Time

Researchers who investigate how emotions change over time often turn to one of two classes of models for their analyses, namely the autoregressive models and discounting models. Both modeling traditions seem to differ in their structure and interpretation.: Autoregressive models regress the value of the dependent variable at time t on the value of the same variable at the previous timepoint t – 1 without reference to any independent variables that may influence the dependent variable. Discounting models, on the other hand, regress the value of the dependent variable at time t on a cumulative discounted sum of independent variables so that values of these variables influence the dependent variable more at proximal rather than distant times in the past. Despite the apparent difference between both modeling traditions, we show mathematically that some discounting models can be rewritten to a specific case of the VARMAX, an instance of the autoregressive model. This research therefore explicates some of the similarities and shared assumptions of both modeling traditions, opening up new pathways to study emotion dynamics.

Stochastic Delay Differential Equations (SDDEs) have been proposed as models for stochastic systems that exhibit a time-delayed dependence on earlier system states. SDDEs have been used to describe neurophysiological phenomena such postural control and pupil light reflexes. We propose an SDDE model for driving performance that accounts for time-delayed processing of visual information related to lane-keeping in terms of three parameters: sensitivity to changing visual information, processing time-lag, and inherent noise level. We apply the model to time-series data of steering behaviour from a driving simulation. Concurrently with the primary tracking task, participants performed secondary tasks that require either purely cognitive or cognitive and visual-manual resources. Our results suggest that visual-manual secondary tasks mainly affect sensitivity to changing visual information and inherent noise, whereas cognitive secondary tasks mainly affect processing time-lag. Our model thus provides more fine-grained insight into the mechanisms underlying driver distraction than conventional behavioural measures such as the steering wheel reversal rate or mean deviation from the optimal driving performance, which remain at a purely descriptive level.

Model discovery techniques can help discover plausible candidate models from data and can aid theory-building in areas of cognitive science where empirical work has not yet led to formal specification. In this project we introduce a data-driven framework for discovery of parsimonious stochastic differential equation models from time series data in two or more dimensions. We discuss the theoretical foundation of the framework from stochastic calculus and illustrate the application to coupled time series. We first demonstrate the general approach through numerical examples. Then, we evaluate the viability of an extended approach in which we include exogenous predictors in both the deterministic and the stochastic components of the discovered model. Finally, we will discuss the development and use of inferential statistics within this framework. We illustrate the framework with an application in which we explore the relationship dynamics between dimensions of core affect from a daily life study.