Incremental-validity questions: does a new construct explain variance beyond established controls?
Order of entry is dictated by theory or temporal precedence (controls first, focal predictors next, interactions last).
Standard framework for testing moderation: main effects in Block 1, product term in Block 2.
✗ When NOT to use
No principled entry order — plain simultaneous regression is more honest.
Confused with stepwise regression — hierarchical is researcher-ordered, stepwise is algorithm-ordered; do not substitute one for the other.
Outcome not continuous — use the corresponding hierarchical logistic models.
Blocks defined post hoc to flatter the focal variable.
Data requirements
Dependent / outcome variable
One continuous variable.
Independent / grouping variable
Predictors grouped into 2+ blocks with an a priori order.
Design
One sample; independent observations.
Sample size guidance
As multiple regression, counting ALL predictors across blocks; the ΔR² F-test needs adequate power for the increment, which is often small.
Assumptions
All multiple-regression assumptions apply to the final (full) model.
Entry order justified before analysis.
Same cases across blocks (no shifting missing-data base).
Hypotheses
H₀ — The focal block adds no explained variance (ΔR² = 0).
H₁ — The block adds explained variance (ΔR² > 0).
The concept
Fit Model 1 with the control block; fit Model 2 adding the focal block; the change in R² is the focal block's incremental contribution, tested with an F-change statistic: F = (ΔR²/k_added) / ((1 − R²_full)/(n − p_full − 1)).
This reframes 'is my construct significant?' into the sharper 'does my construct matter beyond what we already knew?' — the natural test for incremental validity claims (e.g., emotional intelligence beyond cognitive ability and Big Five). Report each step's R², the ΔR² with its F-change and p, and the final-model coefficients.