Building path analysis model in SEM with SPSS Amos
Path analysis is a statistical method used for establishing a causal relationship between variables. It is used when there are multiple variables in a study. It is an important Structural Equation Modeling (SEM) analysis type used commonly by researchers for testing the hypothesis. The previous article explained how to conduct path analysis in SPSS Amos. This article demonstrates through a case study how to interpret the findings from a path analysis model in your research.
The impact of job satisfaction on organisational commitment using the path analysis model
Employees are an integral part of any organization. If they are satisfied with their job, they will be more committed to their organisation (Ćulibrk et al., 2018). In this case study, the path analysis model of SEM is used to examine the influence of job satisfaction on organisational commitment. For this, first-hand data was obtained from 350 employees of a company using a close-ended questionnaire. It contained questions related to organisational commitment and job satisfaction.
Job satisfaction and organisational commitment were the main variables in the questionnaire. Each of them contained sub-variables which are as follows.
SEM for impact assessment
The path analysis model used showing the linkage between organisational commitment and job satisfaction is shown below.
In the above model. JS1, JS2, JS3 and JS4 denote the sub-variables of job satisfaction. OC1, OC2, OC3 and OC4 denote sub-variables of organisational commitment.
The first step towards the finalisation of the path analysis model is to establish the validity and reliability of the model.
Reliability and validity of path analysis model in SEM
Model fitness in an SEM model is established only after reliability and validity are proven. This is denoted through four types of validity:
- Convergent validity
- Internal consistency
- Composite reliability
- Discriminant validity
The below table presents the results of the model for this present case study.
| AVE | CR | Cronbach alpha | SQRT(AVE) | |
|---|---|---|---|---|
| Job satisfaction | 0.76 | 0.85 | 0.85 | 0.87 |
| Organization Commitment | 0.62 | 0.78 | 0.78 | 0.79 |
In the above table, AVE (Average variance extracted) determines the convergent validity of the model. It should be at least 0.5 (Alarcón & Sánchez, 2015). Here, the AVE value for job satisfaction is 0.76 and organizational commitment is 0.62 > 0.5, thus, there is a presence of convergent validity in the model.
The examination of internal consistency by the Cronbach alpha test depicts each construct linkage with the other. Herein, as the value of Cronbach alpha shows that job satisfaction is 0.85 and job satisfaction is 0.78 > 0.7 (Alarcón & Sánchez, 2015), thus, internal consistency is present in the model.
Composite reliability depicts each construct’s significance in the model. For job satisfaction, the CR value is 0.85 while organizational commitment is 0.78. As the values are more than 0.7, composite reliability exists in the model.
Lastly, discriminant validity defines the difference between each construct from others. The below table shows that the correlation value of organizational commitment and job satisfaction is 0.70. As the value is less than the square root of the average variance extracted, i.e. 0.87 and 0.79, discriminant validity is present in the model.
| Job satisfaction | Organization Commitment | |
|---|---|---|
| Job satisfaction | 0.87 | |
| Organization Commitment | 0.70 | 0.79 |
Since all the conditions are being met, this path model is valid and reliable.
Model fitness in SEM
The next step is to assess the model’s fitness. For this, values of different indices are examined. Results for the model are shown below.
| Name of category | Name of index | Index value | Adequate fit |
|---|---|---|---|
| Absolute fit measure | CMIN/Df (normed/relative Chi-Square) | 5.119 | Less than 5 |
| GFI (Goodness of fit) | 0.935 | Greater than 0.90 | |
| AGFI (adjusted goodness of fit) | 0.882 | Greater than 0.90 | |
| RMSEA (root mean square of approximation) | 0.109 | Less than 0.10 | |
| Incremental fit measure | NFI (normal fit index) | 0.93 | Greater than 0.90 |
| CFI (comparative fit index) | 0.942 | Greater than 0.90 | |
| TLI (Tucker Lewis index) | 0.919 | Greater than 0.90 | |
| IFI (Incremental fit index) | 0.943 | Greater than 0.90 | |
| Parsimonious fit measure | PGFI (parsimony goodness of fit index) | 0.519 | Greater than 0.50 |
| PCFI (parsimony comparative fit index) | 0.673 | Greater than 0.50 | |
| PNFI (parsimony normed fit index) | 0.664 | Greater than 0.50 |
In the above table, ‘Absolute fitness measure’ indices represent that CMIN/Df is 5.119 > 5, GFI is 0.935 > 0.90, AGFI is 0.882 < 0.9, and RMSEA is 0.109 > 0.10. As 3 out of 4 indices are not fulfilling fitness requirements, the model is not absolutely fit.
In ‘incremental fitness’ indices, the value of NFI is 0.93 > 0.90, CFI is 0.942 > 0.9, TLI is 0.919 > 0.9, and IFI is 0.943 > 0.9. As all the incremental fitness measures have required indices values, the model is incrementally fit.
For ‘parsimonious fitness measure’, PGFI is 0.519 > 0.5, PCFI is 0.673 > 0.5 and even PNFI is 0.664 . 0.5. Hence, the model is incrementally and parsimoniously fit but not absolutely.
For improving the fitness of the model, based on the modification values computed in AMOS, the covariance-based linkage is developed between variables. With this, the results of modified path model fitness indices are shown below.
| Name of category | Name of index | Index value | Adequate fit |
|---|---|---|---|
| Absolute fit measure | CMIN/Df | 4.346 | Less than 5 |
| GFI | 0.948 | Greater than 0.90 | |
| AGFI | 0.896 | Greater than 0.90 | |
| RMSEA | 0.098 | Less than 0.10 | |
| Incremental fit measure | NFI | 0.958 | Greater than 0.90 |
| CFI | 0.958 | Greater than 0.90 | |
| TLI | 0.934 | Greater than 0.90 | |
| IFI | 0.958 | Greater than 0.90 | |
| Parsimonious fit measure | PGFI | 0.474 | Greater than 0.50 |
| PCFI | 0.616 | Greater than 0.50 | |
| PNFI | 0.608 | Greater than 0.50 |
In the above table, a majority of the indices in the ‘Absolute fit measure’ are within the required limit and even if AGFI is close to the desired value, a modified model is absolutely fit. For ‘incremental fit measure’, all indices are greater than 0.9. Thus, the model is incrementally fit. Lastly, for ‘parsimonious’ indices, the majority of indices value is within the desired limit, thus, the model is parsimoniously fit.
Thus, this model can now be used for examining the impact and understanding the influence of job satisfaction on organisational commitment.
Impact determination using SEM
After establishing the model’s fitness, reliability and validity, the next step is the final step. The hypothesis is tested to establish the relationship between employee satisfaction and organisational commitment. The hypothesis is as follows:
H01: Job satisfaction does not have a significant influence on the organizational commitment
HA1: Job satisfaction has a significant influence on the organizational commitment
The results of the hypothesis are shown below.
| Dependent Variable | Independent Variable | Estimate | S.E. | C.R. | P-value |
|---|---|---|---|---|---|
| Organizational Commitment | Job Satisfaction | 0.89 | 0.07 | 12.68 | 0.00 |
Table 5 depicts that as the standard error (S.E.) value is 0.07 which is low, there are fewer biases present in the model to determine the relationship. Further, the p-value of the model is 0.00 < 0.05 and the CR value is 12.68 > 1.96 (z-value at 5% significance). Thus, the null hypothesis H0 is rejected. Hence, this study proves that there is an impact of job satisfaction on organizational commitment.
Why path analysis?
The path analysis model is the most widely used SEM model to examine the direct and indirect relationships, especially in the management field. This method enables the linkage building between multiple variables but does not have complex relationships. For instance, it cannot create a model with two mediators or a mediator and moderator. Thus most researchers adopt a path analysis model to assess a single impact of either direct or indirect nature. The above case study had only two constructs- job satisfaction and organizational commitment. The aim was to simply examine the direct impact. There were no complex constructs. Therefore path analysis was most suitable. Alternative methods such as MANOVA would have failed to derive the true impact because it does not take into consideration latent constructs. SPSS Amos is one of the simplest software for conducting SEM.
References
- Alarcón, D., & Sánchez, J. A. (2015). Assessing convergent and discriminant validity in the ADHD-R IV rating scale : User-written commands for Average Variance Extracted ( AVE ), Composite Reliability ( CR ), and Heterotrait-Monotrait ratio of correlations ( HTMT ). Spanish STATA Meeting, 1–39.
- Ćulibrk, J., Delić, M., Mitrović, S., & Ćulibrk, D. (2018). Job Satisfaction, Organizational Commitment and Job Involvement: The Mediating Role of Job Involvement. Frontiers in Psychology, February.
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