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1. A Multiplicative Model of Psychopathology Measurement: An Application to Depression
Defining and quantifying uncertainty play vital roles in measuring psychopathology. Additive error models, which are a common approach to modeling uncertainty, maintain that each individual component (e.g., symptom) contributes only to the overall construct and this contribution does not depend on other components. However, in psychopathology research, multiplicative models may sometimes be more appropriate. For instance, the magnitude of one symptom may multiplicatively increase the severity of the overall psychopathology, and interventions, as reported in literature for various depression treatments, may cause multiplicative decreases in symptom severity. Multiplicative models can also realistically represent that severity converges at high levels of psychopathology and that a large proportion of general population would score low on psychopathology measures. Moreover, multiplicative models are invariant across scales, intuitive in interpretation, and robust against outliers. We applied multiplicative models to depression by reanalyzing data from 178 participants in three panels of the PROMIS dataset. Consistent with literature, multiplicative models can provide better fit than additive models both in terms of item-total and inter-panel relations, along with interpretive benefits. Our results demonstrate the potential informativeness of multiplicative models in psychopathology research. In addition, we provide a software implementation through an R package `lamme` and offer discussions on limitations and future directions.