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Partial Correlations

Goal - Associate canonical scores or PCs with outcomes controlling covariates.

Context in integration plan

  • Use this after you have stable embeddings and late-fusion baselines: it helps interpret axes (CCA components, PCs) rather than build new predictors.
  • Treat it as an analysis layer sitting on top of the late-fusion-first stack, not as a standalone modeling approach.
  • Prefer simple, regularized models here; if interpretation depends on heavy models, revisit whether the underlying embeddings/CCA steps are well-behaved.

Continuous outcome (e.g., PHQ-9) - Residualize x and y on covariates within train folds → rx, ry. - Correlate rx, ry (Pearson/Spearman); aggregate across folds.

Binary outcome (e.g., MDD) - Preferred: logistic regression y ~ x + covariates; report OR, CI, p. - Optional: approximate partial correlation via residuals y − p̂ from covariate-only logistic.

Report - Per-axis coefficients/correlations with CIs; FDR across multiple tests if many axes.