From Zero to Sixty: Calibrating Real-Time Responses

Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying covariates to a continuous response variate. Using real-time data obtained from an experiment in psychoacoustics, we showcase new statistical tools that incorporate dynamical elements of an input-output system. We employ functional data analysis (FDA) methods and a simple differential equation to analyze and model the continuous responses. Furthermore, we outline the issues involved in analyzing input-output systems when the exact form of the underlying mathematical model is not known. Finally, we develop a calibration method to facilitate inter-subject and intra-subject comparisons. This work was supported by grants from the National Sciences and Engineering Research Council (NSERC) to J. O. Ramsay and to D. J. Levitin, and by a grant from the Social Sciences and Humanities Research Council (SSHRC) to D. J. Levitin. We would like to thank Bennett Smith for designing and implementing the software used to conduct the pitch tracking experiment. Also, we wish to thank the research assistants in the Levitin Laboratory involved in the data collection: Catherine Chapados, Andrew Schaaf and Carla Himmelman. We would also like to acknowledge Giles Hooker’s work on implementing the generalized profiling software used within this paper.