Covariance Estimation Matters for Multidimensional Normative Modeling: A Demonstration with Obsessive–Compulsive Disorder
Abstract
Normative models characterize individuals relative to a reference distribution, but choices used to estimate that distribution may change who appears most atypical. We examined how covariance estimation affects Mahalanobis-based deviation scores when reference measures concentrate at their minimum. Study 1 compared minimum covariance determinant (MCD), Ledoit–Wolf shrinkage, and sample covariance across 11 simulated conditions varying distributional shape, floor prevalence, and contamination, with reference samples of 62–5,000. Estimates and distances were evaluated against benchmarks derived from the generating distributions. All three estimators approached the target covariance under multivariate normality. MCD had the lowest covariance bias in the Gaussian contamination conditions. In uncontaminated floor conditions, its bias persisted at the examined prevalences of .25 or greater, while both alternatives approached the target. Study 2 examined 263 adults with obsessive–compulsive disorder and 62 screened controls. MCD excluded 24 controls whose profiles were consistent with ordinary reference variation. Ledoit–Wolf deviation scores correlated with quality of life (r = −.53). Across five scoring specifications, however, deviation added little explained variance beyond depression and obsessive–compulsive severity (ΔR² ≤ .003). Default MCD and Ledoit–Wolf shared only 17 of the 27 patients in their respective highest-deviation deciles. These findings show that stability of a group-level conclusion does not establish stability of individual characterization. Covariance estimation should be evaluated in relation to the reference distribution and intended use, including sensitivity of individual scores and rankings.
Related
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BibTeX
@misc{zaboski2026covariance,
title = {{Covariance Estimation Matters for Multidimensional Normative Modeling: A Demonstration with Obsessive–Compulsive Disorder}},
author = {Brian Zaboski and Christopher Pittenger},
howpublished = {PsyArXiv},
year = {2026},
month = sep,
doi = {10.31234/osf.io/yb86p_v1},
url = {https://osf.io/preprints/psyarxiv/yb86p_v1/},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Covariance Estimation Matters for Multidimensional Normative Modeling: A Demonstration with Obsessive–Compulsive Disorder
AU - Brian Zaboski
AU - Christopher Pittenger
PY - 2026
DA - 2026/09/22
PB - PsyArXiv
DO - 10.31234/osf.io/yb86p_v1
UR - https://osf.io/preprints/psyarxiv/yb86p_v1/
AB - Normative models characterize individuals relative to a reference distribution, but choices used to estimate that distribution may change who appears most atypical. We examined how covariance estimation affects Mahalanobis-based deviation scores when reference measures concentrate at their minimum. Study 1 compared minimum covariance determinant (MCD), Ledoit–Wolf shrinkage, and sample covariance across 11 simulated conditions varying distributional shape, floor prevalence, and contamination, with reference samples of 62–5,000. Estimates and distances were evaluated against benchmarks derived from the generating distributions. All three estimators approached the target covariance under multivariate normality. MCD had the lowest covariance bias in the Gaussian contamination conditions. In uncontaminated floor conditions, its bias persisted at the examined prevalences of .25 or greater, while both alternatives approached the target. Study 2 examined 263 adults with obsessive–compulsive disorder and 62 screened controls. MCD excluded 24 controls whose profiles were consistent with ordinary reference variation. Ledoit–Wolf deviation scores correlated with quality of life (r = −.53). Across five scoring specifications, however, deviation added little explained variance beyond depression and obsessive–compulsive severity (ΔR² ≤ .003). Default MCD and Ledoit–Wolf shared only 17 of the 27 patients in their respective highest-deviation deciles. These findings show that stability of a group-level conclusion does not establish stability of individual characterization. Covariance estimation should be evaluated in relation to the reference distribution and intended use, including sensitivity of individual scores and rankings.
ER -