Quantifying Heuristics in A/B Tests

Following up on the previous discussions regarding the challenges in applying behavioral economics, I'm now facing a deeper technical hurdle. Specifically, how can one ensure robust causal inference when quantifying the isolated impact of various heuristics within complex multivariate testing frameworks? I'm seeking specific methodologies or advanced statistical approaches, beyond standard ANOVA, that can reliably attribute incremental lift solely to the application of a particular behavioral heuristic, rather than confounding variables. Thanks in advance!