Section 7 — Two-intercept models

What you are practising: the 0 + gender parameterisation trick that directly estimates separate intercepts per group, and its SEM analogue.

Reference: Two-intercept tutorial.

Goal

For each outcome, fit three nested MLMs and compare adjacent models with LRTs. Also fit the SEM analogue in wide format and confirm the intercept estimates match.

Tasks

Three nested MLMs for each outcome:
- Model 1: Equal intercepts, equal slopes (most constrained).
- Model 2: Separate intercepts for each gender, equal slopes (recommended baseline). Use the 0 + gender syntax.
- Model 3: Separate intercepts, separate slopes (full model). Use 0 + gender + gender:wnc + ....
LRTs for each outcome:
- Test A: Model 1 vs Model 2 (intercepts differ?).
- Test B: Model 2 vs Model 3 (slopes differ?).
SEM analogue. Fit the wide-format model with two intercepts and equal slopes for each outcome. Confirm the intercept estimates match the MLM Model 2.

Reflection prompt

The two-intercept approach is recommended when you want to report the absolute mean of each group (not the contrast with a reference). Which of the three outcomes has the most substantively different male vs. female mean, and is that consistent with what you saw in Section 1?

Hints & solution outline

Tutorial reference: Two-intercept tutorial. The three models are in “The three nested models”; the LRTs are in “The two likelihood ratio tests”; the SEM analogue is in “The SEM analogue (wide format)”.

Substitutions: - ddl → ddl2 - Replace the four within-dyad predictors with the six (3 actor + 3 partner) - In Model 2, the formula becomes: r satisfaction ~ 0 + gender + affect + partner_affect + sdt + partner_sdt + job_crafting + partner_job_crafting + live_together + years_together + time_spent_this_morning_together + (1 | dyad_id) - In Model 3, use 0 + gender + gender:(affect + partner_affect + sdt + ...) + ...

What to expect. Test A (intercepts differ) should reject for all three outcomes. Test B (slopes differ) should reject only for engagement (the one outcome with a gender × slope interaction in the DGP). The MLM gendermale and genderfemale intercepts should match the int_a and int_p labels from the SEM.

What to record. For each outcome: “Test A: χ² = XX.X, df = 1, p = .XXXX. Test B: χ² = XX.X, df = X, p = .XXXX. Male intercept ≈ X.XX, female intercept ≈ X.XX.”

--- title: "Section 7 — Two-intercept models" --- # Section 7 — Two-intercept models **What you are practising:** the `0 + gender` parameterisation trick that directly estimates separate intercepts per group, and its SEM analogue. **Reference:** [Two-intercept tutorial](../../tutorials/distinguishable/two-intercept.html). ::: {.callout-note} ## Goal For each outcome, fit three nested MLMs and compare adjacent models with LRTs. Also fit the SEM analogue in wide format and confirm the intercept estimates match. ::: ## Tasks 1. **Three nested MLMs for each outcome:** - **Model 1:** Equal intercepts, equal slopes (most constrained). - **Model 2:** Separate intercepts for each gender, equal slopes (recommended baseline). Use the `0 + gender` syntax. - **Model 3:** Separate intercepts, separate slopes (full model). Use `0 + gender + gender:wnc + ...`. 2. **LRTs for each outcome:** - Test A: Model 1 vs Model 2 (intercepts differ?). - Test B: Model 2 vs Model 3 (slopes differ?). 3. **SEM analogue.** Fit the wide-format model with two intercepts and equal slopes for each outcome. Confirm the intercept estimates match the MLM Model 2. ## Reflection prompt The two-intercept approach is recommended when you want to report the absolute mean of each group (not the contrast with a reference). Which of the three outcomes has the most substantively different male vs. female mean, and is that consistent with what you saw in Section 1? ::: {.callout-tip collapse="true"} ## Hints & solution outline **Tutorial reference:** [Two-intercept tutorial](../../tutorials/distinguishable/two-intercept.html). The three models are in "The three nested models"; the LRTs are in "The two likelihood ratio tests"; the SEM analogue is in "The SEM analogue (wide format)". **Substitutions:** - `ddl` → `ddl2` - Replace the four within-dyad predictors with the six (3 actor + 3 partner) - In Model 2, the formula becomes: ```r satisfaction ~ 0 + gender + affect + partner_affect + sdt + partner_sdt + job_crafting + partner_job_crafting + live_together + years_together + time_spent_this_morning_together + (1 | dyad_id) ``` - In Model 3, use `0 + gender + gender:(affect + partner_affect + sdt + ...) + ...` **What to expect.** Test A (intercepts differ) should reject for all three outcomes. Test B (slopes differ) should reject only for `engagement` (the one outcome with a gender × slope interaction in the DGP). The MLM `gendermale` and `genderfemale` intercepts should match the `int_a` and `int_p` labels from the SEM. **What to record.** For each outcome: *"Test A: χ² = XX.X, df = 1, p = .XXXX. Test B: χ² = XX.X, df = X, p = .XXXX. Male intercept ≈ X.XX, female intercept ≈ X.XX."* :::