A Hierarchical Latent Stochastic Differential Equation Model for Affective Dynamics

• Published in: Psychological methods 2011-12, Vol.16 (4), p.468-490
• Main Authors: Oravecz, Zita, Tuerlinckx, Francis, Vandekerckhove, Joachim
• Format: Article
• Language: English
• Subjects: Affect; Bayes Theorem; Belgium; Biological and medical sciences; Calculus; Computation; Computer Assisted Instruction; Correlation; Data Analysis; Data collection; Diaries; Emotions; Foreign Countries; Fundamental and applied biological sciences. Psychology; Graphs; Human; Humans; Individual Differences; Individuality; Investigations; Longitudinal Studies; Measurement; Models, Statistical; Models, Theoretical; Observation; Parameters; Process models; Psychology - statistics & numerical data; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics. Statistics. Methodology; Research Design; Statistical Probability; Statistics; Statistics. Mathematics; Stochastic Modeling; Stochastic models; Stochastic Processes; Time Factors; Time Perspective; Undergraduate Students; Universities
• ISSN: 1082-989X; 1939-1463
• DOI: 10.1037/a0024375

In this article a continuous-time stochastic model (the Ornstein-Uhlenbeck process) is presented to model the perpetually altering states of the core affect, which is a 2-dimensional concept underlying all our affective experiences. The process model that we propose can account for the temporal changes in core affect on the latent level. The key parameters of the model are the average position (also called home base), the variances and covariances of the process, and the regulatory mechanisms that keep the process in the vicinity of the average position. To account for individual differences, the model is extended hierarchically. A particularly novel contribution is that in principle all parameters of the stochastic process (not only the mean but also its variance and the regulatory parameters) are allowed to differ between individuals. In this way, the aim is to understand the affective dynamics of single individuals and at the same time investigate how these individuals differ from one another. The final model is a continuous-time state-space model for repeated measurement data taken at possibly irregular time points. Both time-invariant and time-varying covariates can be included to investigate sources of individual differences. As an illustration, the model is applied to a diary study measuring core affect repeatedly for several individuals (thereby generating intensive longitudinal data). (Contains 3 tables, 10 footnotes and 11 figures.)