Full Structural Model Analysis
The Focus of the video tutorial is guiding how to designing, interpreting, and reporting a full structural model in SPSS AMOS.
SPSS AMOS Full Structural Model Analysis
Full Structural Model Analysis
- A full structural model assesses the relationships between constructs but also includes the measurement indicators for each variable.
- A full structural model will allow you to account for the measurement error in a construct’s indicators while also assessing the relationships between constructs.
- You will initially draw all the constructs and indicators like you did in the CFA, then you will start including the direct paths between constructs. This is a more robust model and will account for each indicator individually.
- Unlike a composite variable path model, each indicator of a construct is included along with its effect on other constructs.
- Just like in the path model, you need to include error terms for each dependent construct and to make sure all error terms are labeled. In the CFA, all constructs were considered independent constructs, but that is not the case in a full structural model.
- A construct is considered an independent if it has a structural relationship that influences another construct and is not being influenced by any other construct in the model.
- In this example, Authentic Leadership and Ethical Leadership are the only independent variables. Since these two constructs are considered independent, a covariance needs to be added between them.
- After adding the structural relationships and labeling all error terms, you are ready to run the analysis. A full structural analysis will give you not only the structural relationships between constructs but also the measurement properties or factor loadings for each construct.
- Let’s take a closer look at the output of this full structural model test;
Interpreting the Output
A brief Review of the Output
Analyzing the Model Fit
Modification Indices
- Next, let’s look at the modification indices. With the full structural model, we should have already assessed the measurement model when we performed a CFA; thus, our focus is not on adjusting/covarying error terms with constructs.
- At this point, the modifications that concern us are the regression weights between constructs. As you can see, there are no modifications that are substantial or worthy of consideration.
- The modification indices will suggest unacceptable alterations such as indicators having structural relationships with other indicators. Even if the modification index is high, these are nonsensical suggestions and should not be considered.
How Do I Report My Full Structural Model Results?
- With the structural model, it is a good idea to present standardized regression weights, t-values, model fit statistics, and R2 values. I like to present R2 values of the dependent constructs so the reader can see how much of the variance is being explained with my independent variables.
- I also like to state if my hypotheses were supported or not. I feel like there is no need to present the measurement indicators again because you should have presented this with a confirmatory factor analysis prior to performing the structural analysis.
- Ultimately, you want to say a lot in a little amount of space. Presenting your results in a table should be done in a manner where the reader can see all the necessary information to determine the final results of your SEM test. This is not the only way to present structural results, but it is a good template.
Report Results
Structural Model Results are reported in two steps.
- First, The Fit Indices are reported for the model
- Second, the hypothesized relationships are assessed for significance and results reported accordingly. Following two sections present a sample of reporting full structural model.
Report Structural Model Fit Parameters
A structural equation model generated through AMOS was used to test the relationships. A good-fitting model was accepted if the value of the CMIN/df, the goodness-of-fit (GFI) indices (Hair et al., 2010); the Tucker and Lewis (1973) index (TLI); the Confirmatory fit index (CFI) (Bentler, 1990) is ⩾ 0.90 (Hair et al., 2010). In addition, an adequate-fitting model was accepted if the AMOS computed value of the standardized root mean square residual (RMR) < 0.05, and the root mean square error approximation (RMSEA) is between 0.05 and 0.08 (Hair et al., 2010). The fit indices for the model shown in Table 1 fell within the acceptable range: CMIN/df = , the goodness-of-fit (GFI) = , TLI = , CFI = , SRMR = , and RMSEA = .
The squared multiple correlation was ______ for life satisfaction, this shows that _______ variance in life satisfaction is accounted by ____________ and ________________.
Reporting Hypothesized Relationships
The study assessed the impact of authentic and ethical leadership on life satisfaction. The impact of Authentic Leadership on life satisfaction was positive and significant (b= _____, t = _____, p < _____), supporting H1. The impact of Ethical Leadership on self-efficacy was positive and significant (b= _____, t = _____, p < _____), supporting H2. Model fit indices and Hypotheses results are presented in Table 1.
Reference
Collier, J. E. (2020). Applied structural equation modeling using AMOS: Basic to advanced techniques. Routledge.