Time Will Tell: Time Series Modeling in Psychology

Abstract

The increasing popularity of intensive longitudinal research designs in psychology, such as the experience sampling method (ESM), calls for methodological research into optimal ways of analyzing the resulting intensive longitudinal data (ILD). Due to the high number of repeated measurements in this type of study, it is possible to look beyond the traditional toolbox of statistical techniques in psychology and to use time series analysis approaches. Time series models can be used to uncover the dynamics of a process as it unfolds over time and to investigate how individual people may differ in these process dynamics. The goal of this dissertation was to broaden our understanding of the possibilities as well as the challenges for applying time series techniques to ILD in psychology. The first chapter presented an exploratory study, which considered the usefulness of mixed (i.e., multilevel) Markov models for the ILD context, and which aimed to demonstrate the potential of this modeling approach for the study of state-switching processes. The chapter brought together information and examples concerning Markov modeling found in literature scattered across various fields of science, while focusing on those aspects most relevant to modeling ILD in psychology. Chapters 3 to 5 focused on a different class of time series models, which has already gained popularity with psychological researchers and which is often applied to ILD, namely the class of autoregressive models. In Chapter 3, a multilevel threshold-autoregressive (TAR) model for affect regulation was developed, building on existing applications of multilevel AR(1) models and the TAR model for a single time series. Although the substantive focus of the chapter is on affect dynamics, the modeling approach can be seen as a basic framework that could be applied to any psychological process involving (potentially) state-dependent inertia or autocorrelation. Chapters 4 and 5 investigated two somewhat related issues in the analysis of ESM data with time series techniques such as autoregressive modeling. Both have to do with the typical design of ESM studies and how this affects the resulting data: Typically, measurements are taken at semi-random times throughout the day and over multiple days. The individual data points are nested within persons, but can also be considered to be nested within days, which in turn are nested within persons. In Chapter 4, a novel three-level AR(1) model was proposed, which enables us to study the inertia of affect from day to day as well as from moment to moment within a day. Moreover, it was demonstrated that the question of the number of levels in ESM data deserves careful consideration, because misspecification of the number of levels can distort conclusions based on AR(1) modeling. Chapter 5 focused on an issue caused by the varying measurement intervals in many ESM studies, namely, that they result in unequally spaced data that violate an assumption of discrete-time (DT) models. In this chapter it was explained why bias in the parameters of interest is to be expected under these circumstances, and simulations were used to investigate the practical relevance of this bias.