1. Using the SmartPLS Software “Structural Model Assessment”
Joe F. Hair, Jr.
Founder & Senior Scholar
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2. Structural Model Assessment
Once the construct measures have been confirmed as reliable and valid, the next step is to assess the structural model results. This involves examining the model’s predictive capabilities and the relationships between the constructs. Exhibit 6.1 (next slide) shows a systematic approach to the assessment of structural model results.
Before assessing the structural model, you must examine the structural model for collinearity (Step 1). The reason is that the estimation of path coefficients in the structural model is based on OLS regressions of each endogenous latent variable on its corresponding predecessor constructs. Just as in a regular multiple regression, the path coefficients may be biased if the estimation involves significant levels of collinearity among the predictor constructs.
After checking for collinearity, the key criteria for assessing the structural model in PLS-SEM are: Step 2 – the significance of the path coefficients, Step 3 – the level of the R² values, Step 4 – the f² effect size, and Step 5 – the predictive relevance (Q² & the q² effect size).
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4. Step 1: Collinearity Assessment
To assess collinearity, we apply the same measures as in the evaluation of formative measurement model indicators (i.e., tolerance and VIF values). To do so, we need to examine each set of predictor constructs separately for each subpart of the structural model. For instance, in the model shown in Exhibit 6.2 (next slide), Y1 and Y2 jointly explain Y3. Likewise, Y2 and Y3 act as predictors of Y4. Therefore, you need to check whether there are significant levels of collinearity between each set of predictor variables (constructs). In other words, you need to check the collinearity between Y1 and Y2 as well as between Y2 and Y3.
Similar to the assessment of formative measurement model indicators, we consider tolerance levels below 0.20 (VIF above 5.00) in the predictor constructs as indicative of collinearity that is too high. If collinearity is exceeds these thresholds, you should consider eliminating constructs, merging predictors into a single construct, or creating higher-order constructs to deal with collinearity problems.
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6. Evaluating Construct Collinearity – Extended Reputation Model
The following sets of (predictor) constructs are run to assess collinearity: (1) ATTR, CSOR, PERF, and QUAL as predictors of COMP; (2) COMP and LIKE as predictors of CUSA; and (3) COMP, LIKE, and CUSA as predictors of CUSL.
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7. Evaluating Construct Collinearity – Extended Reputation Model.
To assess construct collinearity, run the extended reputation model and open the default report by going to Menu → Report → Default Report. Next, you need to extract the latent variable scores from the default report, which you can find under PLS → Calculation Results → Latent Variable Scores. The scores are shown on this slide. Copy these scores to an SPSS file to run this analysis (right click to highlight scores, left click to copy, then paste in SPSS).
Using the SPSS linear regression option, the following sets of (predictor) constructs are run to assess collinearity: (1) ATTR, CSOR, PERF, and QUAL as predictors of COMP; (2) COMP and LIKE as predictors of CUSA; and (3) COMP, LIKE, and CUSA as predictors of CUSL.
The SPSS steps for testing collinearity are shown on the next slide for the first regression run.
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8. Using SPSS to Assess Collinearity.
These are the four exogenous constructs that are being tested for multicollinearity.
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9. Evaluating Collinearity Among Exogenous Constructs
Below are the SPSS collinearity results from using ATTR, CSOR, PERF, and QUAL as predictors of COMP.
All VIF values are clearly below the threshold of 5.
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10. Evaluating Collinearity Among Exogenous Constructs
Below are the collinearity results from using COMP and LIKE as predictors of CUSA (top table), and COMP, LIKE and CUSA as predictors of CUSL (bottom table). All VIF values are well below the threshold of 5.
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11. Step 2: Assess Significance and Relevance of the Structural Model Relationships
After applying the PLS-SEM algorithm, estimates are obtained for the structural model relationships (the path coefficients), which represent the hypothesized relationships between the constructs.
The path coefficients for the structural model are shown in the next several slides. These results were obtained from the SmartPLS Default Report with the following sequence:
PLS Algorithm → Calculation Results → Path Coefficients
Before examining the sizes of the path coefficients we will first examine their significance. To do so, we must first run the Bootstrapping option.
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12. Reputation Model Results
– Path Coefficients –
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13. Bootstrapping Which path coefficients are significant?
Click here to run Bootstrapping
When you run bootstrapping select mean replacement for missing data, no sign changes, your actual sample size = cases, and 5,000 samples.
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14. . Bootstrapping Default Report – Significance of Path Coefficients
T Statistics are found beside the tab below.
The above results show the significance of the path coefficients. Recall that a T Statistic > 1.96 is significant with a two-tailed test, and >.98 is significant for a one-tailed test. Note: path coefficients are shown in Original Sample column.
The results indicate that all paths are statistically significant using a one-tailed test except COMP – CUSL. But eight of the thirteen structural paths are significant based on a two-tailed test.
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15. Obtaining the Default Report to Evaluate Path Coefficients
Click here to obtain Default Report
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16. SmartPLS Default Report – Path Coefficients
After examining the significance of relationships, it is important to assess the relevance of significant relationships. Path coefficients in the structural model may be significant, but their size may be so small that they do not warrant managerial attention.
Structural model path coefficients can be interpreted relative to one another. If one path coefficient is larger than another, its effect on the endogenous latent variable is greater. More specifically, the individual path coefficients of the path model can be interpreted just as the standardized beta coefficients in an OLS regression. These coefficients represent the estimated change in the endogenous construct for a unit change in a predictor construct.
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17. PLS Algorithm Default Report – Path Coefficients
Looking at the relative importance of the exogenous driver constructs in predicting the dependent construct perceived competence (COMP), we see that customer perceptions of the company’s quality of products and services (QUAL = ) is most important, followed by performance (PERF = ). In contrast, the perceived attractiveness (ATTR = ) and degree to which the company acts in socially conscious ways (CSOR = ) have very little influence on COMP. These last two drivers are, however, more important in predicting a company’s likeability (LIKE) – ATTR = and CSOR = , but the most important predictor of LIKE is QUAL (0.3800).
When you examine the endogenous likability construct (LIKE) you see that it is the primary driver (predictor) of customer satisfaction (CUSA = ), and a meaningful predictor of loyalty (CUSL = ), and COMP has little impact on CUSL (0.0057).
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18. Understanding Direct and Indirect Effects
Researchers are often interested in evaluating not only one construct’s direct effect on another but also its indirect effects via one or more mediating constructs. The sum of direct and indirect effects is referred to as the total effect.
In Exhibit 6.4 on the next slide, constructs Y1 and Y3 are linked by a direct effect (p13 = 0.20) In addition, there is an indirect effect between the two constructs via the mediating construct Y2. This indirect effect can be calculated as the product of the two effects p12 and p23 (p12 x p23 = 0.80 x 0.50 = 0.40). The total effect is 0.60, which is calculated as p13 + (p12 x p23) = (0.80 x 0.50) = = 0.60.
Although the direct effect of Y1 to Y3 is not very strong (i.e., 0.20), the total effect (both direct and indirect combined) is quite pronounced (i.e., 0.60), indicating the relevance of Y1 in explaining Y3. This type of result suggests that the direct relationship from Y1 to Y3 is mediated by Y2.
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19. .

20. PLS Algorithm Default Report – Total Effects = Sizes
The four driver constructs for loyalty (CUSL) are the exogenous constructs on the left side of the SEM model (these constructs are actionable because they are formative and thus of primary concern for the total effects analysis). The findings shown above indicate that quality (QUAL = ) has the strongest total effect on loyalty, followed by corporate social responsibility (CSOR = ), attractiveness (ATTR = ), and performance (PERF = ).
Note that there are three mediating constructs (COMP, CUSA & LIKE) between the exogenous driver constructs and the endogenous construct CUSL whose role must be considered, but they are relatively less actionable because they are reflective – not formative.
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21. Bootstrapping Default Report – Total Effects = Significance
You can also examine the significance of the total effects. Above are the T statistics for the total effects from the bootstrapping default report.
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22. .
Note: In the above table we only show the total effects for the four exogenous driver constructs to the satisfaction and loyalty endogenous constructs, because these are the outcomes the company is most interested in managing.
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23. To get outer weights:
PLS → Calculation Results → Outer Weights
Identifying actionable strategies based on sizes of exogenous construct weights.
By examining the outer weights of the construct indicators, we can identify which specific element of quality (QUAL) needs to be addressed. Note that qual_6 has the highest outer weight (0.3980). This survey question was “[the company] seems to be a reliable partner for customers” so perceptions of reliability should be enhanced and communicated to customers.