Magnitude Without Direction: A Representational Limit on the General Factor of Psychopathology

The general factor of psychopathology, p, orders people on a broad dimension of psychiatric burden and predicts impairment, developmental risk, and other adverse outcomes. Debate has focused on which latent-variable structure best recovers p, but comparative fit cannot resolve that question cleanly because bifactor models possess high fitting propensity. This article identifies a prior problem at measurement. Many psychiatric instruments convert directionally opposite manifestations into the same severity value. Major-depression criteria and the PHQ-9, for example, count insomnia or hypersomnia, appetite loss or overeating, and psychomotor retardation or agitation toward the same syndrome and severity score. Human data show that the discarded direction can carry biological signal: depressed patients with increased versus decreased appetite show different endocrine, inflammatory, metabolic, and neural profiles despite comparable overall depressive severity, and genetic analyses likewise distinguish directionally defined neurovegetative symptoms. I formalize the consequence as a non-injective measurement map. If two distinct latent states map to the same observed score vector on a rectified coordinate, no covariance model or downstream factor score can recover the information that the instrument removed. This result does not imply that p is artifactual or useless; it implies that magnitude is not generally sufficient for representation. Developmental neuroscience provides biological plausibility for signed latent disturbances because opposing structural changes can be dissociated experimentally, but the formal result does not depend on any particular developmental mechanism. I propose tests based on bipolar rescoring, held-out prediction, treatment-by-direction interactions, and etiologically anchored contrasts. The appropriate remedy is not necessarily a different factor model. It is measurement that preserves which way a clinically relevant system deviated.