A comparative analysis of multivariate approaches for data analysis in management sciences

192 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management A comparative analysis of multivariate approaches for data analysis in management sciences Rizwan Raheem Ahmed1, Dalia Streimikiene2, Justas Streimikis3, Indre Siksnelyte-Butkiene4 1 Indus University, Faculty of Management Sciences, Department of Business Administration, Pakistan, ORCID: 0000-0001-5844-5502, [email protected]; 2 Lithuanian Sports University, Lithuania, ORCID: 0000-0002-3247-9912, [email protected] (corresponding author); 3 Lithuanian Centre for Social Sciences, Institute of Economics and Rural Development, Lithuania; University of Economics and Human Science in Warsaw, Faculty of Management and Finances, Poland, ORCID: 0000-00032619-3229, [email protected]; 4 Kauno Kolegija Higher Education Institution, Lithuania, ORCID: 0000-0002-0927-4847, [email protected]. Abstract: The researchers use the SEM-based multivariate approach to analyze the data in different fields, including management sciences and economics. Partial least square structural equation modeling (PLS-SEM) and covariance-based structural equation modeling (CB-SEM) are powerful data analysis techniques. This paper aims to compare both models, their efficiencies and deficiencies, methodologies, procedures, and how to employ the models. The outcomes of this paper exhibited that the PLS-SEM is a technique that combines the strengths of structural equation modeling and partial least squares. It is imperative to know that the PLS-SEM is a powerful technique that can handle measurement error at the highest levels, trim and unbalanced datasets, and latent variables. It is beneficial for analyzing relationships among latent constructs that may not be candidly witnessed and might not be applied in situations where traditional SEM would be infeasible. However, the CB-SEM approach is a procedure that pools the strengths of both structural equation modeling and confirmatory factor analysis. The CB-SEM is a dominant multivariate technique that can grip multiple groups and indicators; it is beneficial for analyzing relationships among latent variables and multiple manifest variables, which can be directly observed. The paper concluded that the PLS-SEM is a more suitable technique for analyzing relations among latent constructs, generally for a small dataset, and the measurement error is high. However, the CB-SEM is suitable for analyzing compound latent and manifest constructs, mainly when the goal is to generalize results to specific population subgroups. The PLS-SEM and CB-SEM have specific efficiencies and deficiencies that determine which technique to use depending on resource availability, the research question, the dataset, and the available time. Keywords: Partial least square-SEM (PLS-SEM), covariance-based-SEM (CB-SEM), SEM-based multivariate approach, multiple manifest variables, PLS-SEM vs. CB-SEM modeling. JEL Classification: C8, C42, C52. APA Style Citation: Ahmed, R. R., Streimikiene, D., Streimikis, J., & Siksnelyte-Butkiene, I. (2024). A comparative analysis of multivariate approaches for data analysis in management sciences. E&M Economics and Management, 27(1), 192–210. https://doi.org/10.15240/ tul/001/2024-5-001. Early Access Publication Date: January 23, 2024. 193 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management Introduction The researchers use covariance-based structural equation modeling (CB-SEM) and partial least square structural equation modeling (CB-SEM) to analyze the data of complicated connections among the latent and manifest constructs (Ahmed et al., 2021; Hair et al., 2022). Still, there are some vital differences between the two multivariate techniques; for example, PLS-SEM and CB-SEM modeling handle collinearity differently (Ahmed et al., 2022; Hair et al., 2019; Sarstedt et al., 2019). However, the PLS-SEM is very beneficial for managing data with a high degree of collinearity because it divides the data into latent variables uncorrelated using the PLS-SEM method (Sarstedt et al., 2022). On the other hand, the CB-SEM modeling is founded on multivariate normality and necessitates the data to be uncorrelated, as highlighted by Lu et al. (2020) and Hair Jr. et al. (2017). When the data is highly correlated, CB-SEM may generate unreliable or inconsistent results (Becker et al., 2022; Legate et al., 2022). Another difference is how the models are estimated, as Sarstedt et al. (2019) demonstrate. The PLS-SEM modeling uses a technique called bootstrapping to estimate the model parameters. This method can be computationally intensive but allows for a trustworthy approximation of factors in the presence of outliers and non-normality. The CB-SEM uses maximum likelihood approximation, which is computationally efficient but may not work well with non-normal data or outliers, according to Hair Jr. et al. (2017) and Mueller and Hancock (2018). The CB-SEM bases its assumptions on the multivariate normality hypothesis and demands that the data be uncorrelated (Ahmed et al., 2021; Hair et al., 2019; Hayes et al., 2017). For handling data with non-normality, outliers, and missing values, the PLS-SEM is not based on distributional assumptions and is, therefore, more flexible (Ringle et al., 2022; Sarstedt & Cheah, 2019). In light of this, it has been proven by Hwang et al. (2020), Ringle et al. (2015), and Hair et al. (2018) that PLS-SEM is a more reliable and adaptable method for assessing complex and correlated data than CB-SEM, which is based on multivariate normality assumptions. However, the technique chosen depends on the goals, research questions, and dataset characteristics (Hair et al., 2022). The CB-SEM and PLS-SEM are multivariate methodologies, but each has strengths and weaknesses. The PLS-SEM is a statistical technique that combines the benefits of structural equation modeling partial and least squares to evaluate complex associations between latent variables and observable datasets, as highlighted by Sarstedt et al. (2019), and Ahmed et al. (2022). The PLS-SEM is particularly helpful in handling data with a high degree of collinearity since it uses the PLS-SEM technique to break the dataset down into uncorrelated latent variables. The PLS-SEM employs a more suitable parameter estimation technique for examining the model’s parameters in the presence of outliers and non-normality (Memon et al., 2019). PLS-SEM has excellent flexibility because it does not rely on distributional assumptions and can handle data with non-normality, outliers, and missing values, according to Hair et al. (2010) and Sarstedt et al. (2021). The PLS-SEM technique can estimate latent variables that symbolize unobserved or underlying constructs in the data (Hair & Sarstedt, 2021; Legate et al., 2022). The PLS-SEM technique permits the study of numerous groups/subpopulations in the data, which can help compare groups or measurement invariance tests. According to Sarstedt et al. (2019) claim, the PLS-SEM can also handle correlations between constructs that are not linear. The PLS-SEM enables an understanding of the interactions between constructs by providing details on the intensity and direction of the associations and the comparative significance of each construct in the considered model (Legate et al., 2022). The PLS-SEM analysis can be performed using various programs, including the Smart-PLS, Warp-PLS, XLSTAT, and R packages for PLS-SEM (Memon et al., 2019; Parmar et al., 2022). Hence, it can be supposed that the PLS-SEM is an effective technique for evaluating complex, highly connected data since it enables the modeling and handling of non-linear relationships in a robust, flexible, and understandable manner (Hair et al., 2014; Hair et al., 2019). The CB-SEM is used by Hayes et al. (2017) and Lu et al. (2020) to examine a complicated relationship between latent constructs and observable data. The CB-SEM uses maximum likelihood approximation to estimate the model parameters, which is computationally efficient as one of its essential characteristics (Ahmed et al., 2022; Hooper et al., 2008). Given that the CB-SEM technique is founded on the assumptions of multivariate normality, 194 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management an uncorrelated dataset is needed (Hair et al., 2018). Latent variables, or unseen or underlying constructs in the data, can be estimated using CB-SEM (Hair et al., 2011; Hooper et al., 2008). The CB-SEM offers many fit indices that could be employed to examine the model fit and spot any potential issues under consideration (Bentler, 1990). Several groups or subpopulations can be analyzed using CB-SEM, allowing for comparing groups or testing invariance measurements (Sarstedt et al., 2021). According to Sarstedt et al. (2019) and Rigdon (2016), the CB-SEM enables model adjustment by introducing or eliminating latent structures or routes. Various softwares are available for CB-SEM analysis, including AMOS, LISREL, and M-Plus (Becker et al., 2022; Hair et al., 2018). By providing details on the strength and direction of the link and the relative prominence of each construct in the model under consideration, CB-SEM enables the analysis of relationships between variables (Parmar et al., 2022). Thus, it is debated that CB-SEM is a statistical methodology using the computationally effective maximum likelihood method to examine the model’s parameters. It is predicated on multivariate normalcy and necessitates the absence of correlation in the data. Additionally, it offers many goodness-of-fit statistics, allows for model adjustment and estimation of latent variables, and makes software available (Hair et al., 2014). This paper’s goal is to assess and contrast PLS-SEM vs. CB-SEM modeling. This study may be helpful to future researchers, who may use it to decide which approach to use under particular circumstances. The CB-SEM and PLS-SEM multivariate approaches are also covered comprehensively in this study. The CB-SEM and PLS-SEM multivariate approaches have also been described in earlier research, but that literature does not discuss every aspect of both multivariate techniques (Becker et al., 2022; Hair et al., 2019; Legate et al., 2022; Ringle et al., 2022), and several other studies, which had several drawbacks. Previous literature, for instance, does not address several features, such as sample size, multicollinearity issues, components, types of CB-SEM and PLS-SEM, model fit indices, measurement, and structural models. The current study provides an in-depth analysis of the CB-SEM and PLS-SEM multivariate techniques’ features, benefits, shortcomings, and methodology. The remaining sections of the paper are divided into numerous sections, such as section 2 (Theoretical Background), section 3 (Research methodology), section 4 (Results and discussion), section 5 (Conclusions), and Limitations and future research orientations. 1. Theoretical background Previous literature has explored the difference between PLS-SEM and CB-SEM modeling. The literature differentiated their categories and demonstrated the efficiencies and deficiencies of both models (Hair et al., 2006; Hair & Sarstedt, 2021). Several studies have demonstrated that PLS-SEM is an SEM to explore complex relationships between numerous parameters (Hair et al., 2022; Henseler et al., 2015). Similarly, previous literature exhibited that CB-SEM models could be used depending on the research goals, research questions, and data arrangements. PLS-PM (PLS path modeling) is a PLS-SEM variant used to evaluate associations between observed and unobserved elements in the model and to estimate the path coefficients connecting these variables. PLS-SEM and CB-SEM modeling come in a multiplicity of different forms (Memon et al., 2019; Ringle et al., 2015). According to Hair et al. (2022) and Sarstedt and Cheah (2019), PLS-CFA (PLS-confirmatory factor analysis) is used to gauge theories about the structure of the measurement model, including theories about the number of components, factor loadings, and measurement errors. The PLS-SEM is a method to estimate the path coefficients between constructs and investigate associations between unobserved elements in a model (Ringle et al., 2022). PLS-regression is accustomed to evaluating the association among predetermined predictors of a construct of interest, such as a dependent variable (Hair & Sarstedt, 2021; Legate et al., 2022). By identifying the linear blend of components that maximizes the covariance among constructs, PLS-canonical analysis is used to categorize the underlying structure of a dataset, as demonstrated by Richter et al. (2020) and Hair et al. (2017). A set of data is divided into groups using PLS-DA (PLS-discriminant analysis), a kind of PLS-SEM grounded on the values of predictors (Hair et al., 2022). PLS-SEM with small data is the type of PLS-SEM that is very helpful when several constructs are more incredibly associated with a small sample size; missing 195 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management data, non-normality, and multicollinearity can all be accommodated by it (Matthews, 2017; Ringle et al., 2015). According to previous studies, there are other varieties of CB-SEM modeling, including confirmatory factor analysis, a sort of CB-SEM accustomed to testing a considered measurement model based on fixed latent variables and preset manifest factors (Ahmed et al., 2022; Hair et al., 2022). It could support or disprove a scale’s or measure’s factor structure (Hair et al., 2010; Hussain & Ahmed, 2020). Path analysis assesses the direction, strength, and correlation between various parameters. It can evaluate theories of causal relationships between many components (Hayes et al., 2017). This kind of CB-SEM, known as latent growth curve modeling (LGCM), looks at how variables change over time. Examining a variable’s rate of change and its consistency across time is a common practice (Hair et al., 2011). Grounded on the provisions of answers to a set of observed factors, latent class analysis (LCA) is frequently used to ascertain subdivisions or classes within a population (Nunkoo et al., 2020). The CB-SEM method, known as multigroup SEM, compares an association among constructs across various groups or populations. It can be used to look for variations or patterns in the relationships between variables between various groups (Cohen, 1992; Hayes et al., 2017). This kind of CB-SEM, SEM with missing data, deals with missing data in the analysis. It is customary to look at the parameters of the model and missing data simultaneously (Hair et al., 2006). SEM without normality data is the type of CB-SEM that works with nonnormal data for the analysis. Using reliable estimating approaches, the model’s parameters could be evaluated (Henseler et al., 2015). According to Ringle et al. (2015) and Hair et al. (2010), the sample size for PLS-SEM should be sizable to ensure adequate power for the statistical analysis and to obtain a suitable level of generalizability (Hair et al., 2010; Ringle et al., 2015). However, PLS-SEM sample size recommendations are less accurate than those for traditional SEM (Sharma et al., 2021). PLS-SEM is considered a more reliable method than traditional SEM regarding sample size and measurement error because it can tolerate higher levels of measurement error (Ahmed et al., 2019; Hair et al., 2019). As a result, PLS-SEM frequently has more flexible sample size requirements than typical SEM. It is vital to keep in mind that sample size is always determined by the study purpose, the resources available, and the amount of time available, even if some studies have shown that PLS-SEM may be employed with datasets as low as 50–100 instances (Hayes et al., 2017). Previous literature also discussed the required sample for PLS-SEM modeling; according to Hussain and Ahmed (2020), Hussain et al. (2021), and Zaidi et al. (2022), the sample size required to achieve a specific power level, for instance, 80% or 90%, can be determined in various ways, including simulation studies and power analysis techniques. The sample size is calculated considering the research topic, the resources available, and the amount of time available. It is crucial to remember that sample size estimations are frequently approximate. It is also critical to remember that the PLS-SEM sample size requirements vary depending on the number of predictors and model complexity (Sarstedt & Cheah, 2019). As models become more complicated, sample sizes become more critical. The sample size must be proficient at ensuring the accuracy and objectivity of the estimated values (Shmueli et al., 2019). Similarly, previous literature also discussed that the sample size is a vital concern in the CB-SEM technique since it can affect the valuation of the considered model’s parameters and the model’s capacity to fix the dataset. A larger sample size will produce more precise parameter estimates and a better model-data fit (Hair et al., 2014; Sharma et al., 2021). According to Hair et al. (2011), the optimal sample size will depend on the complexity of the model, the number of indicators, the latent factors quantity, and the level of measurement error. There are numerous methods for computing the sample size for the CB-SEM. The recommendations for the sample size for the CB-SEM depend on various aspects, among them the number of factors, the number of estimated parameters, and the amount of measurement error (Hair et al., 2011). One of several recommended sample size criteria is the “10:1 rule”, which describes that the sample size must be ten times the parameters, which has to be evaluated. This rule, though, only functions under certain circumstances (Hussain & Ahmed, 2020; Streukens & LeroiWerelds, 2016). Power analysis techniques or simulation studies can be used to calculate 196 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management the sample size required to attain a given power level, for instance, 80% or 90%, to establish the sample size that provides a high likelihood of detecting a particular effect. In general, SEM requires a sample size of 200 or more. However, this guideline might only apply to particular models; thus, employing more sophisticated sample size estimation techniques is always a good idea. According to Kang (2021) and Hoenig and Heisey (2001), power analysis can decide the desired sample size to identify a particular effect size at a specific power level. Power analysis can consider the magnitude of measurement error, the complexity of the model, and the number of indicators. Simulators de Monte Carlo – this method simulates data and figures out the sample size necessary to accurately estimate model parameters (Hayes et al., 2017; Kroese et al., 2014). It can be accomplished by relating the Akaike information criterion (AIC) or the Bayesian information criterion (BIC) for various sample sizes. It is crucial to remember that sample size is only one consideration when evaluating the fit of a model. Several additional elements, for instance, the number of indicators, the considered model’s complexity, the data distribution, and the estimation method, impact the model fit (Hoenig & Heisey, 2001). Previous literature demonstrated that multicollinearity is a common problem in PLS-SEM and CB-SEM, which occurs when two or more predictor variables are closely associated (Grewal et al., 2004). It occurs when two or more independent variables exhibit strong correlations, and estimating models and explaining their results can be challenging (Wondola et al., 2020). For example, a correlation matrix can determine how every independent construct connects with others to find multicollinearity in PLS-SEM and CB-SEM. Multicollinearity may be present if there is a significant correlation between two or more independent constructs (Wondola et al., 2020). The degree of multicollinearity in a multiple regression model is measured by the variance inflation factor (VIF). The VIF of 1 shows the absence of multicollinearity, while a VIF bigger than 1 specifies the occurrence of multicollinearity. High multicollinearity is frequently indicated by a VIF more significant than five (Chan et al., 2022; Hussain & Ahmed, 2020). The variance amount in a predictor, which other predictors cannot describe, is represented by tolerance, which is the reciprocal of VIF. There is high multicollinearity when the tolerance value is below 0.2. The condition index gauges the level of multicollinearity in a multiple regression model. Multicollinearity is indicated by a number higher than 30 (Arminger & Schoenberg, 1989; Chan et al., 2022). The previous literature has discussed and identified several positive and negative aspects of PLS-SEM and CB-SEM techniques, however, numerous factors are still missing to establish the differentiation between both modeling techniques, thus the current study answers those questions. 2. Research methodology 2.1 Research design and estimation techniques The undertaking is a comparative study, which has differentiated PLS-SEM and CB-SEM modeling; the study also considers the efficiencies and deficiencies of both models in the management sciences field. The comparative studies could be performed qualitatively or quantitatively. However, the research design of this study is qualitative, and researchers have stated the pros and cons of PLS-SEM and CB-SEM techniques; they also compare different parameters of both techniques. This study has used previous literature and thoroughly reviewed previous studies, books, and other relevant publications to analyze both models. This study also used graphical analysis to distinguish between PLS-SEM and CB-SEM modeling. The study examined the criteria to validate measurement models, such as convergent and discriminant validities, using factor loading of items, Cronbach’s alpha, composite reliability, and average variance extracted of constructs to validate the convergent validity and reliability in both PLS-SEM and CB-SEM techniques. Moreover, this study analyzed HTMT, FornellLarcker criterion, and cross-loading to validate discriminant validity for both SEM techniques. Similarly, this study also examined the parameters for validating a structural model for PLS-SEM modeling. For this purpose, the researchers used the coefficient of determination (R2), effect size (f 2), path coefficient analysis (direct, indirect relationship of constructs), goodness of fit measures, and predictive relevance (Q2). This research used confirmatory factor analysis, structural equation modeling, path coefficient analysis (direct, indirect relationship of constructs), and goodness of fit measures 197 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management to validate structural models in CB-SEM techniques. This study also used the graphical analysis to examine the observed, unobserved, convergent, and discriminant validity to endorse the measurement model for both PLS-SEM and CB-SEM techniques. The graphical analysis also defined the path coefficient relationship (direct and indirect relationship of constructs) to validate the structural model for both PLS-SEM and CB-SEM techniques. 2.2 Acronyms and full names Tab. 1 exhibited the acronyms and full names of different abbreviations used in this paper. 3. Results and discussion The results of this study demonstrated the parameters of the measurement and structu ral models for both PLS-SEM and CB-SEM techniques. 3.1 The measurement model in CB-SEM and PLS-SEM modeling In PLS-SEM & CB-SEM modeling, validating the measurement model entails evaluating the fitness of the dataset and the reliability of indicators chosen to represent the latent variables (Hair et al., 2019). This procedure includes the following steps as the factor loadings indicate how intensely indicators and unobserved factors are linked. Significant factor loadings show that the indicators and latent variables are closely connected (Hair et al., 2014; Rigdon, 2016). Factor loadings have a conventional cut-off of 0.7, which can change depending on the research environment (Ringle et al., 2015). The measuring model must be validated by evaluating the indicators’ reliability and validity. While validity narrates how well the indicators measure the latent variable, reliability Acronyms Full names Acronyms Full names PLS-SEM Partial least square structural equation modeling PLS-CFA Partial least square confirmatory factor analysis CB-SEM Covariance-based structural equation modeling PLS-DA Partial least square discriminant analysis SEM Structural equation modeling LGCM Latent growth curve modeling Smart-PLS Smart partial least square software LCA Latent class analysis Warp-PLS Variance-based and factor-based structural equation modeling software SRMR Standardized root mean square residual XLSTAT Excel statistical software HTMT Heterotrait monotrait ratio of correlation AMOS Analysis of moment structures AVE Average variance extracted LISREL Linear structure relations D_ULS The squared euclidean distance M-Plus Microdia plus software AGFI Adjusted goodness of fit index RMSEA Root mean square error of approximation RNI Relative non-centrality index CFI Comparative fit index PCFI Parsimonious-adjusted fit index GFI The goodness of the fit index PNFI Parsimony-adjusted normed fit index TLI Tucker Lewis index G_D Geodesic distance NFI Normal fit index VIF Variance inflation factor Source: own Tab. 1: Acronyms and full names 198 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management refers to the indicators’ consistency across time (Byrne, 2013; Ringle et al., 2015). The model must offer a good match for the dataset; in PLS-SEM modeling, several fit indices, including R2 and Q2, can be applied to measure how well the model fixes the dataset. These indices show the percentage of the variance in outcome constructs the model justifications (Henseler et al., 2015; Parmar et al., 2022). Similarly, many fit indices, including the RMSEA, chi-square statistic, and comparative fit index (CFI), can be applied to measure the model’s fitness in CB-SEM modeling (Hooper et al., 2008). The importance of path coefficients and the overall model should be tested by examining the structural model (Bentler & Bonett, 1980; Hair et al., 2022). Suppose the factor loadings or the model do not match the data well. In that case, it may be essential to re-specify the model by modifying the path coefficients, adding or removing variables, or making other modifications (Sarstedt et al., 2022). It is essential to remember that measurement model validation is an iterative process, and the model should be refined and re-evaluated as needed until an acceptable level. It is crucial to remember that when working with CB-SEM, using multiple data sources, such as self-report surveys, behavioral observations, and physiological measures, can increase the rationality of the measurement model. Additionally, the validation process should be done with the sample used in the study and not just in the population in general (Hair et al., 2014). The annotated graphical form of the measurement model of PLS-SEM is provided in Fig. 1 (Ahmed et al., 2021). Fig. 1 demonstrated that the factor loadings of each item are higher than 0.70, and the average variance extracted is more significant than 0.50, which fulfilled the convergent validity requirement. Moreover, the path analysis between the construct validated the discriminant validity; thus, this endorsed the measurement model. Fig. 1: Measurement model in PLS-SEM modeling Source: Ahmed et al. (2021) 199 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management The annotated graphical form of the measurement model of CB-SEM is provided in Fig. 2 (Ashraf et al., 2018). Fig. 2 also demonstrated that each observed variable has a factor loading of more than 0.70, values of path coefficient between the unobserved variables, and values of goodness of fit measures have followed the cut-offs. Thus, Fig. 2 demonstrates that the measurement model is validated in CB-SEM modeling. 3.2 The structural model in CB-SEM and PLS-SEM modeling In CB-SEM and PLS-SEM modeling, validating the structural model entails analyzing the model’s fitness to the dataset, determining the importance of the path coefficient, and reviewing the overall model (Kline, 2015). This procedure includes several steps; for example, the path coefficients show how strong and in what direction the latent variables are related. High positive path coefficients indicate a strong positive relationship between the latent variables, while high negative path coefficients indicate a strong negative relationship (Hair et al., 2019; Raza et al., 2021). T-tests or bootstrapping techniques can be used to conclude the significance of the path coefficients. If the path coefficient is significant, the latent variables must be statistically related (Hair et al., 2014; Hayes et al., 2017; Henseler et al., 2015). In PLS-SEM modeling, fit indices like R2 and Q2 could be applied to measure the overall fitness of the model. These indices indicate the variance proportion in dependent factors that the model explains (Bentler, 1990). The overall fitness of the CB-SEM model can be evaluated using fit indices such as the RMSEA, chisquare statistic, and comparative fit index (CFI; Hooper et al., 2008). Discriminant validity examines how little latent variables connect with measurements of unrelated constructs. It can Fig. 2: Measurement model in CB-SEM modeling Source: Ashraf et al. (2018) 200 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management be assessed by contrasting the latent variables’ average variance extracted with their squared correlation to unrelated factors (Ahmed et al., 2021; Fornell & Larcker, 1981; Hair Jr. et al., 2017; Malhotra et al., 2006). The model may need to be re-specified by adding or removing variables, changing the path coefficients, or modifying the model in other ways if it does not fit the data well or if the path coefficients are not significant (Kaufmann & Gaeckler, 2015; Sarstedt et al., 2022). It is crucial to remember that structural model validation is an iterative process. The model must be polished and reexamined until an acceptable fit level and significance are achieved (Sarstedt et al., 2019). It is essential to remember that when working with CB-SEM, using multiple data sources, such as self-report surveys, behavioral observations, and physiological measures, can increase the validity of the structural model. Additionally, the validation process should be done with the sample used in the study and not just in the population in general (Malhotra et al., 2006). The annotated graphical form depicted the structural model of PLS-SEM in Fig. 3 (Ahmed et al., 2021). Fig. 3 demonstrated the path coefficient between the constructs (direct and indirect relationship), which shows significant values; moreover, R-square values showed the impact of exogenous variables on endogenous variables. Thus, Fig. 3 validated the structural model in PLS-SEM modeling. The annotated graphical shape of the structural model of CB-SEM is provided in Fig. 4 (Ashraf et al., 2018). Fig. 4 demonstrates the path coefficient between the constructs (direct and indirect relationship), which shows significant values. Moreover, fit indices values meet the required threshold. Thus, Fig. 4 validated the structural model for CB-SEM modeling. Fig. 3: Structural model in PLS-SEM Source: Ahmed et al. (2021) 207 2024, volume 27, issue 1, pp. 192–210, DOI: 10.15240/tul/001/2024-5-001 Information Management Management, 23(1), 82–104. https://doi.org/ 10.3846/jbem.2021.15664 Arminger, G., & Schoenberg, R. J. (1989). Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models. Psychometrika, 54(3), 409–425. https://doi.org/10.1007/bf02294626 Ashraf, M., Vveinhardt, J., Ahmed, R. R., Štreimikienė, D., & Mangi, R. A. (2018). 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