Section 6 — Distinguishable dyads: SEM wide

Section 6 — Distinguishable dyads: SEM wide

What you are practising: the unconstrained / slopes-equal / fully-constrained model sequence and the three nested likelihood ratio tests.

Reference: Distinguishable dyads: SEM wide tutorial.

NoteGoal

For each outcome, fit the three wide-format SEMs and run the three nested LRTs. Build a fit-indices table.

Tasks

  1. Three wide-format SEMs for each outcome. Use ddw2:
    • Unconstrained — separate parameter labels for actor and partner paths.
    • Slopes equal — one label per path (so the actor and partner slopes share a label) but free intercepts.
    • Fully constrained — equal slopes, equal intercepts, equal residual variances.
  2. Three nested LRTs for each outcome. Use lavTestLRT():
    • LRT 1: unconstrained vs slopes-equal (do slopes differ by gender?).
    • LRT 2: slopes-equal vs fully-constrained (do intercepts differ?).
    • LRT 3: unconstrained vs fully-constrained (overall indistinguishability).
  3. Fit-indices table. Use fitMeasures() to extract the standard SEM fit measures (chisq, df, pvalue, cfi, tli, rmsea, srmr) for each model, and arrange them side by side, rounded to four decimals.

Reflection prompt

For which outcome is the slope-equality test (LRT 1) most likely to be non-significant — and is that consistent with the single actor_sdt × gender_male interaction in the data-generating process?

Tutorial reference: SEM wide. The three models are in the section “Model 1, 2, 3”; the LRTs are in “The three nested LRTs”; the fit-indices table is at the end.

Substitutions: - ddw → ddw2 - The model needs to be expanded to include six predictors instead of four - Use engagement_a / engagement_p as the outcome pair (and the same for the other two outcomes)

What to expect. LRT 1 is most likely to be non-significant for performance and creativity (where the DGP has no gender × slope interactions). For engagement, LRT 1 is most likely to be significant because of the one non-zero actor_sdt × gender_male interaction.

What to record. A small table with three rows (one per outcome) and the LRT 1 / LRT 2 / LRT 3 chi-squares and p-values.