Auditing longitudinal data across institutional regimes: a graph-based compatibility protocol with evidence from Tunisia

Technical Summary: Auditing Longitudinal Data Across Institutional Regimes

Problem Statement
Longitudinal datasets often concatenate records generated under distinct legal, administrative, or statistical regimes. While a common scale or variable name may persist, the underlying meaning, sampling frames, coding rules, or legal categories frequently change. Standard data quality metrics (e.g., missingness, measurement error) and statistical techniques (e.g., structural break detection, measurement invariance) are insufficient for this specific challenge. Structural break methods identify changes in stochastic laws but do not distinguish between a legitimate administrative level shift and a fundamental disagreement in temporal shape. Similarly, measurement invariance requires latent variable models often unavailable for public-sector aggregates. The core problem is determining when records from successive regimes can be treated as a single analytical object without conflating distinct administrative realities.

Methodology: The Graph-Based Compatibility Protocol
The paper proposes a deterministic, ordered audit framework that decomposes inter-regime disagreement into distinct, auditable components. The method models the data environment as a finite connected graph $G=(V, E)$, where vertices represent regime-specific data environments and edges represent registered comparison windows.

The audit proceeds through four ordered stages:

1. Level Registration: For each edge (pair of regimes), the method estimates a constant level crosswalk using coordinatewise median minimization ($L_1$ norm). This isolates the "level shift" from the data.
2. Authorized Correction: The residual difference is projected onto a pre-authorized, compact convex set of corrections ($C_e$). This set allows for declared, bounded normalizations or recodings (e.g., a 15% adjustment) but prohibits discretionary changes to the historical series.
3. Shape Disagreement Measurement: The residual after registration and authorized correction ($D_e$) measures the "shape" disagreement—the part of the difference that cannot be absorbed by a constant translation or declared normalization.
4. Global Consistency and Feasibility:
   • Cycle Consistency: The system of pairwise translations is tested for global coherence using graph incidence matrices. If the signed sum of translations around a cycle is non-zero, the crosswalks are inconsistent regardless of individual edge residuals.
   • Full-Record Lift: The method tests whether the numerically reconciled vectors can be "lifted" to a full record that satisfies administrative, legal, and capacity constraints (e.g., non-negativity, budget caps). This is formulated as a linear feasibility problem; if infeasible, a dual certificate proves the impossibility of a valid full record.

The final output is not a composite quality score but an ordered disposition (Keep Separate, Review, or Conditional Pooling) based on the magnitude of the shape residual, its rank against within-regime controls, and the presence of hard incompatibilities.

Key Contributions

• Decomposition of Disagreement: The paper rigorously separates level conversion (admissible translation) from shape disagreement (structural incompatibility), demonstrating that a large level shift can coexist with a small residual, and vice versa.
• Graph-Theoretic Formulation: It adapts sheaf-theoretic concepts (local agreement vs. global exactness) to policy data, explicitly identifying cycle inconsistencies in crosswalk networks that pairwise diagnostics miss.
• Administrative Admissibility: It introduces a "full-record lift" test, ensuring that numerical reconciliation does not violate legal or physical constraints (e.g., a reconciled total that exceeds the sum of admissible sub-components).
• Ordered Audit Procedure: The method enforces a strict sequence where variables, windows, and correction sets are registered before residuals are inspected, preventing retroactive model tuning to achieve desired outcomes.

Empirical Results: Evidence from Tunisia
The method is applied to a constructed quarterly panel for Tunisia (2000Q1–2019Q4) covering three coordinates: institutional trust, crisis stress, and policy response. The analysis focuses on three historical boundaries: Pre-Shock (2010), Shock-Transition (2011), and Transition-Post (2014).

• Residual Analysis: After level registration and bounded correction, the Shock-Transition boundary (2010Q4–2012Q2) exhibited the largest shape residual (0.209) in 30 of 36 model specifications. It exceeded all 33 within-regime pseudo-boundary controls.
• Contrast with Level Diagnostics: Conventional level diagnostics (mean/median shifts) highlighted the Pre-Shock and Transition-Post boundaries as most prominent. However, the post-registration shape residual uniquely identified the Shock-Transition boundary as exceptional.
• Sensitivity: The Shock-Transition boundary remained the most exceptional across variations in polynomial degree, ridge penalties, and window lengths, though absolute magnitudes varied.
• Disposition: Based on the protocol, the Shock-Transition boundary requires "Keep Separate" (preserving the regime break), while the other boundaries require "Review before pooling."

Significance and Claims
The paper modestly claims to provide a protocol for accountable integration rather than a causal analysis of the Tunisian transition.

• Not Causal: The audit does not estimate the causal effect of the revolution or the constitution; the boundaries are institutionally fixed, not statistically estimated.
• Separation of Claims: It demonstrates that numerical reconciliation, shape compatibility, coherent conversion, and administrative admissibility are distinct propositions. A series can be numerically reconciled yet administratively inadmissible.
• Governance Utility: The method supports public-sector data governance by providing a transparent, reproducible audit trail that distinguishes between legitimate level conversions and fundamental structural incompatibilities, ensuring that heterogeneous records are not pooled without explicit justification.

The study concludes that computational continuity (concatenating time series) is not evidence of institutional comparability. The proposed graph-based audit offers a structured mechanism to verify compatibility before integration, preserving the integrity of longitudinal analysis across institutional regimes.