Kap 16 · SEM

Structural Equation Models

The last chapter. Measuring what you can’t put a ruler to — constructs that live in the respondent’s head — and judging whether the model actually holds.

Two kinds of variable. Observed ones you measure directly; latent ones you reach only through several indicators that move together. SEM ties them with two halves: a measurement model that turns indicators into a construct, and a structural model that lets constructs predict each other.

Reading the output — lavaan in R

=~ “is measured by” — the measurement model (latent =~ indicators).

~ “is regressed on” — the structural model (outcome ~ predictor).

~~ “covaries with”.

cfa() measurement model only · sem() full model.

summary(fit, fit.measures = TRUE, standardized = TRUE) prints loadings, structural coefficients and the fit indices.

Formula reference

Measurement model: X = λ·η + δ

Structural model: η₂ = β·η₁ + ζ

Explained variance of an indicator: λ² (strong >0.70 · moderate 0.40–0.70 · weak <0.40)

Indirect effect: β₁·β₂ · Total: direct + indirect

Fit thresholds: CFI ≥ 0.95 · TLI ≥ 0.95 · RMSEA ≤ 0.06 · SRMR ≤ 0.08