A Computational Framework for Metric Calibration and Budget Reallocation of Cross-Platform Retail Media Incremental Effects

Retail media refers to retailer-operated online and offline media environments in which brands place advertisements and retailers use first-party transaction data to measure and attribute advertising outcomes. By 2026, spending in North America will rise by 17.8% year-on-year to $71.09 billion, and by 2030, it is expected to reach $142.07 billion and account for 23.9% of the total U.S. digital ad spend. In-store digital media is one of the fastest-growing types of this. The attribution rules for this format are defined independently by each network; attribution windows vary substantially, from seven days after a view to same-day click attribution, and performance metrics range from total sales to gross merchandise value (GMV).The network cannot determine whether the same consumer has been identified by another network, and according to industry surveys, the performance data of the same advertising campaign across different networks may differ by as much as 15 per cent. Seventy-five per cent of the advertisers are unaware of how to determine an additional effect, and only 15 per cent believe their organisation can measure such changes. As the number of networks run by brands has increased from six to eleven, the total self-reported incremental effects across networks have been consistently higher than the actual incremental effects at the brand level; in-store digital media is understated under the last-click attribution model because it lacks a click signal. This study develops a computational calibration and budget-reallocation framework that preserves the original attribution rules of individual retail media networks while mapping their self-reported effects onto a unified incremental scale. Geographic holdout experiments are used as attribution-independent anchors, and network-specific conversion relationships are estimated through a hierarchical Bayesian model implemented by parallel NUTS sampling. Cross-network repeated exposure is encoded in a sparse user–network–time matrix using anonymized identifiers, duplicated increments are corrected through vectorized contribution reallocation, and monotonic cubic-spline response curves are fitted for constrained budget optimization at 1% budget increments. The computational dataset contains nine retail media networks, 42 brands, and 317 advertising campaigns; all cross-platform records are organized in 24-hour aggregation windows, with a maximum association window of seven days.The in-store calibration anchor contains 23 cities, 133 stores, and 23,901 ad-slot weeks, with the spatial-recognition error radius controlled within 20 m to provide a high-precision offline reference for computational calibrationComputational evaluation shows that the mean absolute cross-network discrepancy decreases from 14.8% to 3.2% after Bayesian calibration. Duplicate reach accounts for 27.4% of total reach, including 21.3% from users reached by exactly two networks and 6.1% from users reached by three or more networks. For in-store digital media, the normalized incremental effect increases from 0.583 under last-click attribution to 0.90 after Bayesian calibration and 0.96 after overlap correction, while the median unit-budget return rank improves from 6 to 3. Under a fixed total budget, the constrained reallocation algorithm predicts a 12.6% increase in brand-level incremental response, including 7.9 percentage points associated with reallocating budget toward complementary in-store reach and 4.7 percentage points associated with redistribution among online networks. The resulting workflow provides a reusable computer-side procedure for cross-platform data standardization, Bayesian metric calibration, sparse-matrix overlap correction, marginal-response estimation, and constrained budget optimization, thereby improving the reproducibility of cross-network incremental-effect measurement and allocation analysis.