Latent Emotional Dimensions in Bach Flower Remedy Co-Prescription: A PCA Simulation Study of Student Stress and Burnout Patterns

Abstract

Bach Flower Remedies are prescribed in combination, not individually, because emotional states co-occur: a university student in examination stress typically presents with several concurrent emotional disturbances whose joint pattern determines the prescription. This co-prescription structure — which remedies practitioners select together — carries latent information about the underlying emotional architecture of student stress that standard remedy-frequency analyses discard. This simulation study applies principal component analysis (PCA) to a synthetic co-prescription dataset generated from a known three-factor latent structure representing emotional dimensions of student burnout: Demand Overload (Elm, Oak, White Chestnut, Vervain), Vital Depletion (Hornbeam, Olive, Centaury), and Evaluative Fear (Larch, Cerato, Mimulus, Rock Rose, Cherry Plum). The simulation embeds twelve remedies curated for student stress and burnout presentations across 240 hypothetical consultation records drawn from a generic university student practitioner caseload. The base scenario recovers all three components with Tucker's congruence coefficient φ = 0.954 and explains 81.9% of total variance in the co-prescription matrix. A PCA-based regression model predicting overall emotional burden score outperforms a twelve-predictor conventional model by ΔAIC = 30.6 — the strongest parsimony advantage reported across a series of parallel simulation studies. A systematic sensitivity analysis across eight sample sizes (n = 40 to 400) and seven co-prescription correlation levels establishes that component recovery reaches φ ≥ 0.95 in 97% of replications at n = 320 and that the AIC advantage holds consistently across all correlation conditions (ΔAIC = 26.7 to 32.1). Bridge remedies — Oak (spanning Overload and Depletion) and Cherry Plum (spanning Depletion and Fear) — emerge as theoretically coherent transitional prescriptions whose cross-component loadings reflect their recognized role in presentations where emotional states compound across dimensions. The paper introduces the concept of the dynamic remedy signature: each student's characteristic temporal sequence of dominant emotional components across the academic calendar, recoverable by longitudinal PCA of serial consultation records and directly informative for adaptive remedy selection. No clinical efficacy claims are made; the analysis treats prescription records as structural behavioural data from which latent co-occurrence patterns are extracted.