Performing Confirmatory Composite Analysis (CCA) test using SPSS AMOS

By Riya Jain & Priya Chetty on May 19, 2022

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.

Impact of project management practices
Figure 1: Impact of project management practices

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.

Confirmatory Composite Analysis model for project management effectiveness
Figure 2: Confirmatory Composite Analysis model for project management effectiveness

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.

VariableCRAVECronbach alpha
Project Management Effectiveness0.910.580.91
Table 1: Reliability and validity of the model

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 categoryName of indexIndex valueAdequate fit
Absolute fit measureCMIN/Df6.04Less than 5
GFI0.94Greater than 0.90
AGFI0.83Greater than 0.90
RMSEA0.16Less than 0.10
Incremental fit measureNFI0.95Greater than 0.90
CFI0.96Greater than 0.90
TLI0.92Greater than 0.90
IFI0.96Greater than 0.90
Parsimonious fit measurePGFI0.31Greater than 0.50
PCFI0.48Greater than 0.50
PNFI0.48Greater than 0.50
Table 2: Original model fitness

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 categoryName of indexIndex valueAdequate fit
Absolute fit measureCMIN/Df3.37Less than 5
GFI0.97Greater than 0.90
AGFI0.90Greater than 0.90
RMSEA0.11Less than 0.10
Incremental fit measureNFI0.98Greater than 0.90
CFI0.98Greater than 0.90
TLI0.96Greater than 0.90
IFI0.99Greater than 0.90
Parsimonious fit measurePGFI0.26Greater than 0.50
PCFI0.39Greater than 0.50
PNFI0.39Greater than 0.50
Table 3: Final CCA model fitness indices

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.

Project EffectivenessEstimateS.E.C.R.P
Time management1.00   
Quality management0.950.0713.750.00
Cost management1.110.0714.990.00
Resource management0.950.0811.930.00
Scope management0.740.079.940.00
Table 4: Project management practices impact project effectiveness

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.

References

  • 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
NOTES

Priya is the co-founder and Managing Partner of Project Guru, a research and analytics firm based in Gurgaon. She is responsible for the human resource planning and operations functions. Her expertise in analytics has been used in a number of service-based industries like education and financial services.

Her foundational educational is from St. Xaviers High School (Mumbai). She also holds MBA degree in Marketing and Finance from the Indian Institute of Planning and Management, Delhi (2008).

Some of the notable projects she has worked on include:

  • Using systems thinking to improve sustainability in operations: A study carried out in Malaysia in partnership with Universiti Kuala Lumpur.
  • Assessing customer satisfaction with in-house doctors of Jiva Ayurveda (a project executed for the company)
  • Predicting the potential impact of green hydrogen microgirds (A project executed for the Government of South Africa)

She is a key contributor to the in-house research platform Knowledge Tank.

She currently holds over 300 citations from her contributions to the platform.

She has also been a guest speaker at various institutes such as JIMS (Delhi), BPIT (Delhi), and SVU (Tirupati).

 

I am a master's in Economics from Amity University. Having a keen interest in Econometrics and data analysis, I was a part of the Innovation Project of Daulat Ram College, Delhi University. My core expertise and interest are in environment-related issues. Apart from academics, I love music and exploring new places.

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