Path Analysis

Path analysis is the observed-variable special case of SEM. Both test specified causal diagrams using covariance structure, but SEM additionally incorporates latent variables measured by multiple indicators, thus explicitly modelling measurement error. If all your constructs are single observed variables, path analysis and SEM give identical results.

No. A fitting path model is consistent with the hypothesised causal structure but does not rule out equivalent alternative models that fit equally well, nor does it account for unmeasured confounders. Causal conclusions require strong theoretical justification, ideally experimental or longitudinal design, in addition to statistical fit.

Use bias-corrected bootstrap confidence intervals (e.g., 5,000 resamples). If the 95% CI for the indirect effect a × b does not include zero, the mediated effect is statistically significant. Avoid the Sobel test, which assumes a normal sampling distribution for the product that is often violated.

A common heuristic is at least 10 observations per freely estimated parameter, with a practical minimum of around 100–200 cases. Small samples yield unstable path estimates and low power to detect model misfit via chi-square.

Examine modification indices to see which fixed paths, if freed, would most improve fit. Consider whether the original theoretical diagram omitted important causal links. However, any post-hoc modification must be theoretically defensible and the modified model cross-validated on an independent sample, because modifications capitalise on sample-specific noise.