How to build a PLS-SEM model using AMOS?
Partial Least Square Structural Equation Modeling (PLS-SEM) is a statistical multivariate analysis method which combines linear relationship and regression analysis methodologies. In today’s world, people have to deal with a large amount of data for decision-making. The PLS-SEM model enables the discovery of new findings in complex data. This model is different from other SEM models like Confirmatory Factor Analysis (CFA) and path analysis such that it not only develops a linkage between latent and observed variables but also between multiple latent variables. This article demonstrates through a case study how to use the PLS-SEM model for examining an indirect linear relationship.
PLS-SEM to examine the relationship between variables of sustainability
Recently businesses have started to focus on the concept of sustainability for economic development. Sustainability has three main dimensions (Gelashvili et al., 2021):
- economic sustainability
- social sustainability
- environmental sustainability.
All these three are interdependent. Thus, there is a presence of a relationship between environmental, social, and economic sustainability. We examined the perception of 300 people from the Delhi NCR region regarding sustainability and its dimensions which are as follows:
Path building using PLS-SEM for assessing the impact
We used the PLS-SEM model in this case because it helps us understand the direct as well as the indirect linkage between these three dimensions of sustainability. The components of each sustainability are coded as follows:
- economic sustainability factors: E1 to E3
- social sustainability factors: S1 to S2,
- environmental sustainability factors: ES1 to ES2
The linkage has been developed wherein each sustainability type (latent variable) is computed with its components (observed variables). The relationship between latent variables is stated by including social sustainability as mediating variable. This is represented below.
After this, the first step is to examine the efficiency of the results. Hence, we perform the reliability and validity test.
Reliability and validity in PLS-SEM
Reliability and validity help us evaluate the suitability of variables in measuring the impact. After running the test on SPSS Amos, the results for the composite reliability, internal consistency, convergent validity, and discriminant validity are shown in the below table.
| Construct | CR | AVE | Cronbach alpha | Sq (AVE) |
|---|---|---|---|---|
| Economic Sustainability | 0.89 | 0.88 | 0.88 | 0.94 |
| Social Sustainability | 0.79 | 0.78 | 0.76 | 0.88 |
| Environmental Sustainability | 0.87 | 0.89 | 0.85 | 0.94 |
Internal consistency
It is the reliability method wherein the linkage between the constructs is assessed to understand the effectiveness of its components in measuring that variable. For this, the Cronbach alpha test is used. Herein, the value of economic sustainability is 0.88, social sustainability is 0.76, and even environmental sustainability is 0.85. As each construct value is more than the required value of 0.7, there is a presence of internal consistency in the model.
Convergent validity
It is the method of determining the presence of any close relationship of the variable with other variables or the statements measuring the construct. The average variance extracted (AVE) enables convergent validity determination. With the value of economic sustainability as 0.88, social sustainability as 0.78, and even environmental sustainability as 0.89 which are all greater than 0.5. The examination represents that convergent validity is present in the model.
Composite reliability
It is another reliability measure used for understanding the significance of using any construct in the model. The value of composite reliability for economic sustainability is 0.89, social sustainability is 0.79, and even environmental sustainability is 0.87 which are all greater than the required value of 0.7. Thus, the model has composite reliability.
| Economic Sustainability | Environmental Sustainability | Social Sustainability | |
|---|---|---|---|
| Economic Sustainability | 0.94 | ||
| Environmental Sustainability | 0.80 | 0.94 | |
| Social Sustainability | 0.69 | 0.70 | 0.88 |
Discriminant validity
It is the method of highlighting each construct’s difference from other constructs used in the model. AVE value for economic sustainability is 0.94, environmental sustainability is 0.94 and social sustainability is 0.88 which are greater than correlation values (i.e. 0.80 for environment and economic sustainability, 0.69 for social and economic sustainability, and 0.70 for environmental and social sustainability). Thus, there is the existence of discriminant validity in the model.
As all the criteria for reliability and validity are being met, the model is reliable and valid. We can proceed with the next step, i.e. examining model fitness.
Model fitness examination
Model fitness is the method used for assessing the efficiency of the model. It depicts the linkage between variables. The results are shown in the below table.
The above table represents that the value of CMIN/Df is 3.59 < 5, GFI is 0.971 > 0.90, AGFI is 0.91 > 0.90 and RMSEA is 0.09 < 0.10. As all the desired values required for absolute fitness derivation are met, thus, the model is absolutely fit. For the incremental fitness measurement, the value of NFI is 0.98 > 0.9, CFI is 0.98 > 0.9, TLI is 0.97 > 0.9, and IFI is 0.98 > 0.9. Since all the measures of incremental fitness values are within the required limit, the model represents the presence of incremental fitness. Lastly, for parsimonious fitness the value of PGFI is 0.38 < 0.5, PCFI is 0.51 > 0.5, and PNFI is 0.51 > 0.5. With the majority of measures value within the range of adequate fitness, the model depicts parsimonious fitness presence. Hence, as the model fulfils the criteria for the majority of fitness indices, it is absolutely, incrementally, and parsimoniously fit and could be used for impact assessment.
Impact analysis
The PLS-SEM model shows the linkage between variables with reliability, validity, and model fitness assessment. In this case, we test the impact of economic or social sustainability on environmental or social sustainability. The hypothesis is as follows.
H01: There is no significant impact present between different sustainability dimensions in the model
HA1: There is a presence of significant impact between different sustainability dimensions in the model
The significance level was set at 5%. The results are shown below.
| Dependent variable | Independent variable | Estimate | S.E. | C.R. | P |
|---|---|---|---|---|---|
| Social Sustainability | Economic sustainability | 0.84 | 0.05 | 16.00 | 0.00 |
| Environmental Sustainability | Social Sustainability | 0.52 | 0.20 | 2.57 | 0.01 |
| Environment Sustainability | Economic Sustainability | 0.50 | 0.18 | 2.81 | 0.01 |
In the above table, the standard error value of the variables is more than 0.1. However, as the values are still approximately close to 0, there are fewer biases present in the model. The p-value of each variable represents that the values are less than 0.05 i.e. 0.00, 0.01, and 0.01. CR values are 16, 2.58, and 2.81 which are more than 1.96 (Z-value at 5%). Thus the null hypothesis (H0) is rejected.
After testing the hypothesis, we need to assess the impact. We can draw the following observations from our data:
- Relationship between economic and social sustainability: With a 1% rise in economic sustainability social sustainability improves by 0.84%.
- Relationship between social and environmental sustainability: With a 1% rise in social sustainability the environmental sustainability changes by 0.52%.
- Relationship between economic and environmental sustainability: A 1% increase in economic sustainability results in improving environmental sustainability by 0.50%.
Hence, dimensions of sustainability though are determined to have positive contributions but the impact assessment defines that economic sustainability has more contribution to social sustainability compared to environmental sustainability.
Testing the impact of a mediating variable
After successfully establishing an impact between the variables, we will check the indirect effect using social sustainability as mediating variable. The function of each variable and the result of the test is shown below.
| Dependent variable | Independent variable | Mediating variable | Direct effect | Indirect effect |
|---|---|---|---|---|
| Environmental Sustainability | Economic Sustainability | Social Sustainability | 0.50** | 0.44** |
In the above table, the values represent that economic sustainability direct impacts environmental sustainability and economic sustainability impacts environmental sustainability via social sustainability; both are significant and positive. However, as the effective value for direct effect is 0.50 > 0.44 (indirect effect) value, social sustainability partially contributes as a mediating factor between economic and environmental sustainability. However, the direct influence of economic sustainability is more on environmental sustainability.
Why PLS-SEM method?
The PLS-SEM model is popular in SEM for assessing the complex relationship between variables. In the above case, PLS-SEM was most suitable to examine the indirect effects and understand relationships even between latent variables. Our analysis shows that economic sustainability affects environmental sustainability directly as well as indirectly (through social sustainability). But the contribution of direct influence is more. Alternatively, path analysis could have been applied in this case because it has only one mediating factor. However, in cases where more than one mediating or moderating variable is involved, PLS-SEM works perfectly.
References
- Gelashvili, V., Martínez-Navalón, J.-G., & Saura, J. R. (2021). Using Partial Least Squares Structural Equation Modeling to Measure the Moderating Effect of Gender : An Empirical Study. Mathematics.
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