How to perform structural equation modelling (SEM) analysis with AMOS?

Structural equation modelling (SEM) analysis being the multivariate statistical tool helps in determining the direct and indirect linkage between the variables. As the previous article has discussed structural equation modelling analysis in detail, this article explains the process of performing structural equation modelling analysis using AMOS software.

The causal impact of organizational commitment and job satisfaction

The problem considered for structural equation modelling analysis in the previous article was to determine the impact of Organizational Commitment and Job satisfaction on the perceived performance of the Employee in an organization. There are factors like:

  • organizational rewards,
  • family support,
  • supervisor support and,
  • favourable working conditions that affect the organizational commitment level of an employee.

Furthermore, factors like advancement opportunity, workload, relationship with supervisor, and financial rewards affect the job satisfaction level of the employee. Based on all these factors the causal impact of organizational commitment and job satisfaction on the perceived performance need to be studied.

The codes that are included in the model for representing different factors and variables are shown in the below:

Factors or VariablesCode
Perceived Performance (Dependent)PP
Organizational CommitmentOC
Organizational Rewardsoc1
Family Supportoc2
Supervisor Supportoc3
Favourable Working Conditionoc4
Job SatisfactionJS
Advancement Opportunityjs1
Workloadjs2
Relationship with Supervisorjs3
Financial Rewardsjs4

Table 1: Variables coding

Important icons and their functions in AMOS

Important icon list for structural equation modelling analysis in AMOS.
Figure 1: Important icon list for structural equation modelling analysis in AMOS

Steps for performing structural equation modelling (SEM) analysis

Step 1: Open IBM SPSS Amos and save the file by selecting File > Save. The following window will open.

Amos window
Figure 1: Amos window
Save the file
Figure 2: Save the file

Step 2: Import the SPSS dataset by selecting “Data Files” from the menu. A below-shown dialogue box will appear.

Import data
Figure 3: Import data

Select File Name > location of file > file > open > Ok

Open file
Figure 4: Open file

Step 3: Draw the path diagram using the draw latent or its indicator icon. As the organizational commitment is affected by 4 factors thus by clicking 4 times on the latent variable, 4 observed variables are drawn i.e.

Draw the first section of the path diagram
Figure 5: Draw the first section of the path diagram

Similarly, for job satisfaction too, the path diagram is drawn i.e.

Figure 6: Path Diagram for organizational commitment and Job satisfaction
Figure 6: Path Diagram for organizational commitment and Job satisfaction

Note: In order to erase a variable click on delete of an object icon and then on the figure that needs to be deleted.

For moving a figure select on moving the object icon and then move the variable as per the requirement. You can also duplicate the model by selecting the duplication of the object icon. For rotating the diagram click of rotating the latent variable icon and for moving the drawn path diagram click on symmetrical movement icon and then move the figure.
Finally, to draw the dependent variable, the observed variable is drawn using draw the observed variable icon and in order to include the measurement error in the computation of the value of perceived performance, click on draw unique variable icon and then on the drawn variable.

Inclusion of Perceive performance (dependent variable) in the model.
Figure 7: Inclusion of Perceive performance (dependent variable) in the model.

Link the constructed variables.

Building a linkage between the variables.
Figure 8: Building a linkage between the variables.

Step 4: Specify each variable using the imported dataset. For this select the icon presenting a list of the dataset. A below-shown dialogue box will appear.

Variables in Dataset
Figure 9: Variables in Dataset

Drag each variable from this dialogue box on the drawn observed variable boxes i.e.

Specification of observed variables
Figure 10: Specification of observed variables

After observed variables specification, state the latent variables by double-clicking on the latent variable. A dialogue box will appear i.e.

Specification of the latent variable
Figure 11: Specification of the latent variable

Enter the name of the variable. Similarly, specify each latent variable.

Figure 12: Specification of the Path Diagram

Step 5: Name all the unobserved variables i.e. residual and measurement error by clicking on Plugins > Name Unobserved Variables

Specification of unobserved variables
Figure 13: Specification of unobserved variables

Step 6: Finally click on the calculate estimates icon to calculate the estimates.
A below-shown dialogue box will appear.

Warning box will appear
Figure 14: Warning box will appear

Click on Proceed with the analysis.
Results of the analysis will appear in the below-shown form.

Results
Figure 15: Results

Further, a new result file will be created at the location where you saved the Amos file. Open the file.

Amos Output file
Figure 16: Amos Output file

Interpreting the results from the output

Initially while interpreting the results of Amos, the fitness of the model is tested. For this click on model fit in the Amos output file and then below shown file will appear.

Model fitness of the structural equation model
Figure 17: Model fitness of the structural equation model

Fitness of the model is tested based on the following criteria i.e.

Name of categoryName of indexAdequate fitIndex Value
Absolute fit measure CMIN/DfLess than 5 13.279
  GFIGreater than 0.90 0.864
  AGFIGreater than 0.90 0.765
  RMSEALess than 0.10 0.175
Incremental fit measure NFIGreater than 0.90 0.879
  CFIGreater than 0.90 0.887
  TLIGreater than 0.90 0.843
  IFIGreater than 0.90 0.887
Parsimonious fit measure PGFIGreater than 0.50 0.499
  PCFIGreater than 0.50 0.640
  PNFIGreater than 0.50 0.635

Table 2: Model Fitness Criteria

As the adequate fit criteria for the above model are not getting satisfied for many indices like CMIN/Df, GFI, AGFI, or NFI; thus, the modification needs to be done in the model. For this open the file where path diagram is drawn and click on analysis properties icon. The below-shown dialogue box will appear.

Specification of analysis properties
Figure 18: Specification of analysis properties

Click on Output tab > Modification indices and then close the dialogue box. Close the Amos output file and again click on calculate estimated i.e. calculate estimates icon.

Modification index
Figure 19: Modification index

Open the Amos Output file and then select the modification indices. The following window will open.

Modification indices output  structural equation modelling
Figure 20: Modification indices output structural equation modelling

Check the covariance value for the unobserved variables and then select those unobserved variables whose MI value is high in linkage with other unobserved variables i.e. e1-e5 in the above case.

Covariance values
Figure 21: Covariance values

Close the output file and draw the covariance between the above stated unobserved variables in the path diagram using draw covariance icon.

Modification in the path diagram for structural equation modelling
Figure 22: Modification in the path diagram for structural equation modelling

Again, calculate the estimates using calculate estimates icon and open the structural equation modelling output file.

Modified fitness index values
Figure 23: Modified fitness index values

Though the values have changed still, adequate fitness value is not derived. Repeat the process until the adequate fitness value is derived.

Interpreting the final path diagram of the structural equation modelling

Final Path Diagram for structural equation modelling
Figure 24: Final path diagram for structural equation modelling

The above figure shows that the factor loadings of each variable. In the above diagram, the value of the factors considered for deriving the value of Organizational Commitment and Job satisfaction is considered. For all the factors which affect the organizational commitment i.e. organizational rewards (18.42), family support (19.15), supervisor support (20.88), and favourable working condition (1.00) is greater than the absolute value of 0.7; thus all the factors are relevant in studying their contribution in determination of organizational commitment value. Furthermore, the factor loading of job satisfaction factors i.e. advancement opportunity (1.17), workload (1.15), relationship with supervisor (1.06), and financial rewards (1.00) is also greater than the absolute value of 0.7. Thus, all the factors included in the model for determining the value of latent variables are relevant.

Interpreting the final value of moderation indices of structural equation modelling

Name of categoryName of indexAdequate fitIndex ValueComments
Absolute Fit measureCMIN/DfLess than 5 1.540Required level is derived
 GFIGreater than 0.90 0.983Required level is derived
 AGFIGreater than 0.90 0.962Required level is derived
 RMSEALess than 0.10 0.037Required level is derived
Incremental fit measureNFIGreater than 0.90 0.989Required level is derived
 CFIGreater than 0.90 0.996Required level is derived
 TLIGreater than 0.90 0.993Required level is derived
 IFIGreater than 0.90 0.996Required level is derived
Parsimonious fit measurePGFIGreater than 0.50 0.437Required level is not derived
 PCFIGreater than 0.50 0.553Required level is derived
 PNFIGreater than 0.50 0.550Required level is derived

Table 3: Final modification indices value

The above table shows the model fitness. In case of absolute fitness, the value of relative/normed Chi-Square (CHIN/Df), the goodness of fit (GFI), adjusted goodness of fit (AGFI) and the root mean square error of approximation (RMSEA) is satisfying the required criteria. CHIN/Df value is 1.540 that is less than 5, GFI is 0.983 which is greater than 0.9, AGFI is 0.962 that is greater than 0.9, and RMSEA is 0.037 which is less than 0.10. Thus, the model for studying the impact of organizational commitment and job satisfaction on the perceived performance is adequately fit.

The value of Normal Fit index (NFI), Comparative Fit Index (CFI), Tucker Lewis index (TLI), and Incremental Fit Index (IFI) shows the incremental fitness of the model. NFI value is 0.989 > 0.9, CFI value is 0.996 > 0.9, TLI value is 0.993 > 0.9, and IFI value is 0.996 > 0.9. Thus, the value of all the indices satisfies the criteria required for having the incremental fit model.

Parsimony comparative fit index (PCFI) value is 0.550 that is greater than the desired value of 0.5 and Parsimony normed fit Index (PNFI) value is 0.550 greater than the required value of 0.5. Though the value of Parsimony Goodness of fit Index (PGFI) is less than the desired value i.e. 0.437 < 0.50 but still the value is close to the required level. Hence, the model is Parsimoniously fit.

Testing the hypothesis

The hypothesis for studying the impact of organizational commitment on the perceived performance of the employee is:

H01: There is no significant impact of organizational commitment on the perceived performance of employee.
HA1: There is a significant impact of organizational commitment on the perceived performance of employee.

Hypothesis for studying the impact of job satisfaction on the perceived performance of the employee is:

H02: There is no significant impact of job satisfaction on the perceived performance of employee.
HA2: There is a significant impact of job satisfaction on the perceived performance of employee.

Results of the estimates are shown in the below.

PP (Dependent)S.E.C.R. (z-value)p (sig) value
OC16.4721.2020.229
JS0.0261.3260.185

The S.E. shows that there is a high deviation in the computation of Organizational commitment as the value of OC is 16.472 while less deviation is there in the computation of job satisfaction level of the employee as the value of is 0.026. P-value shows that as for each variable the significance value is greater than the significance level of the study i.e. 0.05. Thus, the first and second null hypothesis of having no significant impact of organizational commitment on the perceived performance of an employee, and no significant impact of job satisfaction on the perceived performance of an employee is not rejected. This result is further verified by the z-score value i.e. 1.202 for OC and 1.326 for JS which is less than the tabulate Z-value of 1.96. Hence, for the present study, the analysis of the perception of the people shows that organizational commitment level and job satisfaction does not have a significant influence on the perceived performance of an employee.

Riya Jain
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