Section 8 — Moderated APIM (the centrepiece)

Section 8 — Moderated APIM (the centrepiece)

What you are practising: testing whether the partner crossover effect on each outcome is moderated by a dyad-level variable, using both multilevel modelling and SEM.

Reference: Hahn et al. (2014) replication tutorial.

NoteFocal interactions to test
Outcome Focal partner predictor Focal moderator DGP interaction
engagement partner_job_crafting live_together partner_jc × live_together = 0.15
performance partner_sdt years_together partner_sdt × years_together = 0.015
creativity partner_affect time_spent_this_morning_together partner_affect × time = 0.003

Tasks

  1. MLM. For each outcome, fit a baseline multilevel model (the full APIM from Section 2) and a moderated model that includes the focal partner-by-moderator interaction. Use interactions::sim_slopes() to extract the partner predictor’s effect at low and high levels of the focal moderator. Run the LRT comparing base to moderated.

  2. SEM. For each outcome, build the corresponding wide-format SEM with a manually created product indicator and computed simple-slope parameters. Compare the simple-slope estimates with the MLM.

Reflection prompt

Compare the MLM and SEM simple-slope estimates for each outcome. Where do they differ, and is the difference larger when the moderator is binary (live_together) or continuous (years_together, time_spent_this_morning_together)? Why might that be?

Tutorial reference: Hahn et al. (2014) tutorial. The MLM moderation is in “MLM specification”; the SEM moderation is in “SEM specification (wide format)”; the comparison is in “Compare MLM and SEM”.

Substitutions: - partner_wnc:has_children → focal partner × focal moderator for each outcome - wnc:has_children → focal actor × focal moderator (test jointly with the partner interaction) - The wide-format SEM needs the manual product indicators: ddw2$engagement_jc_livetogether etc.

What to expect. All three focal interactions are non-zero in the DGP, so all three LRTs should reject. The simple-slope estimates for the partner effect should differ at low and high levels of the moderator. The MLM and SEM should agree closely. The continuous moderators should give a wider simple-slope interval than the binary live_together, because the low/high values of a continuous variable (e.g. mean ± 1 SD) are more conservative.

What to record. For each outcome: “LRT for [focal interaction]: χ² = XX.X, df = 1, p = .XXXX. Partner slope at low moderator = X.XX; at high moderator = X.XX.”