Section 4 — Distinguishable dyads: MLM moderator

What you are practising: adding gender as a moderator of actor and partner effects in a multilevel model.

Reference: Distinguishable dyads: MLM moderator tutorial.

Goal

For each outcome, compare a baseline (no gender interactions) with a full moderator model (gender × every actor and partner predictor), and report the simple slopes for each gender.

Tasks

Baseline model. For each outcome, fit the full APIM with no gender interactions (the same as Section 2). Save as model_base_eng, model_base_perf, model_base_creat.
Full moderator model. For each outcome, wrap the six predictors in parentheses and multiply by gender, so that every actor and partner predictor interacts with gender. Keep the three moderators as main effects only (they have no within-dyad variance). Save as mod_eng, mod_perf, mod_creat.
LRT. For each outcome, compare the baseline and the moderator model with anova().
Simple slopes. For each outcome, use interactions::sim_slopes() to extract the actor effects separately for each gender (johnson_neyman = FALSE). Repeat for any partner effect whose gender interaction is significant.
Profile-likelihood confidence intervals for each of the three moderator models.

Reflection prompt

The data-generating process specifies that only actor_sdt × gender_male on engagement is non-zero. Do the simple-slope plots and LRTs pick this up cleanly, or do other interactions appear spuriously significant?

Hints & solution outline

Tutorial reference: MLM moderator. The model syntax is in Step 2; the LRT is in Step 3; the simple slopes are in Step 4.

Substitutions: - ddl → ddl2 - Replace the four within-dyad predictors with the six (3 actor + 3 partner) - The full moderator formula becomes: r satisfaction ~ (affect + partner_affect + sdt + partner_sdt + job_crafting + partner_job_crafting) * gender + live_together + years_together + time_spent_this_morning_together + (1 | dyad_id)

What to expect. Only the actor_sdt × gender_male interaction on engagement is non-zero in the DGP. The LRT for engagement should reject (because of that one true interaction), while the LRTs for performance and creativity should not reject. Other interactions may appear spuriously significant at the conventional 0.05 level, especially with six predictors and N = 250 couples.

What to record. For each outcome: “LRT χ² = XX.X, df = 6, p = .XXXX. The simple slopes of [focal actor effect] are X.XX (male) vs X.XX (female).”

--- title: "Section 4 — Distinguishable dyads: MLM moderator" --- # Section 4 — Distinguishable dyads: MLM moderator **What you are practising:** adding `gender` as a moderator of actor and partner effects in a multilevel model. **Reference:** [Distinguishable dyads: MLM moderator tutorial](../../tutorials/distinguishable/mlm-moderator.html). ::: {.callout-note} ## Goal For each outcome, compare a baseline (no gender interactions) with a full moderator model (gender × every actor and partner predictor), and report the simple slopes for each gender. ::: ## Tasks 1. **Baseline model.** For each outcome, fit the full APIM with no gender interactions (the same as Section 2). Save as `model_base_eng`, `model_base_perf`, `model_base_creat`. 2. **Full moderator model.** For each outcome, wrap the six predictors in parentheses and multiply by `gender`, so that every actor and partner predictor interacts with gender. Keep the three moderators as main effects only (they have no within-dyad variance). Save as `mod_eng`, `mod_perf`, `mod_creat`. 3. **LRT.** For each outcome, compare the baseline and the moderator model with `anova()`. 4. **Simple slopes.** For each outcome, use `interactions::sim_slopes()` to extract the actor effects separately for each gender (`johnson_neyman = FALSE`). Repeat for any partner effect whose gender interaction is significant. 5. **Profile-likelihood confidence intervals** for each of the three moderator models. ## Reflection prompt The data-generating process specifies that only `actor_sdt × gender_male` on `engagement` is non-zero. Do the simple-slope plots and LRTs pick this up cleanly, or do other interactions appear spuriously significant? ::: {.callout-tip collapse="true"} ## Hints & solution outline **Tutorial reference:** [MLM moderator](../../tutorials/distinguishable/mlm-moderator.html). The model syntax is in Step 2; the LRT is in Step 3; the simple slopes are in Step 4. **Substitutions:** - `ddl` → `ddl2` - Replace the four within-dyad predictors with the six (3 actor + 3 partner) - The full moderator formula becomes: ```r satisfaction ~ (affect + partner_affect + sdt + partner_sdt + job_crafting + partner_job_crafting) * gender + live_together + years_together + time_spent_this_morning_together + (1 | dyad_id) ``` **What to expect.** Only the `actor_sdt × gender_male` interaction on `engagement` is non-zero in the DGP. The LRT for `engagement` should reject (because of that one true interaction), while the LRTs for `performance` and `creativity` should not reject. Other interactions may appear spuriously significant at the conventional 0.05 level, especially with six predictors and N = 250 couples. **What to record.** For each outcome: *"LRT χ² = XX.X, df = 6, p = .XXXX. The simple slopes of [focal actor effect] are X.XX (male) vs X.XX (female)."* :::