Confirmatory Composite Analysis (CCA) is a type of Structural Equation Modeling (SEM) analysis which develops composites to assess the relationship between variables. Composites are variables formulated with a linear combination of observed variables. The confirmatory composite analysis model assumes that only an observed variable helps to compute other variables and examine the linkage between them. It is best suited for studies wherein an aspect has many dimensions.
For example; social media consists of Twitter, Facebook, YouTube and Instagram. This article explains using a case study how to present the findings of the Confirmatory Composite Analysis test conducted in SPSS Amos software.
Assessing the impact of management practices on project effectiveness
Project management practices have become important for successful project completion and the attainment of goals and objectives. A survey of 189 employees’ on the perception of the contribution of different project management practices to project effectiveness was conducted. 5 dimensions were studied i.e, time management, scope management, resource management, cost management, and quality management. Thus, the linkage between the factors can be represented as follows.
Confirmatory Composite Analysis model for determining the project effectiveness
For examining the contribution of the 5 project management practices, which are the observed variables, they have been coded as P1, P2, P3, P4 and P5. Since project effectiveness depends upon these 5 practices, it is the dependent (latent) variable. With this, the CCA model is represented as follows.
Firstly, the Confirmatory Composite Analysis model for project management effectiveness model shows the extent to which each practice affects project effectiveness via factor loading.
For instance, 0.70 for P1, 0.79 for P2, and so on. But it is important to also examine the efficiency of the model. Therefore, conduct the reliability, validity and fitness of the model.
Testing the reliability and validity of the model
Using the factor loadings, error variance and Cronbach alpha value the composite reliability, convergent validity and internal consistency of the model were computed. Results of the validity and reliability are shown in the below table.
|Project Management Effectiveness||0.91||0.58||0.91|
The Cronbach’s alpha value measuring the internal consistency of the model helps in determining the stability of construct linkage with other variables. Here, the value is 0.91 which is more than the required level of 0.7, thus, internal consistency exists in the model.
Convergent validity measured by average variance extracted (AVE) defines the construct association with other variables and the respective statements used for measuring the construct. Herein the AVE value is 0.58 which is again more than 0.5, thus, convergent validity exists in the model.
Lastly, the composite reliability depicting the significance of constructs defines project management effectiveness and computation efficiency with associated project management practices. Herein, having a value of 0.91 which is more than 0.7, the composite reliability is maintained in the model.
Since internal consistency, convergent validity, and even composite reliability are present in the model, it is effective in measuring the construct. We can now use the model for further examination of developed the CCA model fitness.
Checking the model fitness
Model fitness examines the linkage between variables in the built Confirmatory Composite Analysis model. The fitness indices are shown in the below table.
|Name of category||Name of index||Index value||Adequate fit|
|Absolute fit measure||CMIN/Df||6.04||Less than 5|
|GFI||0.94||Greater than 0.90|
|AGFI||0.83||Greater than 0.90|
|RMSEA||0.16||Less than 0.10|
|Incremental fit measure||NFI||0.95||Greater than 0.90|
|CFI||0.96||Greater than 0.90|
|TLI||0.92||Greater than 0.90|
|IFI||0.96||Greater than 0.90|
|Parsimonious fit measure||PGFI||0.31||Greater than 0.50|
|PCFI||0.48||Greater than 0.50|
|PNFI||0.48||Greater than 0.50|
For the absolute fitness values, CMIN/Df is 6.04 > 5, GFI is 0.94 > 0.9, AGFI is 0.83 < 0.9 and even RMSEA is 0.16 > 0.10. As the majority of indices are not meeting the required criteria for absolute fitness, the model is not absolutely fit.
For incremental fitness measures, the NFI is 0.95 > 0.9, CFI is 0.96 > 0.9, TLI is 0.92 > 0.9 and even IFI is 0.96 > 0.9. All the index’s values are within the desired fitness criteria. Therefore the model is incrementally fit.
Lastly, parsimonious fitness measures define that PGFI is 0.32 < 0.5, PCFI is 0.48 < 0.5, and PNFI is 0.48 < 0.5. All the index’s values are outside the required limit, thus, fitness is not derived. As the model is only incrementally fit and not absolutely or parsimoniously, we need to modify the model to improve its fitness.
For this, we will first establish covariance linkage between the observed variables. With this, the fitness for the modified model is examined and the results of the model are shown below.
|Name of category||Name of index||Index value||Adequate fit|
|Absolute fit measure||CMIN/Df||3.37||Less than 5|
|GFI||0.97||Greater than 0.90|
|AGFI||0.90||Greater than 0.90|
|RMSEA||0.11||Less than 0.10|
|Incremental fit measure||NFI||0.98||Greater than 0.90|
|CFI||0.98||Greater than 0.90|
|TLI||0.96||Greater than 0.90|
|IFI||0.99||Greater than 0.90|
|Parsimonious fit measure||PGFI||0.26||Greater than 0.50|
|PCFI||0.39||Greater than 0.50|
|PNFI||0.39||Greater than 0.50|
In the above table, the value for absolute fitness measures defines CMIN.Df value is 3.37 < 5, GFI is 0.97 > 0.9, AGFI is 0.9 = 0.9, and RMSEA is 0.11 > 0.10 but close to it. As the majority of absolute fitness indices values are within the desired limit, the modified model is absolutely fit.
For the incremental fitness, NFI value is 0.98 > 0.9, CFI is 0.98 > 0.9, TLI is 0.96 > 0.9 and IFI is 0.99 > 0.9. All the incremental fitness indices value more than the required limit. Thus the modified model defines the presence of incremental fitness in the model.
Lastly, parsimonious fitness measures depict that PGFI is 0.26 < 0.5, PCFI is 0.39 < 0.5 and even PNFI is 0.39 < 0.5. As all the indices values of parsimonious indices are lower than the required limit, the model is still not parsimoniously fit.
Since the model has absolute fitness and incremental fitness, we can proceed with an examination of the linkage between the variables, i.e. project management practices and project effectiveness.
Computing the impact using the Confirmatory Composite Analysis model of SEM
Since we have established the reliability and validity of this mode, the linkage identified by the model is adequate. We examine the impact at a 5% level of significance. We will now test the hypothesis.
H01: Project management practices do not have a significant influence on the project effectiveness
HA1: Project management practices have a significant influence on the project effectiveness
The results of the contribution examination for the linkage are shown in the below table.
In the above table, the standard error value for all the dimensions of project management practices is less than 0.1. Since the value is more than 0.05, there is less biasness or error possibility in the model and hence the results derived from linkage development would be effective. Further, a p-value of 0.00 for all statements is less than the required 0.05 (at a 5% level of significance). Moreover, C.R. values are more than 1.96 (z-value at 5% level). Thus, the null hypothesis of having no significant influence of project management practices on project effectiveness is rejected.
The estimated value identifies the contribution. Since the value of each dimension is more than 0.5, we can conclude that project management practices have a positive contribution to project effectiveness. Cost management constitutes the major part followed by time management. Hence, for an organization’s project success, companies should majorly focus on cost and time management practices followed by quality and cost management.
The Confirmatory Composite Analysis model in SEM is not as popular as the other models like CFA and PLS-SEM. However, it is recommended when the aim is to check impact based on related dimensions and build linear relationships between variables. It is suitable for complex studies which involve a great number of variables that need to be broken down yet exhibit a holistic situation.
- Fraz, A., Waris, A., Afzal, S., Jamil, M., Tasweer, S., Shah, H., & Sultana, S. (2016). Effect of Project Management Practices on Project Success in Make-to-Order Manufacturing Organizations. Indian Journal of Science and Technology, 9(21). https://doi.org/10.17485/ijst/2016/v9i21/94818