577237 0.085219 0.116570 4.95185 B -> D 0.021616 0.010850 0.093155 0.232046 C -> D 0.776656 0.788306 0.084766 9.162370

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