Scale Invariance and Symmetry-Breaking Predictor Selection in Modeling the Accreditation Status of Chilean Universities from Financial and Management Indicators

Institutional accreditation is a high-stakes decision under uncertainty: Chilean universities commit strategic resources years before knowing which indicators will weigh the most in the National Accreditation Commission’s judgment. We characterize the accreditation status of 48 Chilean universities from financial, academic and management indicators reported to the Higher Education Information System (SIES) for 2017–2021 (240 institution-year observations). Three symmetry structures organize the analysis: scale invariance (indicators normalized per student or per academic), the symmetric correlation matrix under hierarchical clustering, and a permutation-symmetric specification that variable selection deliberately breaks. A stable core of predictors, admission selectivity, the net financial result per student, and students per doctoral full-time-equivalent, survives four robustness checks: ordered logit re-estimation, institution-clustered errors, a 2000-replication institution-level bootstrap, and leave-one-institution-out cross-validation (out-of-sample cross-validated coefficient of determination, Q2, near 0.71). Research output per academic, decisive in M2, falls outside that battery and is not claimed as verified. First-year retention is significant under clustered errors but clears neither the ordinal re-estimation (p = 0.614) nor the 95% sign stability threshold (88.2%) and is reported as suggestive rather than stable. The institutional-type intercept is absorbed once research intensity enters, but interaction tests reject slope symmetry between CRUCH (the Chilean Council of Rectors) and private universities: the association structure is partially, not fully, symmetric. We discuss implications for strategic planning and Goodhart risks.