Continuous time modelling with individually varying time intervals for oscillating and non‐oscillating processes
- 15 March 2012
- journal article
- Published by Wiley in British Journal of Mathematical and Statistical Psychology
- Vol. 66 (1), 103-126
- https://doi.org/10.1111/j.2044-8317.2012.02043.x
Abstract
When designing longitudinal studies, researchers often aim at equal intervals. In practice, however, this goal is hardly ever met, with different time intervals between assessment waves and different time intervals between individuals being more the rule than the exception. One of the reasons for the introduction of continuous time models by means of structural equation modelling has been to deal with irregularly spaced assessment waves (e.g., Oud & Delsing, 2010). In the present paper we extend the approach to individually varying time intervals for oscillating and non-oscillating processes. In addition, we show not only that equal intervals are unnecessary but also that it can be advantageous to use unequal sampling intervals, in particular when the sampling rate is low. Two examples are provided to support our arguments. In the first example we compare a continuous time model of a bivariate coupled process with varying time intervals to a standard discrete time model to illustrate the importance of accounting for the exact time intervals. In the second example the effect of different sampling intervals on estimating a damped linear oscillator is investigated by means of a Monte Carlo simulation. We conclude that it is important to account for individually varying time intervals, and encourage researchers to conceive of longitudinal studies with different time intervals within and between individuals as an opportunity rather than a problem.Keywords
This publication has 35 references indexed in Scilit:
- The Disaggregation of Within-Person and Between-Person Effects in Longitudinal Models of ChangeAnnual Review of Psychology, 2011
- OpenMx: An Open Source Extended Structural Equation Modeling FrameworkPsychometrika, 2011
- Estimating Dynamical Systems: Derivative Estimation Hints From Sir Ronald A. FisherMultivariate Behavioral Research, 2010
- Power equivalence in structural equation modellingBritish Journal of Mathematical and Statistical Psychology, 2010
- Automatic search for fMRI connectivity mapping: An alternative to Granger causality testing using formal equivalences among SEM path modeling, VAR, and unified SEMNeuroImage, 2010
- Analyzing reciprocal relationships by means of the continuous‐time autoregressive latent trajectory modelStatistica Neerlandica, 2008
- Focus Article: Idiographic Filters for Psychological ConstructsMeasurement: Interdisciplinary Research and Perspectives, 2007
- Continuous time modeling of panel data: SEM versus filter techniquesStatistica Neerlandica, 2007
- The origins of the sampling theoremIEEE Communications Magazine, 1999
- Power and money: Designing statistically powerful studies while minimizing financial costs.Psychological Methods, 1997