Structural Equation Modeling

A direct effect is the path from X to Y, quantifying how X influences Y directly. An indirect effect is the path X→M→Y, quantifying how X influences Y through mediator M. The indirect effect equals the product of the X→M path times the M→Y path. Total effect = direct + indirect. Mediation occurs when: (1) X→Y direct effect decreases after controlling for M, and (2) X→M→Y indirect effect is significant (bootstrap CI excludes zero). Full mediation: direct effect becomes nonsignificant after including mediator. Partial mediation: both direct and indirect effects significant, meaning X affects Y through multiple pathways.

Model fit is judged by multiple indices (Hu & Bentler, 1999 criteria): CFI (Comparative Fit Index) compares your model to a null model (all variables uncorrelated); CFI > 0.95 indicates good fit (ranges 0–1). RMSEA (Root Mean Square Error of Approximation) quantifies discrepancy between model and data per degree of freedom; RMSEA < 0.06 excellent, 0.06–0.08 good, >0.10 poor (close to zero better). TLI > 0.95 and SRMR < 0.08 also recommended. Meeting all criteria simultaneously indicates good fit. However, good overall fit does not guarantee all pathways fit; examine standardized residuals (should be < |2|) and modification indices.

A latent variable is an unobserved construct (e.g., depression, intelligence, organizational culture) measured indirectly through multiple observed indicators (questionnaire items, test scores). Each indicator reflects the latent construct plus measurement error. In SEM, you specify which observed variables measure which latent variables via factor loadings. For example, the latent variable 'depression' might be measured by items: sadness, hopelessness, sleep disturbance (observed indicators). Each loading should be ≥0.5; if an indicator loads weakly, consider removing it or reconceptualizing the latent construct.

No. SEM estimates associations and tests whether a hypothesized causal model reproduces the correlation structure in data. Path coefficients represent regression weights (conditional associations), not causal effects. Causality requires: (1) temporal precedence (X measured before Y), (2) covariation (X and Y correlate), (3) no plausible alternatives (confounding, reverse causality). Observational SEM violates criterion 3: confounding variables and unmeasured causes threaten validity. SEM's statistical fit alone cannot prove causality. Use SEM with theory, qualitative evidence, and study design (randomization, instrumental variables) to strengthen causal inference. Consider sensitivity analyses testing alternative models.