How to analyze data through a structural equation model (SEM)?

Structural equation modeling (SEM) analyzes data by statistically testing hypothesized relationships between observed variables and latent constructs. It integrates factor analysis and path analysis to evaluate complex causal and correlational pathways within a theoretical model simultaneously. Successful SEM analysis requires several key steps and considerations. First, a strong theoretical foundation is essential to specify the hypothesized model, defining latent variables and their relationships clearly. Data must meet core assumptions: multivariate normality (requiring transformations or robust estimators otherwise), sufficient sample size (typically N>200, depending on model complexity), and absence of excessive multicollinearity. Model identification requires sufficient observed indicators for each latent variable and appropriate parameter constraints. Estimation, usually via Maximum Likelihood, yields global fit indices (CFI, TLI >0.90/0.95; RMSEA, SRMR <0.08/0.06) and local parameter estimates (path coefficients, significance) to evaluate model adequacy; modification indices guide potential improvements only if theoretically sound. To implement SEM, follow these core steps: formulate the theoretical model diagrammatically, specifying all latent constructs, observed indicators, and hypothesized paths. Collect appropriate multivariate data. Use dedicated software (e.g., lavaan in R, Amos, Mplus) to specify the model using syntax or graphical interface, define relevant estimation options, and run the analysis. Rigorously evaluate overall model fit using multiple indices before interpreting the significance and magnitude of individual structural coefficients. Iteratively refine the model based on diagnostics *only* if supported by theoretical reasoning to avoid capitalizing on chance. This approach tests intricate theoretical frameworks involving unobserved concepts and mediation more effectively than traditional regression.