Real-time detection of mean and variance changes in experience sampling data: A comparison of existing and novel statistical process control approaches

Abstract

Retrospective analyses of experience sampling (ESM) data have shown that changes in mean and variance levels may serve as early warning signs of an imminent depression. Detecting such early warning signs prospectively would pave the way for timely intervention and prevention. The exponentially weighted moving average (EWMA) procedure seems a promising method to scan ESM data for the presence of mean changes in real-time. Based on simulation and empirical studies, computing and monitoring day averages using EWMA works particularly well. We therefore expand this idea to the detection of variance changes and propose to use EWMA to prospectively scan for mean changes in day variability statistics (i.e., s2, s, ln(s)). When both mean and variance changes are of interest, the multivariate extension of the EWMA procedure (MEWMA) can be applied to both the day averages and a day statistic of variability. We evaluate these novel approaches to detecting variance changes by comparing them to EWMA-type procedures that have been specifically developed to detect a combination of mean and variance changes in the raw data: EWMA-S2 and EWMA-ln(S2). We ran a simulation study to examine the performance of the two types of approaches in detecting mean, variance or both types of changes. The results indicate that monitoring day statistics using (M)EWMA works well and outperforms the EWMA-S2 and EWMA-ln(S2) procedures. Based on the results, we provide recommendations on which statistic of variability to monitor based on the type of change (i.e., variance increase or decrease) one expects.

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