Archive for December, 2012

A Differential Equations Model for the Ovarian Hormone Cycle

Monday, December 17th, 2012

Boker, S. M., Neale, M. C. & Klump, K. L. (in press) A Differential Equations Model for the Ovarian Hormone Cycle. In Handbook of Relational Developmental Systems: Emerging Methods and Concepts, P. C. Molenaar, R. Lerner, & K. Newell (Eds). New York: John Wiley & Sons

Dynamical systems models of behavior and regulation have become increasingly popular due to the promise that within-person mechanisms can be modeled and explained. However, it can be difficult to construct differential equation models of regulatory dynamics which test specific theoretically interesting mechanisms. The current chapter uses the example of ovarian hormone regulation and develops a model step by step in order for the model to be able to capture features of observed hormone levels as well as to link parameters of the model to biological mechanisms. Ovarian hormones regulate the monthly female reproductive cycle and have been implicated as having effects on affective states and eating behavior. The three major hormones in this system are estrogen, progesterone, and lutenizing hormone. These hormones are coupled together as a regulatory system. Estrogen level is associated with the release of lutenizing hormone by the hypothalamus. Lutenizing hormone triggers ovulation and the transformation of the dominant follicle into the corpus luteus which in turn produces progesterone. A differential equations model is developed that is biologically plausible and produces nonlinear cycling similar to that seen in a large ongoing daily-measure study of ovarian hormones and eating behavior.

The manuscript of this article accepted for publication can be requested as a pdf file from the first author: Steve Boker.

On the Equilibrium Dynamics of Meaning

Monday, December 17th, 2012

Boker, S. M. & Martin, M. (in press) On the Equilibrium Dynamics of Meaning. In Current Issues in the Theory and Application of Latent Variable Models, M. Edwards & R. MacCallum, (Eds). New York: Taylor & Francis.

Meaning is at the heart of what we do in latent variable modeling. A latent construct is a way to aggregate and focus meaning into quantifiable constructs. Structural models, and in particular factor models, are a way to use the considerable power of product moment matrices to focus meaning in such a way that it aggregates across participants (or within participant across time) in the hope that the meaning that the psychologist had in mind is the meaning that emerges in the latent variable indicated by the participants’ responses. But, what is meaning? And how is it attached to words or utterances? Philosophers of language have written about this problem, and so we review some recent arguments in epistemology in order to build the central thesis of this paper: If one takes context into account, intraindividual meanings are likely to have intrinsic dynamics that tend towards stable equilibria. We then discuss the implications from a lifespan psychological perspective for the meaning of an example variable: quality of life. Finally, some we discuss some ideas about what might be necessary in order to specify a factor analysis of sufficiency rather than a factor analysis of aggregation.

The manuscript of this article accepted for publication can be requested as a pdf file from the first author: Steve Boker.

Dynamical Systems and Differential Equation Models of Change

Monday, December 17th, 2012

Boker, S. M. (2012) Dynamical Systems and Differential Equation Models of Change. In APA Handbook of Research Methods in Psychology, Volume 3, H. Cooper, A. Panter, P. Camic, R. Gonzalez, D. Long, & K. Sher, (Eds). Washington, DC: American Psychological Association, pp 323-333.

This chapter provides a brief introduction to dynamical systems modeling from the standpoint of latent differential equations.

The manuscript of this article accepted for publication can be requested as a pdf file from the author: Steve Boker.

Correlational Methods for Analysis of Dance Movements

Monday, December 17th, 2012

Brick, T. R. & Boker, S. M. (2011) Correlational Methods for Analysis of Dance Movements. Dance Research, Special Electronic Issue: Dance and Neuroscience: New Partnerships, 29:2, 283–304

We propose to present three methods for the exploration of symmetry and synchrony in motion-capture data as is it applied to dance and illustrate these with examples from a study of free-form dance. First, Generalized Local Linear Approximation (GLLA) provides a transformation from the positional data returned by such a system into a representation including approximations of velocity and acceleration. Using these newly transformed data, time-lagged autocorrelation can provide insight into the structure of temporal symmetry within a single person’s movements during the dance. Windowed cross-correlation can show other kinds of symmetry between individuals or between an individual and an outside stimuli, such as a rhythm or musical work. Combined, these techniques provide powerful tools for the examination of the structure of symmetry and synchrony in dance.

The manuscript of this article accepted for publication can be requested as a pdf file from the first author: Timothy Brick at the Max Planck Institute for Human Development.

OpenMx: An Open Source Extended Structural Equation Modeling Framework

Monday, December 17th, 2012

Boker, S. M., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., Spies, J., Estabrook, R., Kenny, S., Bates, T., Mehta, P., & Fox, J. (2011) OpenMx: An Open Source Extended Structural Equation Modeling Framework. Psychometrika, 76:2, 306-317. NIHMS ID: 427396

OpenMx is free, full-featured, open source, structural equation modeling (SEM) software. OpenMx runs within the R statistical programming environment on Windows, Mac OS-X, and Linux computers. The rationale for developing OpenMx is discussed along with the philosophy behind the user interface. The OpenMx data structures are introduced — these novel structures define the user interface framework and provide new opportunities for model specification. Two short example scripts for the specification and fitting of a confirmatory factor model are next presented. We end with an abbreviated list of modeling applications available in OpenMx 1.0 and a discussion of directions for future development.

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.

Time Delay Embedding Increases Estimation Precision of Models of Intraindividual Variability

Monday, December 17th, 2012

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.