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.
Highlights
AR(1) models have previously been applied to ILD to study the regulation of affect and the between-person differences in affect dynamics
As we showed above, distinguishing between two-level and three-level time series data is tricky because beep-level inertia and day-level variance can be confounded
Based on our illustration data, using the Akaike Information Criterion (AIC) and/or Bayesian Information Criterion (BIC) to select between the AR models seems to be a feasible alternative
Summary
AR(1) models have previously been applied to ILD to study the regulation of affect and the between-person differences in affect dynamics. In this context, the autoregressive parameter of the AR(1) model is interpreted as the inertia of affect, indicating how much carry-over there is from one measurement to the next. Inertia research has been done with observational data (e.g., Kuppens et al, 2012), daily diary data (e.g., Wang et al, 2012; Brose et al, 2015), and ESM data (e.g., Suls et al, 1998; Koval and Kuppens, 2011). The recently developed network approach to psychopathology involves (vector) autoregressive modeling of ESM data (Borsboom and Cramer, 2013; Bringmann et al, 2013)
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