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

Structural equation modeling (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 modeling analysis in detail, this article explains the process of performing structural equation modeling analysis using AMOS software.

## The causal impact of organizational commitment and job satisfaction

The problem considered for structural equation modeling 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 perceived performance needs to be studied.

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

Factors or Variables | Code |
---|---|

Perceived Performance (Dependent) | PP |

Organizational Commitment | OC |

Organizational Rewards | oc1 |

Family Support | oc2 |

Supervisor Support | oc3 |

Favourable Working Condition | oc4 |

Job Satisfaction | JS |

Advancement Opportunity | js1 |

Workload | js2 |

Relationship with Supervisor | js3 |

Financial Rewards | js4 |

## Important icons and their functions in AMOS

## Steps for performing structural equation modeling (SEM) analysis

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

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

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

**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.

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

For moving a figure select 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 the symmetrical movement icon and then move the figure.

Finally, to draw the dependent variable, the observed variable is drawn using the draw the observed variable icon and in order to include the measurement error in the computation of the value of perceived performance, click on the draw unique variable icon and then on the drawn variable.

Link the constructed 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.

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

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

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

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

**Step 6:** Finally click on the calculate estimates icon to calculate the estimates.

A below-shown dialogue box will appear.

Click on Proceed with the analysis.

The results of the analysis will appear in the below-shown form.

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

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

Name of category | Name of index | Adequate fit | Index Value |
---|---|---|---|

Absolute fit measure | CMIN/Df | Less than 5 | 13.279 |

GFI | Greater than 0.90 | 0.864 | |

AGFI | Greater than 0.90 | 0.765 | |

RMSEA | Less than 0.10 | 0.175 | |

Incremental fit measure | NFI | Greater than 0.90 | 0.879 |

CFI | Greater than 0.90 | 0.887 | |

TLI | Greater than 0.90 | 0.843 | |

IFI | Greater than 0.90 | 0.887 | |

Parsimonious fit measure | PGFI | Greater than 0.50 | 0.499 |

PCFI | Greater than 0.50 | 0.640 | |

PNFI | Greater than 0.50 | 0.635 |

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

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.

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

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.

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

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

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 modeling

The above figure shows 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 organizational commitment i.e. organizational rewards (18.42), family support (19.15), supervisor support (20.88), and favourable working condition (1.00) are greater than the absolute value of 0.7; thus all the factors are relevant in studying their contribution in the 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 a structural equation modeling

Name of category | Name of index | Adequate fit | Index Value | Comments |
---|---|---|---|---|

Absolute Fit measure | CMIN/Df | Less than 5 | 1.540 | The required level is derived |

GFI | Greater than 0.90 | 0.983 | The required level is derived | |

AGFI | Greater than 0.90 | 0.962 | The required level is derived | |

RMSEA | Less than 0.10 | 0.037 | The required level is derived | |

Incremental fit measure | NFI | Greater than 0.90 | 0.989 | The required level is derived |

CFI | Greater than 0.90 | 0.996 | The required level is derived | |

TLI | Greater than 0.90 | 0.993 | The required level is derived | |

IFI | Greater than 0.90 | 0.996 | The required level is derived | |

Parsimonious fit measure | PGFI | Greater than 0.50 | 0.437 | The required level is not derived |

PCFI | Greater than 0.50 | 0.553 | The required level is derived | |

PNFI | Greater than 0.50 | 0.550 | The required level is derived |

The above table shows the model’s fitness. In the 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 is less than 5, GFI is 0.983 which is greater than 0.9, AGFI is 0.962 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 perceived performance is an adequately fit.

The value of the Normal Fit index (NFI), Comparative Fit Index (CFI), Tucker Lewis index (TLI), and Incremental Fit Index (IFI) show 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 is greater than the desired value of 0.5 and the Parsimony normed fit Index (PNFI) value is 0.550 greater than the required value of 0.5. Though the value of the 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.

The 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.

The results of the estimates are shown below.

PP (Dependent) | S.E. | C.R. (z-value) | p (sig) value |
---|---|---|---|

OC | 16.472 | 1.202 | 0.229 |

JS | 0.026 | 1.326 | 0.185 |

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 the job satisfaction level of the employee as the value is 0.026. The P-value shows that 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 hypotheses 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 tabulated 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 do not have a significant influence on the perceived performance of an employee.

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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.

I am currently working as a Research Associate. My work is centered on Macroeconomics with modern econometric approach. Broadly, the methodological research focuses on Panel data and Times series data analysis for causal inference and prediction. I also served as a reviewer to Journals of Taylor & Francis Group, Emerald, Sage.

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