The Limits of Recovering Latent Mood from Fallible Indicators: An Exploratory Simulation Study

Abstract

Studies that monitor mood with self-report diaries and passive behavioral measures usually ask how well a chosen model predicts the self-report. They rarely ask the question that comes before it: how much of the person’s underlying affective state those measures can recover at all. A disappointing prediction can mean a weak model or a weak set of measures, and the two problems have opposite remedies. We treat the self-report diary not as ground truth but as one fallible indicator with a specified reliability, and ask how far a latent mood state can be recovered from a small set of indicators of varying quality. In a generative simulation of a bipolar-type affective process, where the latent state is known by construction, we compare a linear filter and a flexible machine-learning model with an oracle reference: a smoother told the true phase and episode path. Across 120 conditions, (1) neither estimator exceeded the reference on average in any condition (median shortfall 0.018 for the linear filter and 0.035 for the flexible model, in proportion of latent variance), although the reference is a linear-Gaussian approximation and not a proven upper bound; (2) the reference rose monotonically with self-report reliability, from 0.62 to 0.93, a result that is built into the generator and illustrates attenuation for a dynamic latent state; (3) the self-report carried the mood level far more than the timing of onset, while the added value of behavioral indicators for detecting the current episode was small for a within-person reference and larger for a model that pools people; and (4) an oracle given the true parameters detected episode onset less well, at longer horizons, for irregular than for regular cyclers. The study was not prospectively registered, two of its four questions did not meet the decision rules written in the analysis code, and the reference has a known limitation that we document. We offer the design as a way to ask, before collecting data, whether better measures or better models are likely to be needed.