Pre-Empirical Design Validation of BIM–AI Construction Management Models: A Monte Carlo Framework for Effect Recoverability and Sample-Size Adequacy

BIM–AI construction management studies increasingly use multivariate models in which theoretically important relationships may be weaker than dominant technology adoption paths. This study develops a pre-empirical Monte Carlo design audit framework for testing whether such relationships are recoverable before field data are collected. A five-construct BIM–AI architecture with 28 ordinal indicators was evaluated through the original 33-scenario design and three additional stress tests, yielding 48,000 Monte Carlo replications. The extension introduces a finer sample size grid, missing completely at random (MCAR) block missingness conditions, and score construction sensitivity. For β = 0.15, empirical power increased from 0.292 at N = 100 to 0.824 at N = 400 and 0.906 at N = 500. With 20% block missingness, power was 0.604 at N = 286 and 0.808 at N = 500. Principal component analysis (PCA)-based scoring produced only modest differences relative to equal-weight composites. The findings show that sample size, measurement quality, data completeness, and effect magnitude must be audited jointly. The empirical power recoverability map is proposed as a transparent model-specific planning tool rather than a universal minimum sample rule.