A method for modeling the intrinsic dynamics of intraindividual variability: Recovering the parameters of simulated oscillators in multi-wave panel data

Abstract

A simple method for fitting differential equations to multi-wave panel data performs remarkably well in recovering parameters from underlying continuous models with as few as three waves of data. Two techniques for fitting models of intrinsic dynamics to intraindividual variability data are examined by testing these techniques' behavior in recovering the parameters from data generated by two simulated systems of differential equations. Each simulated data set contains 100 "subjects" each of whom are measured at only three points in time. A local linear approximation of the first and second derivatives of the subject's data accurately recovers the true parameters of each simulation. A state-space embedding technique for estimating the first and second derivatives does not recover the parameters as well. An optimum sampling interval can be estimated for this model as that interval at which multiple R2 first nears its asymptotic value.