The Results of Partial Least Squares-Structural Equation Modelling Analyses (PLS-SEM)

Transcription

1 The Results of Partial Least Squares-Structural Equation Modelling Analyses (PLS-SEM) Hengky Latan University of Pattimura, Economic and Accounting Department Indonesia Nur Ainna Ramli Lincoln University, Finance and Accounting Department, Lincoln 7647, New Zealand Abstract The purpose of this paper is to complete prior studies reports related to Partial Least Square-Structural Equation Modelling (PLS-SEM, hereafter) analysis. It is also to provide more specific elements for the academic and practitioner to report the outcome analysis from PLS-SEM using six examples of the PLS-SEM type models. These are the recursive, interaction, intervening, second-order, heterogeneity and multi-group models. Each of the models will be discussed in more detail with all circumstances that ought to be reported in their analysis from other literature recommendations and suggestions. The discussion is divided into two sections using the two-step approach. The two approaches are for: (i) the PLS-SEM outer model and, (ii) the PLS-SEM inner model. For the PLS-SEM outer model, the report statement combined all the model s types, whereas for the PLS-SEM inner model, the report discusses for each of the model s types. Keywords: Report, recursive model, interaction model, intervening model, second-order model, heterogeneity model and multi-group model Partial Least Square-Structural Equation Modelling (PLS-SEM) 1 Electronic copy available at:

2 The Results of Partial Least Squares-Structural Equation Modelling Analyses (PLS-SEM) 1.1.Introduction Since it was introduced about three decades ago (Wold, 1982, 1985a, 1985b) the use of PLS- SEM has drastically increased in its popularity from every aspect of fields such as accounting (Lee et al., 2011), advertising (Henseler & Sarstedt, 2012), information systems (Chin, 2003; Goodhue et al., 2006; 2007), management information systems (Chin, 1998a; Goodhue et al., 2012), marketing (Fornell, 1982; Hair et al., 2011; 2012a; Henseler et al., 2009), operational management (Peng & Lai, 2012), strategic management (Furrer et al., 2012; Hair et al., 2012c; Hulland, 1999; Money et al., 2012), technology innovation (Barclay et al., 1995) and total quality management (Tenenhaus, 2008). PLS-SEM is chosen because of its exceptional capability and fewer assumptions than covariance-based structural equation modelling (CB-SEM). The competencies of PLS-SEM are such it is able to handle small sample sizes, no assumptions of the particular scale and as well as the normality of the data distribution (Fornell, 1982, p.449; Hair et al., 2012a, p.314; Wold, 1985a,p.581). This claim is from the study that based on Hair et.al. (2012a, p.421; 2012c, p.322), it is in the 20 top marketing journals and eight top management journals from 1981 to The MIS Quarterly journal article by Ringle et al. (2012, p.iv) for 1992 to 2011, also declares the main reason for PLS-SEM use is due to the small size, non-normal data and the constructs (latent variables) that use mode B. 2 Electronic copy available at:

3 In particular, application of structural equation modelling (SEM) either using CB-SEM or PLS-SEM has to follow its steps analysis. In PLS-SEM, the user should omit any of the five main steps in their data analysis because each step process influences the next step in the analysis and so on. The analysis steps are the conceptual model, the determination of the algorithm method analysis, the determination of the resampling method, verifying the path coefficient diagram and the model evolution (Latan & Ghozali, 2012b, p.33). After the model has been analysed and evaluated, the most crucial phase is how to write a report to express the results of the analysis. This issue that has been highlighted by Steiger (2001, p.333) on how important it is to write a report for each of the model analysis in SEM as follows: Any introductory textbook on SEM is setting the tone for future work in the field. In my opinion, such books should include a chapter with examples of what to do and what not to do when reporting the results of SEM, Figure 1 below shows the steps from the initial analysis process in PLS-SEM from the start until reporting the result of the analysis (Latan & Ghozali, 2012a). The steps of the PLS-SEM analysis process are as follows: Conceptual model Step 1 Determination of the algorithm method analysis Step 2 Determination of the resampling method Step 3 Verifying the path coefficient diagram Step 4 Evaluation Model Step 5 Reporting the results of the analysis Step 6 Figure 1. The steps of the PLS-SEM analysis process 3

4 To date, journal publications and book chapters are more likely to discuss how and way to report CB-SEM analysis (Boomsma, 2000; Boomsma et al., 2012; Hoyle & Panter, 1995; McDonald & Ho, 2002; Steiger, 2001) than PLS-SEM so there is far less discussion (Chin, 2010, p.655; Latan & Ghozali, 2012a, p.329). Nevertheless, the use of PLS-SEM recently is so considerably enlarged with the expansion of several advanced techniques such as interaction model analysis ((Dijkstra & Henseler, 2012; Dijkstra & Schermelleh-Engel, 2012; Henseler & Chin, 2010), heterogeneity analysis (Rigdon et al., 2010; Ringle et al., 2010; 2011), multi-group analysis (Sarstedt et al., 2011) and hierarchical component model analysis ((Furrer et al., 2012; Ringle et al., 2012). Therefore, the key to this study s purpose is to present an inclusive and comprehensive discussion from the prior lack of discussion related to reporting PLS-SEM results (Chin, 2010; Gefen et al., 2011; Hair et al., 2012ac; Latan & Ghozali, 2012a, 2013). In addition, all-encompassing how to report PLS-SEM results are based on six examples of the models dimension. They are the recursive, interaction, intervening, second-order, heterogeneity and multi-group models. Each of those model s examples will be considered in detail what should be reported for the results. In addition, the relevant articles will be given at the end of each section Questions before reporting results Specifically, each journal or research committee has its own results report format, but most of those formats are quite similar. Therefore, this paper discusses the reporting format that has been generally accepted. Before reporting the result of PLS-SEM, it is essential for the reporter to understand and be able to answer all the fundamental questions below. 4

5 a) Is the conceptuality model is accurate? The conceptual model is the initial phase that should be performed in PLS-SEM analysis (Latan & Ghozali, 2012b, p.33). The accurate formation of the conceptual model is the key foundation for the structural model development that answers the researcher s main objective. At this phase, the researcher needs to develop and measure the exact construct as well as verify the dimensionality of the construct. Furthermore, each direction s indicator that represents the construct should be clarified clearly. This means whether the construct is being considered as a reflective or formative construct measurement to avoid Type I or Type II errors (Latan & Ghozali, 2012a). The incorrect construct concept will lead to lower internal validation as well as weak discrimination validity statistics (Latan & Ghozali, 2012a, p.51). For example, some studies use the observed variable for develop the structural model. In this case, the researcher needs to show the readers what types of variables (i.e., observed or unobserved variables) that they used by adding footnotes. This is because the structural model with unobserved variable is different in PLS outer model evaluation. b) What kinds of data have been used? Are there enough data samples for the study? In general, the data features that most researchers have used in the PLS model are from primary data that are from the questionnaire elements (i.e., normally a five or seven point Likert scale). Nevertheless, it is not exceptional to use secondary data (Latan & Ghozali, 2012a, p.303). This is because it is well-known that PLS can handle all data types and scales such as, interval, nominal, ordinal and ratio (Fornell, 1982; Garson, 2012; Latan & Ghozali, 2013). However, it is debatable regarding the type of data for endogenous variables. To be specific, several researchers have stressed that the initial assumption of the PLS algorithm is same as OLS regression (i.e., linear regression), which means that each dependent variable 5

6 (endogenous) is distinguished as a continuous variable (i.e., metric data). It is verified that PLS-SEM variables could not be evaluated using non-metric data. However, some writers claim that PLS-SEM is able to handle all such scale estimations. This issue should be investigated further to substantiate the answer. The contrast with the independent variables (exogenous) has not created any problems in using any kind of scale assessment. Therefore, the use of a single-item to estimate the variables classified as categorical or binary variables strongly suggested. Based on the dispute by Diamantopoulos et al. (2012), a researcher is able to use a single-item if the sample (N) is < 50, effect size < 0.30, inter-item correlation > 0.80, Cronbach alpha > 0.90 and the item should be semantically redundant. The data characteristics from secondary data or a single-item construct should be in the report because conducting outer PLS model evaluation is different compared with primary data. This is especially so if the variables are correspondingly classified as categorical, binary and ratio. In addition, the total data sample for PLS-SEM estimation should be considered in the study even though, the well-known of the benefit of PLS-SEM is that it is able to handle small data samples. This is consistent with the approach by Wold (1982, 1985a) that states the PLS- SEM model estimation should maintain the principle of larger data consistency. This is to gain an unbiased PLS estimate (i.e., under or overestimate) and, to provide a true value (Barclay et al., 1995; Dijkstra, 1983; Wold, 1985a). Some PLS literature has suggested a rule of thumb for the total minimal sample that should be established in PLS-SEM model estimation. The recommendation is such as 10 more than the paths/predictors in the model (Barclay et al., 1995; Chin, 1998b; Chin & Newsted, 1999; Hair et al., 2011). Additionally, some researchers attempt to investigate by comparing PLS-SEM, LISREL and OLS regression in order to know whether the PLS-SEM has any special capability of handling 6

7 small sample sizes. However, surprisingly, they discovered that PLS-SEM is not a Silver Bullet (Goodhue et al., 2006, p.9; Goodhue et al., 2012, p.999; Marcoulides & Saunders, 2006, p.viii). Yet some are still believe that PLS-SEM is Indeed a Silver Bullet in particular circumstances (Hair et al., 2011, p.148; Ringle et al., 2012, p.vii). This condition had been emphasized by Marcoulides et al. (2012, p.726) that PLS-SEM cannot and should not been compared with others analysis techniques. In summary, it should be clear to the IS research community that comparison of PLS-SEM to other methods cannot and should not be applied indiscriminately. As a discipline, we need to compare apples with apples and oranges with oranges, The declaration advocated by Wold (1982) is as follows: The PLS-SEM and ML-LISREL approaches to path with latent variables indirectly observed by multiple indicators are complementary rather than competitive Therefore, the total of the data sample should be reported in PLS-SEM data analysis in order to provide a statistical power analysis. Ringle et al. (2012, p. viii) find that that only three studies report the statistical analysis method in the MIS Quarterly journal from 1991 to Chin (2010) and Hair et al. (2012c) propose using Cohen s (1992) table descriptions in order to distinguish the power analysis. c) Is the algorithm setting and resampling method is accurate? It has been well understood that PLS-SEM algorithm has used the iterative LS procedure thus, it is discerned in three stages (Chin, 1998b; Chin & Newsted, 1999; Tenenhaus et al., 2005; Wold, 1982, 1985a). The three stages are: (i) the weight estimates, (ii) the path estimates reflection, and (iii) the location parameter. In the PLS-SEM algorithm, there are 7

8 three choices of scheme, the centroid, factorial and path. According to Chin (1998a), Chin and Newsted (1999), Latan and Ghozali (2013) and Gefen et al. (2011), regardless of any chosen scheme, the effect confers only small differences such as or less, especially for the structural path coefficient and 0.05 or less for the measurement path coefficient (Noonan & Wold, 1982). In principle, the weighting scheme that is strongly recommended for the PLS-SEM algorithm is the path weighting scheme (Esposito Vinzi et al., 2010; Garson, 2012; Hair et al., 2012b; Henseler, 2010; Latan & Ghozali, 2012a). In addition, Ringle et al. (2005) claim that the total maximum iterations for the PLS-SEM algorithm are approximately 300 with the total of outer weight < 10-5 and initial weight of 1.0 (Wold, 1982). Based on the research by Hair et al. (2012a; 2012c) and Ringle et al. (2012, p.vii), up till now there is little study that enlightens the PLS-SEM algorithm in the 20 top marketing journals and 8 top management journals from 1981 to 2010 and, the journal MIS Quarterly from 1992 to For that reason, Hair et al. (2012a; 2012c) and Ringle et al. (2012) declare a strong suggestion to report this fact in PLS-SEM data analysis (Hair et al., 2013). Besides reporting the setting of PLS-SEM algorithm, the resampling method setting should not be excepted. This is because it is well understood that the path significance effect will not be computed without knowing the estimation of the resampling method (i.e., bootstrapping) (Latan & Ghozali, 2012a; Wold, 1985b). Particularly in PLS-SEM, the resampling method is the bootstrapping technique. This is because this technique is assumed to be more accurate and tends not to avoid the confidence interval like with the jack-knife method (Efron & Tibshirani, 1993). In the PLS-SEM program such as PLS-Graph (Chin, 2003) and SmartPLS (Ringle et al., 2005), there are three choices to assess the bootstrapping method, such as no sign changes, construct level changes and individual sign changes. Many researchers recommend using the individual sign changes (Hair et al., 2012b; Henseler et al., 2009; Latan & Ghozali, 2012a). However, it has also been suggested by other researchers to use no sign 8

9 changes and construct level changes (Chin, 2003; Garson, 2012; Latan & Ghozali, 2012a; Tenenhaus et al., 2005). Regardless of any choices of bootstrap assessment, the difference magnitude of the T-statistic is so small that it is similar to the effect of choosing the scheme for the construct ABC. The total number of cases and resample evaluation for the bootstrap procedure should not be omitted from the PLS-SEM report. The number of cases should report the same as the number of observations or the original sample. In addition, for the number of resample, many recent studies suggest setting up the number of bootstrap samples approximately larger than 5000 (Hair et al., 2011; 2012a; Henseler et al., 2009). Nevertheless, some reports suggest that the number of resample at is already enough to compute the standard error PLS-SEM estimate (Chin, 1998b, 2003; Kock, 2012; Latan & Ghozali, 2012b). The resample number should be more than the number of original samples. This is because, if the model analysed is complex, the larger number of bootstrap samples will result in too slow computation processing. According to Bradley Efron, who develops of the bootstrap method, the number of bootstrap samples of is already adequate for standard error estimation. On the other hand, for the bootstrap confidence interval it is suggested it should be as large as (Efron 2012; Efron et al. 2004). d) Can the outcome analysis be interpreted and summarized? There are two possible questions that should be answered for this last phase. First, can the results from the PLS-SEM model estimation be interpreted and summarized? Second, is the analysis involved with some other problem while the analysis is being conducted?. There are three possible problems that usually occur while doing an analysis in the PLS-SEM model. First, the problem involves high collinearity (Henseler et al., 2009, p.302; Kock & Lynn, 2012, p.547). An indicator that has high collinearity in the PLS-SEM can be seen from a high R-square value. High correlation between the variables is because the outer loading > 1, the 9

10 path coefficient > 1 or <-1 and cross loading > 0.5 (Kock & Lynn, 2012, p.563). They then claim that the best solution to overcome the collinearity problem is by: (i) reducing the indicator that has a high cross loading value, (ii) cutting the single-item or the construct with fewer indicators, (iii) adding more indicators and, (iv) doing a two-step analysis (hierarchical analysis). Second, there are some invalid indicators, especially with the formative construct. However, this subject causes a serious problem because the decline of one indicator from the formative construct changes the construct meaning (Jarvis et al., 2003, p.203; MacKenzie et al., 2005, p.713). In contrast, an indicator from the reflective construct has a similar description. For information, the significant value for the formative indicator in PLS-SEM can be evaluated through the outer weight (Chin, 1998b; Latan & Ghozali, 2012a). Surprisingly, based on the research by Hair et al. (2012c) and Ringle et al. (2012), some studies (i.e. the 8 top management journal from 1981 to 2010 and the journal MIS Quarterly 1992 to 2011) had been set up incorrectly. For example, the criteria indicator that should have been used as the reflective construct had been analysed as the formative construct. Hair et al. (2012c) then claim that if it is found that the outer weight is non-significant and the outer loading is high (i.e., > 0.5), that indicator is still acceptable. Third, the sample data are not from one population or are heterogeneous (Rigdon et al., 2010, p.256). Sometimes researchers make assumptions that their data are homogeneous. This assumption is normally considered as not rational because the data collection is from units or segments. As a result, if the data are truly heterogeneous and have been reported as homogenous, it can cause biased analysis. The methods that can be used to solve this problem are such as FIMIX-PLS, PATHMOX, PLS-Typological, PLS-GAS and REBUS- PLS. 10

11 1.3. Reporting results outer model analysis Chin (2010) advises that the better way to report PLS-SEM analysis is by using the two-stage approach (Anderson & Gerbing, 1988). First, it focuses on the outcome from the scaling or outer model and, second, from the structural or inner model. For the outer model PLS-SEM, all the types of the model need to confer all together, whereas, the inner model needs to clarify each type of model. The scaling or outer model is the relationship between the indicator or item to its latent construct until it can be built two different modes. The modes are mode A or mode B, and these modes will be estimated depending on the construct operation. If the variable from the structural model illustrates a single-item or observation then this kind of variable does not need to evaluate the outer model (Latan & Ghozali, 2012a). At this stage, we need to focus on examining the reliability and validity of the data that represent the latent construct. In order to report the PLS-SEM outer models, it can begin with the mode A estimation to estimate the indicator s reliability for every construct items. It has been suggested that the cut-off for the outer loading be 0.6 for research data that are exploratory and 0.7 for the research data that are confirmatory. Nevertheless, assessment shows the range of is acceptable for construct development as well as for the scaling construct (Chin, 1998b; Götz et al., 2010; Hair et al., 2011; Hulland, 1999; Latan & Ghozali, 2012a). Normally, in order to obtain a model fit the observer needs to drop one item that does not meet any condition above through its indicator s reliability. Normally researchers drop some item indicators in order to obtain model fit. This information ought to tell readers the additional information through footnotes (Gefen et al., 2011; Latan & Ghozali, 2012a). To compute the internal consistency reliability, the composite reliability that has been developed by Werts et al. (1974) can be estimated from the formula below: 11

12 Where: λi is the outer loading, F is the factor variance and, ϴii is the error variance. The composite reliability value will point up from 0-1. This is means that the closer it is to 1 the better the items explain the latent construct s variance. The cut-off factor loading is the same as the indicator reliability, which the composite reliability s value suggests be reached at 0.6 for the data s exploratory and 0.7 for confirmatory features (Bagozzi & Yi, 1988; Götz et al., 2010; Hair et al., 2011; Latan & Ghozali, 2012a). Thus, the value of the indicator reliability will influence the value for composite reliability. Besides the composite reliability, the PLS-SEM also uses Cronbach alpha for measuring internal consistency. The PLS-SEM and SEM literature emphasizes using the composite reliability measurement rather than Cronbach alpha because of more accurate underestimation (Bagozzi & Yi, 1988; Chin, 2010; Hair et al., 2011; 2012a; Raykov, 1998). This is because the composite reliability measurement is not assumed to be equal across items to all indicators do not have a same weight. In addition, the outer model in PLS-SEM also measures convergent and discriminant validity. To estimate convergent validity, Fornell and Lacker (1981) propose calculating the Average Variance Extracted (AVE) with the following formula below: ( ) ( ) Where: λi is the outer loading, F is factor variance and ϴii is error variance. Fornell and Larcker (1981) note that the AVE can be computed by the reliability of the component score 12

13 for the latent variable and the outcome is more conservative than the composite reliability. The AVE value should be more than 0.50, which indicates that 50 % or more of the variance from the indicators can be explained (Chin, 2010). Moreover, the discriminant validity can be computed from each of the construct s AVE model, which is from the construct correlation. The bigger the value of the construct AVE, the better is the discriminant validation that comes from correlation within the model constructs (Fornell & Larcker, 1981). From the previous discussion, the outer model evaluation in PLS-SEM that is viewed as mode B can be seen from the weight significance (Chin, 1998b; Hair et al., 2011; Hair et al., 2012b; Henseler et al., 2009; Latan & Ghozali, 2012a). This evaluation is computed by the bootstrap procedure. Therefore, the AVE and composite reliability estimate is not relevant for mode B s construct. Hair et al. (2012a; 2012c) note that the indicator weight, t-value or p- value and the standard error for the outer model PLS-SEM must be reported. Further, the issue of collinearity is vital for the formative construct since it is categorized as double regression which is from indicator to construct. Most PLS-SEM literature claim to compute VIF and the tolerance the same as for OLS regression. The acceptable cut-off for the VIF is < 5 with a tolerance of > 0.20 (Hair et al., 2011; Hair et al., 2012a; Henseler et al., 2009; Latan & Ghozali, 2012a). However, some literatures suggests that the value of VIF can be acceptable if it is in the range of < to achieve a stable estimate (Kock, 2012; Latan & Ghozali, 2013). Hitherto, PLS-SEM software that can estimate the optimal VIF value is WarpPLS-SEM (Kock, 2012). Other programs that can compute it such as IBM SPSS use the following: 13

14 Table 1 shows the description of the PLS-SEM application that describes what should be reported from the outer model PLS-SEM for every type of model. Table 1 Descriptions of the PLS-SEM applications and reporting of the outer PLS-SEM model Characteristics Recommendation / Rule of Thumb References I. Model and Research Characteristics Research objective Reason for choosing PLS-SEM analysis The purpose of the research should be clarified either it is exploratory or confirmatory research in order to obtain precise model criteria. The reason for choosing PLS-SEM analysis should be explained before starting the model analysis. (Latan & Ghozali, 2012a) (Chin, 2010; Gefen et al., 2011; Ringle et al., 2012) Single-item construct Observed variable Item/indicator description There is no evaluation for the outer model for the single-item construct in the structural model. The single-item construct may provide an underestimation in the inner model. There is no PLS-SEM evaluation for the outer model for the observed variable. Report the list for all the construct indicators in the appendix. (Diamantopoulos et al., 2012; Hair et al., 2012c; Ringle et al., 2012) (Latan & Ghozali, 2012a) (Hair et al., 2012a) Control variable Data and Sampling Characteristics Data characteristics Scale estimation If there is a control variable in the model, should be noted. If the research uses secondary data, the outer model evaluation does not need to be reported. This matter also should provide additional information through footnotes. The outer model should not be evaluated if the construct uses scale estimates such as categorical or binary. Again have to add footnotes and do not needed to conduct the outer PLS-SEM model evaluation. In addition, such estimation is not recommended for the endogenous variables. (Latan & Ghozali, 2012b; Rigdon, 2012) (Hair et al., 2012a; 2012c; Henseler, 2010) - 14

15 The power and total sample Provide a correlation/covariance matrix or raw data in the appendix Setting the algorithm and software features Weighting scheme Data metric Total maximum iteration Abort criterion Starting value for the initial weight Software features Reporting outer model result: mode A Indicator reliability Internal consistency reliability Convergent validity Discriminant validity Cross loadings Item remove In general, the data sample should be 10 more than the total path/predictor in the model. Statistical power can be done by using the Cohen table. In general, the path weighting scheme is strongly recommended. The standardized value is (Mean 0, Var 1) The standard maximum iteration is 300 and, if the model is not so complex, it can be set for 200 iterations. The number is 1.0E-5. Use the value 1 for each of outer weight Report the software name and version Recommended > 0.6 for exploratory research and > 0.7 for confirmatory research. - The cut-off value for composite reliability is > 0.6 for exploratory research and > 0.7 for confirmatory research. The Cronbach alpha is not suggested for distinguishing. The Average Variance Extracted (AVE) is 0.5 SQRT AVE > correlation For each construct is suggested to > 0.70 If some item has been dropped to achieve a model fit give additional information via footnotes. For a second-order model, remove the item in the first-order and also in the second-order (Barclay et al., 1995; Chin, 2010; Hair et al., 2012c) (Hair et al., 2012a; Ringle et al., 2012) (Esposito Vinzi et al., 2010; Garson, 2012; Latan & Ghozali, 2012a; Ringle et al., 2005) (Wold, 1982) (Henseler, 2010; Ringle et al., 2005) (Chin, 2010; Latan & Ghozali, 2012a) (Chin, 1998b; Hair et al., 2011; Latan & Ghozali, 2013) (Chin, 1998b; 2010; Götz et al., 2010; Hair et al., 2012a; Latan & Ghozali, 2012a) (Chin, 1998b; Fornell & Larcker, 1981, Lee et al. 2011) (Chin, 1998b; Gefen et al., 2011; Latan & Ghozali, 2012a) 15

16 Path diagram Reporting outer model result: mode B Verify the construct s indicator Significant weight Collinearity Construct removal Reveal the path diagram from the PLS-SEM algorithm analysis Report the indicator weight The t-value or p-value as well as standard error generated from bootstrap procedure. The cut-off value for VIF should be < 5 with the tolerance > 2.0. A stabilised estimation is suggested as ranging If a construct has been drop due to collinearity the problem should be revealed with footnotes for more information. - (Hair et al., 2012a) (Chin, 1998b; Götz et al., 2010; Hair et al., 2011; Henseler et al., 2009; Kock, 2012; Latan & Ghozali, 2012a) Reporting the PLS-SEM six inner model dimensions There are six examples for inner model dimensions. They are the recursive, interaction, intervening, second-order, heterogeneity and multi-group models. Each model is represented in the following sections Reporting the result inner for the recursive model analysis The recursive model is the same as the structural model that has only one direction of causality and does not contain a direction of loop feedback. The model consists of exogenous and endogenous variables with the construct s indicators that can be generated through modes A or B. The inner recursive model is shown in Figure 2. 16

17 δ1 X1 δ2 δ3 X2 X3 ξ1 ϒ11 zeta1 Y1 Y2 ε1 ε2 δ4 δ5 X4 X5 ξ2 ϒ22 η Y3 Y4 ε3 ε4 δ6 X6 Y5 ε5 δ7 X7 ϒ33 Y6 ε6 δ8 X8 ξ3 Y7 ε7 δ9 X9 Figure 2. The inner recursive model First, reporting the analysis for the inner recursive model can be analysed from the Adjusted R-square for each endogenous variable. This adjusted R-square is revealed for its strong prediction. The interpretation is same as for OLS regression, the bigger the value of the Adjusted R-square, the stronger the model predictor for the variance explanation of the endogenous variable. Adjusted R-Square values of 0.25, 0.40 and 0.75 show weak, moderate and strong models, respectively. The Adjusted R-square is more recommended for use than the R-square. This is because, the value of the additional one exogenous variable is not necessarily changed, either increased or decreased. However, no available software evaluates the Adjusted R-square. Therefore, this measurement can be computed manually as follows: 17

18 Where: R 2 is the R-square, n is the total sample and k is the total predictor. How large the influenced of the exogenous variable on the endogenous variable can be computed by the effect size. To date, the only PLS-SEM software that computes the optimal effect size value is the WarpPLS-SEM (Kock, 2012). It can also be estimated manually as follows: Where; 2 Rincluded and 2 R excluded are the R-Squares from the latent endogenous variable and the latent predictor variable has been exported from the structural model. Value of f 2 of 0.02, 0.15 and 0.35 are the same as been recommended by Cohen (1988) for the definition of twofold operational regression. Nevertheless, if the model is not so multifaceted but comprises one exogenous and endogenous variable, the effect size value is not vital to compute because it is the same as R-square. Besides the Adjusted R-Squares, the value from the structural model evaluation can also be computed through the Q 2 predictive relevance, often called predictive sample reuse (Geisser, 1974; Stone, 1974). This technique can be represent the synthesis from the cross-validation function and function fitting which is between the observed variable prediction and parameter construct estimation. This approach can be done with the blindfold procedure. The optimal value of the Q 2 predictive relevance can be gauge from WarpPLS-SEM (Kock, 2012). This value also can be worked out manually that as follows: Where D is an omission distance, E is the sum of squares of the prediction error and O is the sum of squares errors using the mean for prediction. If Q 2 > 0, it shows that the model has 18

19 predictive relevance, but if Q 2 < 0, it explains that the model has less predictive relevance. This is same as the f 2 value; the changes of Q 2 can confer relatively towards the structural model that can be assessed as follows: The q 2 predictive relevance of 0.02, 0.15 and 0.35 signify a weak, moderate and strong model, respectively. In addition, inner model recursive analysis can be further computed by the redundancy and the goodness of fit (GoF) model developed by Tenenhaus et. al (2004). The formula is: Redundancy = GoF = The Redundancy value represents the level of the structural model for the endogenous variable. The values of 0.125, 0.25 and denote as fit, moderate and large model, respectively. The value for the GoF of 0.35, 0.50 and 0.61 shows that the model is fit, moderate and big, respectively (Latan & Ghozali, 2013, p.73). Table 2 below provides guidance for the inner model recursive indication. Table 2 Description guidance for the inner recursive model Characteristic Recommendation / Rule of Thumb References Setting bootstrapping and blindfolding Sign changes option If the program is such as PLS-SEM-Graph (Chin, 2003) or SmartPLS-SEM (Ringle et al., 2005), the option for sign changes should be reported. In general, it has been suggested to used no sign changes or individual sign changes. (Garson, 2012; Henseler et al., 2009; Latan & Ghozali, 2012a) 19

20 Total cases for the bootstrap Total sample for the bootstrap Cross-Validated Omission distance Reporting Inner model result: Recursive Model Adjusted R-Square Effect Size f 2 Q 2 and q 2 Predictive relevance T-statistic or P- value Redundancy GoF Common Method Variance (CMV) Path diagram The total cases are same as the number of the total observation data. Total resamples are between which is larger than the original samples. The bootstrap confidence interval should be as large as Noted as CV-Redundancy 5 d 10 The value of 0.25, 0.50 and 0.75 denote as weak, moderate and strong, respectively. The value of 0.02, 0.15 and 0.35 denote as weak, moderate and strong, respectively. Use the blindfold procedures. Q 2 > 0 represents the model has predictive relevance with model verification as weak, moderate and strong, 0.02, 0.15 and 0.35, respectively. Bootstrapping is applied for the significance of the path coefficient with two-tails of 5% = 1.96 The values 0.125, 0.25 and denote the model fit for the level of the endogenous variable is small, moderate or big, respectively. The values 0.35, 0.50 and 0.61 shows that the model as a whole is small, moderate large, respectively. The CMV analysis with the approach from the Measured Latent Marker Variable (MLMV) should be reported. The value of the path diagram is from the bootstrapping procedure. (Hair et al., 2011; Latan & Ghozali, 2012a) (Chin, 1998b, 2003; 2010; Efron et al., 2004, 2012 ; Geisser, 1974; Kock, 2012; Latan & Ghozali, 2012a, 2012b; Stone, 1974) (Hair et al., 2011; Latan & Ghozali, 2013) (Cohen, 1988; Cohen, 1992) (Chin, 1998b; 2010; Latan & Ghozali, 2012a) (Chin, 1998b; Chin, 2010; Henseler et al., 2009; Latan & Ghozali, 2012a) - (Latan & Ghozali, 2013) (Chin et al., 2012b; 2012c; Gefen et al., 2011) - 20

21 1.4.2 Reporting results of inner interaction model analysis In principle, the moderation effects demonstrate the interaction between the exogenous variable (predictor) and the endogenous variable (Henseler & Chin, 2010, p.83; Latan & Ghozali, 2012b, p.201). Figure 3 illustrates the model interaction. Variable Moderator (M) Variable Exogenous (X) b a Variable Endogenous (Y) Figure 3. Inner interaction model analysis In PLS-SEM, four approaches can be tested for moderation effects. They are the hybrid approach (Wold, 1982), product indicator approach (Chin et al., 2003), orthogonalizing approach (Little et al., 2006) and the two-stage approach (Henseler & Chin, 2010). Each the approach has its own purpose. For example, the two-stage approach is used if the model represents as mode B or the ortogonalizing approach is for handling the collinearity problem. Therefore, the choice of the interaction method should be reported. Henseler and Chin (2010, p ) claim that the technique of Monte Carlo simulation is summarized into some conditions. The conditions are as follows: 1. Compared with the others the accuracy parameter from the orthogonalizing approach provides the best value analysis especially for small sample sizes. It can be computed using the Mean Relative Bias (MRB). 21

22 2. The statistical power from the hybrid and two-stage approach give the best estimate value compared with the other approaches. 3. The prediction accuracy from the orthogonalizing and product indicator approaches indicates the best value analysis compared with the other approaches. In essence, the analysis of inner interaction model is slightly similar to the analysis of the recursive model. The analyses begin from the value of Adjusted R-square to the estimation of the GoF model. Therefore, we do not need to repeat the explanation in the previous section. The only difference concerns the formula for the effect size value. The effect size for the interaction model can be estimated from: The explanation for the effect size is the same as before where the values of 0.02, 0.15 and 0.35 show that the model is weak, moderate and strong, respectively. The summary for the inner interaction model descriptions are in Table 3. Table 3 Descriptions guidance for the inner interaction model Characteristic Recommendation / Rule of Thumb References Reporting inner model results: interaction model The interaction approaches Category of the moderator variable Report the interaction approach (i.e., hybrid product indicator, orthogonalizing and two-stage approach). If the moderator variable is categorised as categorical/dummy, multi-group analysis is applied. This matter also needs additional information through footnotes. - - Effect interaction size The values 0.02, 0.15 and 0.35 denote as weak, moderate and strong, respectively. (Chin et al., 2003; Latan & Ghozali, 2012a) Note: The descriptions in Table 2 also apply to the inner interaction model. 22

23 1.4.3 Reporting the results for the inner intervening model analysis The mediation/intervention effects are the relationships between the exogenous and endogenous construct as influenced by the mediator variable. The relationships between the exogenous and endogenous construct do not directly influence each other but might be influenced by other variables (intervening) (Latan & Ghozali, 2013, p.142). Figure 4 demonstrates the mediation/intervention effect s model: Mediator Variable Exogenous Variable Endogenous Variable Figure 4.The mediation/intervention effects model In principle, the mediation/intervention model is similar to the recursive model analysis. The difference is only about the significance of the mediation effects. The only PLS-SEM software that can compute significant mediation effects is WarpPLS-SEM (Kock, 2012). It can also be compute by the Sobel Test, which is as follows: 23

24 Where a, b, and c are the values of the path coefficients and and are the standard errors for the path coefficients a and b. The path coefficients used for this Sobel test formula have been supplied from the bootstrapping procedure. The influence of the mediation/indirect effects can be estimated using the formula of Variance Accounted For (VAF). This VAF value is between 0 to 1 (i.e. the higher the VAF value, the larger the influence of the mediation effect). The VAF formula is: VAF Therefore, the summary descriptions for the inner mediation/intervention effects model are given in Table 4. Table 4 Descriptions guidance for the inner mediation/intervention model Characteristic Recommendation / Rule of Thumb References Reporting inner model results: intervening model Significance of the mediation indirect effect Variance Accounted For (VAF) Significance value of two-tail at 5% = 1.96 Each VAF value should be reported for each mediation/indirect effect Note: The descriptions in Table 2 also apply to the inner mediating/intervening model. (Kock, 2012) (Latan & Ghozali, 2013) Reporting the results of the inner second-order order analysis The second-order model, often recognised as the hierarchical component model, is the type model from the second order s dimensions constructs. Figure 5 illustrates the second-order model. 24

25 ξ1 ξ2 ξ3 ξ η ξ4 ξ5 Figure 5. The inner second-order model In general, there are four types of second order constructs. They are: (i) reflective first order and reflective second order (Type I), (ii) reflective first-order and formative second-order (Type II), (iii) formative first-order and reflective second-order (Type III), and (iv) formative first-order and formative second-order (Type IV). There are two approaches for the secondorder model analysis. They are repeated-indicator approach and two-stage approach (Ringle et al., 2012; Wetzels et al., 2009; Wold, 1982). For that reason, the approach applied should be reported. Recently, the study by Ringle et al. (2012, p.6) found that only 7 of 25 studies from the MIS Quarterly journal from 1992 to 2011 reported in detail about the second-order model, including all the analysis procedures. In principle, the way to report the outcome of the second-order model is slightly similar to the recursive model analysis. Therefore, Table 1.2 is a guideline for reporting the inner secondorder model. Only a few descriptions should be added to complete the report for the inner second-order model analysis. The additional descriptions are given in Table 5. 25

26 Table 5 Descriptions guidance for the inner second-order model Characteristic Recommendations / Rule of Thumb References Reporting inner model result: second-order model Type of approach The position of the second-order construct If the model is category Type I or Type IV, the repeated indicator approach is applied. If the model is categorized as Type II or Type III, the two-stage approach is used and the chosen type should be reported. If the second-order construct is from the endogenous variable, it is strongly recommended applying a combination approach (i.e., a combination of the repeated indicator and twostage approach). (Latan & Ghozali, 2013; Ringle et al., 2012; Wetzels et al., 2009; Wold, 1982) (Ringle et al., 2012) Removal from the construct dimension If a construct dimension is not from the type of second-order model and this would be cause for removal. Therefore this also should be stated. However, the construct dimension categorized as Type II and Type IV must hold if the factor loading is > 0.5. Note: The descriptions in Table 2 also apply for reporting the inner second-order model Reporting the results of the inner model for heterogeneity analysis Many researchers assumed that data s features in structural model studies are homogenous. This assumption is totally inappropriate and irrelevant if the collected data are characterized as unit or segmentation. Therefore, biased analysis will occur if the data are truly categorized as heterogonous and treated as homogenous. Several methods can overcome this problem. They are by applying FIMIX-PLS (SmartPLS), PATHMOX (R-CRAN), PLS-Typological (SPAD-PLS-SEM), PLS-GAS (R-CRAN) or REBUS-PLS (XLSTAT-PLSPM). This problem also needs to be reported to the reader, including the program used. In essence, the heterogeneity model analysis is like the recursive model analysis. The only difference is the outcome from the setting algorithm. Hence, again the descriptions from the Table 2 are used 26

27 for the report s guidelines. There are some additional descriptions to be added for the inner heterogeneity model. They can be seen in the Table 6. Table 6 Descriptions guidance for the inner heterogeneity model analysis Characteristic Recommendation / Rule of Thumb References Reporting inner model result: heterogeneity model Type of approach Setting the algorithm Segmentation outcome The type of approach for the heterogeneous model analysis including the software program should be disclosed. Reporting the algorithm such as the total segmentation (N) > 3, iteration maximum and stop criterion < The product analysis of AIC, CAIC and EN from the FIMIX-PLS-SEM are reported. The REBUS- PLS-SEM is from the outcome of the dendrogram. Note: The description in Table2 also apply for the reporting the inner heterogeneous model. - (Ringle et al., 2010; 2011) (Esposito Vinzi et al., 2008; Sarstedt et al. 2011a) Reporting the results of the inner model for multi-group analysis Multi-group analysis, oftener cognised as multisampling analysis, for the purpose of comparing two or more data sets. In PLS-SEM-SEM, multi-group analysis consists of five classifications. They are the parametric, permutation test, non-parametric, moderating, and OTG. As before, all the approaches that have been applied, particularly in PLS-SEM multigroup analysis, must be disclosed. In addition, in order to report the analysis, the descriptions are same as for the recursive model analysis. The differences are with regard to the data groups. First, after estimating the PLS-SEM outer model, the group data should be split. Then, the total resamples should be same while conducting the bootstrapping procedure. Besides that, the most essential issue concern the variance between the groups. To be specific, the group data variances must be recognised as either the same or not (Chin et al., 2012a). According to Ringle et al. (Ringle et al., 2012, p.x), three of six studies report the 27

28 measurement of invariance. This invariance measurement in the PLS-SEM multi-group analysis must be stated in the report. Chin (2000) suggests that the Smith-Satterthwaite test be applied if the situation that the group s variance is different. Again with the same discussion from the previous section, the guidelines from Table 2 are used and only a few extra descriptions. Table 7 gives is the additional descriptions for the inner multi-group model analysis. Table 7 Descriptions guidance for the inner multi-group model Characteristic Recommendation / Rule of Thumb References Reporting inner model result:multigroup model Type of approach Total resamples in the bootstrap The type of approach for the multi-group model analysis including the software program should be disclosed. The total resamples for each group of samples in the bootstrap procedure should be same. (Chin et al., 2012a; Latan & Ghozali, 2012a) - Invariance measurement Total group samples > 2 Report the invariance measurement, the Smith- Satterthwaite test is applied if the group is invariant. If the group sample is more than two, the OTG approach can be applied. (Chin, 2000; Chin et al., 2012a; Latan & Ghozali, 2013) (Sarstedt et al., 2011b) Note: The description in Table 2 also apply for reporting the inner multi-group model analysis 10. Conclusion Recently, according the studies by Hair et al. (2012a; 2012c) and Ringle et al. (2012), it can summarized that, as a whole, most researchers have not understood completely and precisely the way of reporting PLS-SEM analysis. This paper is a platform to explain a comprehensive understanding of the field of PLS-SEM study. This study has concluded with three 28

29 implications. First, this study provides the inclusive guidelines and recommendations for every researcher and readers on the accurate way to report PLS-SEM analysis. These description guidelines provide six examples of the PLS-SEM model dimensions that have commonly been used. Second, all-inclusive journal publications have been included in this study for useful support analysis. Finally, future opportunities for research in the PLS-SEM field should be developed to improve PLS-SEM study. Acknowledgements The author thanks Professor Imam Ghozali (Diponegoro University) for his helpful comments that improved this paper. References Anderson, J. C., and Gerbing, D. W Structural Equation Modelling in Practice: A Review and Recommended Two-Step Approach, Psychological Bulletin (103:3), pp Bagozzi, R. P., and Yi, Y On the evaluation of structural equation models, Journal of the Academy of Marketing Science (16:1), pp Barclay, D., Higgins, C., and Thompson, R The Partial Least Squares (PLS) Approach to Causal Modelling: Personal Computer Adoption and Use as an Illustration, Technology Studies (2:2), pp Boomsma, A Reporting analyses of covariance structures, Structural Equation Modelling (7), pp Boomsma, A., Hoyle, R. H., and Panter, A.T The Structural Equation Modelling Research Report, In R. Hoyle (Ed.), Handbook of Structural Equation Modelling, Guilford Press, pp Chin, W. W. 1998a. Issues and opinions on structural equation modelling, MIS Quarterly (22:1), pp. vii-xvi. Chin, W. W. 1998b. The partial least squares approach for structural equation modelling, In G. A. Marcoulides (Ed.), Modern methods for business research (pp ). London: Lawrence Erlbaum Associates. Chin, W.W. and Newsted, P.R "Structural equation modelling analysis with small samples using partial least squares," In R. Hoyle, (Ed.), Statistical Strategies for Small Sample Research, Sage Publications, Thousand Oaks,CA, pp

30 Chin W.W Frequently Asked Questions Partial Least Squares & PLS-Graph. URL Chin, W. W PLS Graph 3.0. Houston: Soft Modelling Inc. Chin, W. W., Marcolin, B. L., and Newsted, P. R A partial least squares latent variable modelling approach for measuring interaction effects: Results from a Monte Carlo simulation study and an electronic-mail emotion/ adoption study, Information systems research (14:2), pp Chin, W. W How to write up and report PLS analyses. In V.E. Vinzi, W. W. Chin, J. Henseler, & H. Wang (Eds.), Handbook of partial least squares: Concepts, methods and applications in marketing and related fields (pp ).Berlin: Springer. Chin, W.W., Mills, A.M., Steel, D.J., and Schwarz, A. 2012a. Multi-Group Invariance Testing: An Illustrative Comparison of PLS Permutation and Covariance-Based SEM Invariance Analysis, Proceedings: 7th International Conference on Partial Least Squares and Related Methods, Houston, Texas USA, pp Chin, W.W., Thathcer, J.B., Wright, R.T., Steel, D.J. 2012b. Controlling for Common Method Variance in PLS Analysis: The Measured Latent Marker Variable Approach, Proceedings: 7th International Conference on Partial Least Squares and Related Methods, Houston, Texas USA, pp Chin, W.W., Thathcer, J.B., and Wright, R.T. 2012c. Assessing Common Method Bias: Problem with the ULMC Technique," MIS Quarterly (36:3), pp Cohen, J Statistical power analysis for the behavioral sciences. Hillsdale, New Jersey: Lawrence Erlbaum Associates. Cohen, J A Power Primer, Psychological Bulletin (112:1), pp Diamantopoulos, A., Sarstedt, M., Fuchs, C., Kaiser, S., and Wilczynski, P Guidelines for Choosing Between Multi-Item and Single-Item Scales for Construct Measurement: A Predictive Validity Perspective, Journal of the Academy of Marketing Science (40), pp Dijkstra, T. K Some Comments on Maximum Likelihood and Partial Least Squares Methods, Journal of Econometrics (22:1/2), pp Dijkstra, T. K., and Schermelleh-Engel, K Consistent Partial Least Squares for Nonlinear Structural Equation Models, Psychometrika (In Press), pp Dijkstra, T. K., and Henseler, J Consistent and Asymptotically Normal PLS Estimators for Linear Structural Equations. Working Paper, pp Efron, B.,and Tibshirani,R.J An introduction to the bootstrap. New York, NY: Chapman Hall. Efron, B., Rogosa, D., and Tibshirani, R Resampling methods of estimation. In N.J. Smelser, & P.B. Baltes (Eds.). International Encyclopedia of the Social & Behavioral Sciences (pp ). New York, NY: Elsevier. 30