23. SPSS AMOS | Full Structural Model | Analyzing, Interpreting, and Reporting Hypothesis Results

Full structural model analysis in IBM SPSS Amos is a more robust alternative to composite-variable path analysis because it keeps each construct’s measurement indicators in the model and explicitly models measurement error. Instead of collapsing a latent construct into a single composite score, the full structural approach treats constructs as latent variables with their own indicator items and associated error terms, then estimates how constructs influence one another through direct paths. That combination—measurement plus structural relationships in one framework—lets researchers assess relationships between constructs while accounting for the fact that indicators are imperfect measures.

In practice, the model begins like a confirmatory factor analysis (CFA): each construct is drawn with its indicators and error terms, and the measurement portion is set up so the latent variables explain their observed items. The structural step then adds single-headed arrows (direct paths) between constructs. Where path analysis would connect constructs using composite variables, the full structural model connects constructs directly while retaining every indicator, producing a model that can separate “true” relationships between constructs from noise introduced by measurement error.

A key modeling distinction is how variables are classified. In CFA, constructs are typically treated as correlated (covarying) because the goal is measurement validation rather than causal direction. In a full structural model, constructs that have structural influence on others are treated as endogenous (they receive paths), while constructs that influence others but are not influenced by other variables are treated as exogenous. Exogenous constructs can still covary with each other when they are not causally linked in the model. The transcript’s example uses authentic leadership and ethical leadership as exogenous constructs that covary, both predicting life satisfaction, which is modeled as an endogenous outcome.

Building the model in Amos involves transforming an existing measurement diagram into a structural one: removing covariances that should no longer apply once directional paths are specified, enlarging the canvas for layout, and then drawing direct paths from the two leadership constructs to life satisfaction. The model also requires error terms for the remaining variance in the dependent construct and labeled unobserved variables for error terms. Once the diagram is complete, estimates are calculated and the output is interpreted through two lenses: (1) structural relationships via regression weights (standardized estimates, critical ratios/t-values, and p-values) and (2) model fit.

For hypothesis testing, the decision rule highlighted is based on critical ratio (t-value) and p-value: a t-value above 1.96 and p-value below 0.05 indicate support. In the example results, authentic leadership shows a positive but statistically insignificant effect on life satisfaction (t-value 1.61; p-value 0.872), so the hypothesis for authentic leadership is not supported. Ethical leadership shows a positive and significant effect (standardized estimate 0.589; t-value 4.83; p-value < 0.01), so the hypothesis for ethical leadership is supported.

Model fit is assessed using standard Amos fit indices reported from the “Model Fit” output: values such as χ²/df around 2.626, GFI above 0.90 (reported 0.915), CFI and TLI above 0.95 (reported 0.958 and 0.948), SRMR around 0.04, and RMSEA around 0.06. The transcript also explains how to extract R² (squared multiple correlation) for the dependent variable: life satisfaction has an R² of about 0.37, meaning roughly 37% of the variance in life satisfaction is explained by authentic leadership and ethical leadership. Finally, it provides a reporting template: present model fit first, then report squared multiple correlation, then list each hypothesis result with standardized estimates, t-values, p-values, and the accept/reject decision.