Functional Data Analysis for Dynamical System Identification of Behavioral Processes

Efficient new technology has made it straightforward for behavioral scientists to collect anywhere from several dozen to several thousand dense, repeated measurements on one or more time-varying variables. These intensive longitudinal data (ILD) are ideal for examining complex change over time but present new challenges that illustrate the need for more advanced analytic methods. For example, in ILD the temporal spacing of observations may be irregular, and individuals may be sampled at different times. Also, it is important to assess both how the outcome changes over time and the variation between participants' time-varying processes to make inferences about a particular intervention's effectiveness within the population of interest. The methods presented in this article integrate 2 innovative ILD analytic techniques: functional data analysis and dynamical systems modeling. An empirical application is presented using data from a smoking cessation clinical trial. Study participants provided 42 daily assessments of pre-quit and post-quit withdrawal symptoms. Regression splines were used to approximate smooth functions of craving and negative affect and to estimate the variables' derivatives for each participant. We then modeled the dynamics of nicotine craving using standard input-output dynamical systems models. These models provide a more detailed characterization of the post-quit craving process than do traditional longitudinal models, including information regarding the type, magnitude, and speed of the response to an input. The results, in conjunction with standard engineering control theory techniques, could potentially be used by tobacco researchers to develop a more effective smoking intervention.