What's in a Day? A Guide to Decomposing the Variance in Intensive Longitudinal Data

Abstract

In recent years there has been a growing interest in the use of intensive longitudinal research designs to study within-person processes. Examples are studies that use experience sampling data and autoregressive modeling to investigate emotion dynamics and between-person differences therein. Such designs often involve multiple measurements per day and multiple days per person, and it is not clear how this nesting of the data should be accounted for: That is, should such data be considered as two-level data (which is common practice at this point), with occasions nested in persons, or as three-level data with beeps nested in days which are nested in persons. We show that a significance test of the day-level variance in an empty three-level model is not reliable when there is autocorrelation. Furthermore, we show that misspecifying the number of levels can lead to spurious or misleading findings, such as inflated variance or autoregression estimates. Throughout the paper we present instructions and R code for the implementation of the proposed models, which includes a novel three-level AR(1) model that estimates moment-to-moment inertia and day-to-day inertia. Based on our simulations we recommend model selection using autoregressive multilevel models in combination with the AIC. We illustrate this method using empirical emotion data from two independent samples, and discuss the implications and the relevance of the existence of a day level for the field.

Depression symptoms moderate the association between emotion and communal behavior.

“…First, variance decomposition, using the intraclass correlation coefficient (ICC), was used to evaluate whether events or days were exchangeable within the individual. Following recommendations by de Haan-Rietdijk, Kuppens, and Hamaker (2016), variance decomposition models were conducted with an autoregressive 1 covariance matrix over events. For agreeable behavior, 91.29% of variance was explained at the event level, 1.94% at the day level, and 6.77% at the person level.…”

At the Frontiers of Modeling Intensive Longitudinal Data: Dynamic Structural Equation Models for the Affective Measurements from the COGITO Study

“…While some of these models have been used in dynamic mutlilevel analyses, allowing for individual differences in the dynamics parameters through modeling these as random effects at level 2 (see Asparouhov et al, 2017Asparouhov et al, , 2018Haan-Rietdijk, Gottman, Bergeman, & Hamaker, 2016;Wang et al 2012), this area is still largely unexplored. However, the need to move beyond firstorder autoregressive models is undeniable, whether the interest is in mere prediction or in actually understanding the underlying mechanism.…”

“…Haan-Rietdijk, Kuppens, and Hamaker (2016) compared the two-level and three-level approach in the context of experience sampling data, where the two-level model consists of measures nested in persons, and the three-level model consists of beeps nested in days which are nested in persons. The results showed that autoregression in a two-level model may result from ignoring the three-level structure of the data.…”

Discrete- vs. Continuous-Time Modeling of Unequally Spaced Experience Sampling Method Data

“…We focus on the N = 1 case where a model is fit to one person's data, using simulations as well as an empirical illustration to address the question of whether substantial bias in the parameters of interest may result from using DT (vector) autoregressive models. This is an important question because autoregressive (AR) models and extensions such as the vector autoregressive (VAR) model are frequently used in ESM research in areas such as affect dynamics (e.g., Suls et al, 1998 ; Koval and Kuppens, 2012 ; de Haan-Rietdijk et al, 2016 ; Van Roekel et al, 2016 ) and the emerging network approach to psychopathology (Borsboom and Cramer, 2013 ; Bringmann et al, 2013 ; Wichers, 2014 ). Thus, questions about the validity of DT model results for unequally spaced data bear directly on findings reported in these fields and on recommendations for follow-up studies, in addition to general questions about optimal design and data analysis for these types of studies.…”