AHP-MAP: anchoring expert AHP structure with Dirichlet-MAP calibration raises ranking and classification performance for institutional tech-transfer metrics (Spearman ρ 0.655→0.712, AUC 0.742→0.805) while keeping composite scores transparent and decomposable.

Main Finding

The paper proposes AHP-MAP, a transparent, auditable evaluation framework that blends analytic-hierarchy-process (AHP) expert weights with maximum-a-posteriori (MAP) calibration using observed outcomes. Applied to monetized, zero-inflated, long-tailed technology-transfer outputs from 36 institutions (23 indicators), AHP-MAP improves out-of-fold predictive and ranking performance versus a fixed-AHP baseline while remaining closer to the original AHP structure than a purely data-driven estimator. Key numerical improvements: Spearman ρ 0.655 → 0.712; AUC 0.742 → 0.805; RMSE (positive-output magnitude) 1.481 → 1.453; mean joint negative log-likelihood 2.006 → 1.974.

Key Points

• AHP-MAP combines AHP (expert primary and local weights) with MAP calibration by treating AHP weights as modes of Dirichlet priors and estimating posterior-mode weights.
• A single prior-strength parameter κ (controls how strongly prior AHP structure is enforced) is chosen from a candidate set by stratified 4‑fold cross-validation.
• The outcome model is a two-part occurrence–magnitude specification that accommodates zero-inflation (whether any transfer occurs) and long-tailed positive monetary magnitudes.
• Compared with (a) fixed AHP and (b) fully data-driven (κ = 0) approaches, AHP-MAP:
  • Improves rank correlation and classification (occurrence) AUC,
  • Reduces magnitude RMSE and joint negative log-likelihood,
  • Avoids excessive concentration of weights that can arise with unconstrained data-driven estimation,
  • Preserves interpretability: additive composite scores permit exact decomposition into dimension-level and indicator-level contributions.
• Robustness checks include multiple initializations, transformations, bootstrap, jackknife, and Monte Carlo analyses showing weight and ranking stability across settings and sample sizes.

Data & Methods

• Data: 36 institutions, 23 performance indicators, monetized technology-transfer outputs (many zeros, long-tailed positive values).
• Weighting framework:
  • AHP supplies a hierarchical set of expert weights (primary and local) that define modes of Dirichlet priors over indicator weights.
  • A prior-strength parameter κ scales the concentration of the Dirichlet prior around AHP modes.
  • MAP estimation yields calibrated weights balancing prior (AHP) information and empirical fit.
• Outcome model:
  • Two-part model linking composite scores to (1) occurrence of any transfer and (2) magnitude when positive; formulated to handle zero-inflation and long tails.
• Model selection and evaluation:
  • κ selected by stratified 4‑fold cross-validation from a prespecified candidate grid.
  • Out-of-fold performance compared to fixed AHP and κ = 0 (purely data-driven) baselines.
  • Evaluation metrics: Spearman rank correlation, AUC (occurrence), RMSE (positive magnitude), joint negative log-likelihood.
• Diagnostics: additive decomposition yields dimension- and indicator-level contributions for institutional diagnosis; multiple sensitivity analyses conducted.

Implications for AI Economics

• Bridging expert judgement and data: AHP-MAP provides a principled way to combine domain knowledge (AHP) with empirical calibration—valuable for assessing AI R&D and technology-transfer where expert structure matters but outcomes are informative.
• Transparency and auditability: By anchoring weights to AHP priors and using Dirichlet-MAP updates, the framework remains auditable for stakeholders and policymakers who require understandable, explainable evaluation rules.
• Better predictive and diagnostic tools: Improved ranking/classification and decomposable scores support benchmarking, funding allocation, and diagnosing institutional strengths/weaknesses in AI commercialization and R&D translation.
• Robustness in small samples: The prior-based shrinkage mitigates overfitting and weight concentration risks typical in small-N institutional studies, while cross-validation selects appropriate prior strength.
• Practical considerations: Users must supply credible AHP priors and a sensible κ candidate grid; results depend on sample size and outcome-model specification. The method is most useful where a balance of interpretability and empirical performance is desired (e.g., policy evaluation, funding decisions, institutional audits).