Variance decomposition

5.9 Variance Decomposition: What Fraction of Naming Is Cultural?

Nested OLS with incremental R^2 reporting. Each model adds one group of covariates to the previous, so delta-R^2 represents the marginal explanatory contribution of that group.

Step	Group	Features Added	Cumulative R^2	Delta R^2	Adj R^2	n
A	event	4	0.0104	0.0104	-0.0098	200
B	name_matching	4	0.5093	0.4989	0.4887	200
C	name_independent	7	0.5181	0.0088	0.4788	200
D	phonetic	3	0.5222	0.0041	0.4747	200
E	cycle	1	0.5223	0.0001	0.4718	200

Interpretation

Event characteristics alone explain R² = 0.0104 of variation in the per-event synthetic-control divergence (the ate_t2 column). The full model with all four groups reaches R² = 0.5223.

A-209 caveat on the name_matching block. The name_matching block's ΔR² of 0.4989 is partly tautological: those features (syllable count, log_pre_rank, pre_spike_trajectory_3yr, phonetic_neighborhood_size) are inputs to the Phase 8a synthetic-control donor matching. A well-fit donor pool mechanically reduces the divergence variance left over for those variables to explain. The honest comparison is event ΔR² vs name_independent + phonetic + cycle ΔR², where the name features are independent of the matching procedure.

Residual variance: 47.8% — attributable to idiosyncratic factors, measurement error, SUTVA-violation noise from phonetic spillover (see A-208), and fundamentally unpredictable cultural dynamics.

Multicollinearity Warning

The following features have VIF > 10:

• log_budget: VIF = 40.9
• log_revenue: VIF = 38.1

Standard errors on these coefficients may be unreliable.

Analysis based on 200 events with valid causal ATEs.