Specialty › Bayesian

ANCOVA (Bayes factor)

Bayesian ANCOVA compares models by Bayes factor to isolate the group effect after adjusting for a continuous covariate.

What is ANCOVA (Bayes factor)?

Four models are on the table: intercept-only, covariate-only, group-only, group + covariate. The headline BF is BF(group + covariate) / BF(covariate-only) — evidence for a group effect over and above the covariate. The covariate's own adjusted BF is reported symmetrically.

This model-comparison approach is an 'effects' analysis restricted to two predictors.

When should I use ANCOVA (Bayes factor)?

  • Group comparisons with a baseline covariate (pre-score, age) where you want graded evidence rather than a p-value.

What data does it need?

Response (numeric) + factor + covariate (numeric) + prior r-scale.

What does it report?

Adjusted group BF and covariate BF, Jeffreys interpretation, model table (each BF vs intercept-only).

What does it assume?

  • Linear covariate-response relation within groups.
  • Homogeneous regression slopes (no group × covariate interaction in v1).

How do I interpret the result?

A group BF near 1 after adjustment suggests the raw group difference was carried by the covariate.

See also

References

  • Rouder, Morey, Speckman & Province (2012). Default Bayes factors for ANOVA designs. JMP 56.