## Time Delay Embedding Increases Estimation Precision of Models of Intraindividual Variability

Oertzen, T. v. & Boker, S. (2010) Time Delay Embedding Increases Estimation Precision of Models of Intraindividual Variability. *Psychometrika*, **75**:1, 158-175. NIHMS ID: 427398

This paper investigates the precision of parameters estimated from local samples of time dependent functions. We find that *time delay embedding*, i.e., structuring data prior to analysis by constructing a data matrix of overlapping samples, increases the precision of parameter estimates and in turn statistical power compared to standard independent rows of panel data. We show that the reason for this effect is that the sign of estimation bias depends on the position of a misplaced data point if there is no a priori knowledge about initial conditions of the time dependent function. Hence, we reason that the advantage of time delayed embedding is likely to hold true for a wide variety of functions. We support these conclusions both by mathematical analysis and two simulations.

The manuscript of this article accepted for publication can be downloaded as a PDF. This article may not exactly replicate the ﬁnal version published in Psychometrika. It is not the copy of record.

Tags: Dynamical Systems Analysis, Latent Differential Equations, Structural Equation Modeling

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