Compositional Data Structure and Data Transformation in Log-ratio Form: A Theoretical and Methodological Re-Analysis of the Statistical Claims of Acabado and Martin’s Indigenous Archaeology in the Philippines

Myfel D. Paluga* and Andrea Malaya M. Ragragio

We present a theoretical and methodological re-analysis of Acabado and Martin’s Indigenous Archaeology using compositional data analysis. The book’s statistical treatment is critiqued for limited engagement with uncertainty, absence of probabilistic reasoning, and non-systematic use of chi-square tests that neglect Pearson residuals and overlook the compositional constraints of the data. We focus on the Kiangan (Ifugao, Philippines) faunal dataset to (a) demonstrate the necessity of log-ratio transformation for valid inference, and (b) provide a statistically coherent reinterpretation. This reanalysis offers both a revised narrative and a corrective example of unmethodical statistical application. Faunal assemblages are treated explicitly as compositions. Proportions are transformed into isometric log-ratio (ILR) coordinates, mapping the simplex to Euclidean space, allowing standard statistical evaluation while preserving compositional relationships. A closed geometric mean defines the compositional center, and deviations are assessed in ILR space. Uncertainty is incorporated via Dirichlet-based resampling, producing confidence intervals for ILR coordinates. The re-analysis reveals a systematic shift in faunal composition. Early assemblages show negative ILR coordinates, reflecting predominance of non-prestige taxa, whereas the late interval occupies a distinct positive region, indicating a robust transition toward deer and prestige dominance. This represents a structural reorganization rather than an incremental change. The book only hints at broader dynamics in the 11th–15th centuries (even as it strongly asserts a 16th century colonialism-associated breakpoint); these patterns emerge only through formal modeling, simulation, and probabilistic analysis. Overall, log-ratio transformation and probabilistic modeling materially reshape interpretations of faunal data, underscoring the necessity of methodologically rigorous statistical practice in archaeological research.