Detecting association changes in intensive longitudinal data in real time: An exponentially weighted moving average procedure

Abstract

Within-person changes in linear associations may indicate worsening well-being and maladaptive functioning. We investigated whether such changes can be detected in real time using the exponentially weighted moving average (EWMA) procedure. Specifically, we investigated the effectiveness of first calculating association strength within time windows, considering several association measures (i.e. Pearson correlation, Spearman correlation, Pearson covariance, Penrose shape distance, Euclidean distance, Lorentzian distance, Manhattan distance and squared Euclidean distance), and then monitoring mean-level changes in these scores using EWMA. Additionally, we examined how changes in the mean and variance in the observed time series (with or without a correlation change) influence the detection performance of EWMA when applied to association scores. Our simulation results show that monitoring Pearson and Spearman correlation scores is advised, when no additional information is available about the presence of additional mean and/or variance changes in the observed time series. However, using other association measures, which are sensitive to more types of changes apart from the correlation (i.e. mean and/or variance), can improve detection performance given specific combinations of mean, variance and correlation changes. Using other measures can thus be valuable when the presence of such a combination of changes can be predicted before monitoring begins.