What happens at night stays in the dark – Estimating autoregressive effects in three-level experience sampling data
Creators: name: Neubauer, Andreas B.
name: Scott, Stacey B.
name: Sliwinski, Martin J.
name: Smyth, Joshua M.
Publisher: name: ZPID (Leibniz Institute for Psychology)
Year: 2021
Subjects: subject: 150

description: Background: Unequally spaced inter-measurement intervals are common in intensive longitudinal data which can lead to blurred estimates of autoregressive effects. Dynamic structural equation models (DSEM) have been discussed as an approach to accommodate this issue. One core feature of DSEM is that they assume a continuous decay of the autoregressive effect with increasing time between adjacent measurements. However, intervals of the same length can have psychologically different meanings. Specifically, an eight-hour interval from the evening to the next morning may be psychologically distinct from an eight-hour interval during waking hours. This may complicate the interpretation of autoregressive effects estimated by DSEM in three-level experience sampling data. Objective and Research Questions: The central objective of this work is to present conceptual ideas on potential shortcomings of models that assume continuous processes when these processes are in fact interrupted. Simulated data will be presented that might, for instance, represent affective experiences of individuals reported several times per day over multiple days. The implications of different modeling approaches will be illustrated using an empirical example. Method: In the simulated data, different population models were assumed: (a) a continuous autoregressive process that continues overnight or (b) an interrupted overnight autoregressive process (either weaker or stronger autoregressive effect overnight than during the day). These simulated data were re-estimated using different versions of two-level DSEM in Mplus. Further, the implications of assuming continuous autoregressive effects are illustrated in an exemplary experience sampling data set. In this study, 242 participants (age range: 25-65 years) completed five momentary assessments of their current affective well-being per day for 14 consecutive days. Results: Findings from the simulation study show that falsely assuming a continuous process can severely bias the observed autocorrelation within days and across nights. Specifically, a continuous time DSEM approach leads to an underestimation of the across-night autoregressive effect and an overestimation of the within-day autoregressive effect if the true overnight autoregressive effect is larger than a within-day autoregressive effect between two temporally equally distant measurements. In contrast, the across-night autoregressive effect is overestimated and the within-day autoregressive effect is underestimated if the autoregressive effect is terminated across night. Results from the empirical example illustrate that the estimated within-day autoregressive effect (for both positive and negative affect) becomes larger if it is estimated separately from the overnight autoregressive effect. This suggests that the overnight autoregressive effect is interrupted. Overnight autoregressive effects were estimated as ρ = .191 (positive affect) and ρ =.193 (negative affect) and within-day effects were estimated as ρ = .437 (positive affect) and ρ =.379 (negative affect). A DSEM with a continuous autoregression function overestimated within-day autoregressive effects and underestimated the overnight autoregressive effect. Conclusions and implications: Results suggest that the application of DSEM to three-level experience sampling data should be considered carefully. Conventional DSEM analyses assume a continuous process across the whole observation period which may not be appropriate for some applications to experience sampling data. Alternative approaches with separate estimates of within-day and overnight autoregressive effects will be discussed.