February 20th, 2015
Boker, S.M.; (2015) Adaptive Equilibrium Regulation: A Balancing Act in Two Timescales. * Journal of Person-Oriented Research*, 1(1-2), 99-109

An equilibrium involves a balancing of forces. Just as one maintains upright posture in standing or walking, many self-regulatory and interpersonal behaviors can be framed as a balancing act between an ever changing environment and within-person processes. The emerging balance between person and environment, the equilibria, are dynamic and adaptive in response to development and learning. A distinction is made between equilibrium achieved solely due to a short timescale balancing of forces and a longer timescale *preferred equilibrium* which we define as a state towards which the system slowly adapts. Together, these are developed into a framework that this article calls Adaptive Equilibrium Regulation (AER), which separates a regulatory process into two timescales: a faster regulation that automatically balances forces and a slower timescale adaptation process that reconfigures the fast regulation so as to move the system towards its preferred equilibrium when an environmental force persists over the longer timescale. This way of thinking leads to novel models for the interplay between multiple timescales of behavior, learning, and development.

The article accepted for publication can be downloaded as a PDF.

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November 6th, 2014
Neale, M.C., Hunter, M.D., Pritikin, J.N., Zahery, M., Brick, T.R., Kirkpatrick, R., Estabrook, R., Bates, T.C., Maes, H.H., & Boker, S.M.; (in press) OpenMx 2.0: Extended Structural Equation and Statistical Modeling. * Psychometrika*

The new software package OpenMx 2.0 for structural equation and other statistical modeling is introduced and its features are described. OpenMx is evolving in a modular direction and now allows a mix-and-match computational approach that separates model expectations from fit functions and optimizers. Major backend architectural improvements include a move to swappable open-source optimizers such as the newly-written CSOLNP. Entire new methodologies such as Item Factor analysis (IRT) and State-space modeling have been implemented. New model expectation functions including support for the expression of models in LISREL syntax and a simplified multigroup expectation function are available. Ease-of-use improvements include helper functions to standardize model parameters and compute their Jacobian-based standard errors, access to model components through standard R $ mechanisms, and improved tab completion from within the R Graphical User Interface.

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: OpenMx, Structural Equation Modeling

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November 5th, 2014
Pritikin, J. N., Hunter, M. D., & Boker, S. M. (in press) Modular Open-Source Software for Item Factor Analysis. * Educational and Psychological Measurement*

This paper introduces an Item Factor Analysis (IFA) module for OpenMx, a free, open-source, and modular statistical modeling package that runs within the R programming environment on GNU/Linux, Mac OS X, and Microsoft Windows. The IFA module offers a novel model specification language that is well suited to programmatic generation and manipulation of models. Modular organization of the source code facilitates the easy addition of item models, item parameter estimation algorithms, optimizers, test scoring algorithms, and fit diagnostics all within an integrated framework. Three short example scripts are pre- sented for fitting item parameters, latent distribution parameters, and a multiple group model. The availability of both IFA and structural equation modeling in the same software is a step toward the unification of these two methodologies.

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 Educational and Psychological Measurement. It is not the copy of record.

Tags: OpenMx, Structural Equation Modeling

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May 23rd, 2013
McArdle, J. J., Paskus, T. S. & Boker, S. M. (2013) A Multilevel Multivariate Analysis of Academic Success in College based on NCAA Student-Athletes. *Multivariate Behavioral Research*, **48**:1, 57–95.

This is an application of contemporary multilevel regression modeling to the prediction of academic performances of 1st-year college students. At a first level of analysis, the data come from N > 16,000 students who were college freshman in 1994–1995 and who were also participants in high-level college athletics. At a second level of analysis, the student data were related to the different characteristics of the C = 267 colleges in Division I of the NCAA. The analyses presented here initially focus on the prediction of freshman GPA from a variety of high school academic variables. The models used are standard multilevel regression models, but we examine nonlinear prediction within these multilevel models, and additional outcome variables are considered. The multilevel results show that (a) high school grades are the best available predictors of freshman college grades, (b) the ACT and SAT test scores are the next best predictors available, (c) the number of high school core units taken does not add to this prediction but does predict credits attained, (d) college graduation rate has a second-level effect of a small negative outcome on the average grades, and (e) nonlinear models indicate stronger effects for students at higher levels of the academic variables. These results show that standard multilevel models are practically useful for standard validation studies. Some difficulties were found with more advanced uses and interpretations of these techniques, and these problems lead to suggestions for further research.

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

Tags: Academic performance, NCAA

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May 23rd, 2013
Boker, S. M. (2013) Selection, Optimization, Compensation, and Equilibrium Dynamics. *The Journal of Gerontopsychology and Geriatric Psychiatry*, **26**:1, 61-73.

One of the major theoretic frameworks through which human development is studied is a process-oriented model involving selection, optimization, and compensation. These three processes each provide accounts for methods by which gains are maximized and losses minimized throughout the lifespan, and in particular during later life. These processes can be cast within the framework of dynamical systems theory and then modeled using differential equations. The current article will review basic tenets of selection, optimization, and compensation whilst introducing language and concepts from dynamical systems. Four categories of interindividual differences and intraindividual variability in dynamics are then described and discussed in the context of selection, optimization, and compensation.

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 The Journal of Gerontopsychology and Geriatric Psychiatry. It is not the copy of record.

Tags: Aging, Dynamical Systems Analysis, Lifespan Development

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May 23rd, 2013
Klump, K. L., Keel, P. K., Racine, S., Burt, S. A., Sisk, C. L., Neale, M., Boker, S. M. & Hu, J. Y. (2013) The Interactive effects of Estrogen and Progesterone on Changes in Binge Eating Across the Menstrual Cycle. *Journal of Abnormal Psychology*, **122**:1, 131–137.

Studies suggest that within-person changes in estrogen and progesterone predict changes in binge eating across the menstrual cycle. However, samples have been extremely small (maximum N = 9), and analyses have not examined the interactive effects of hormones that are critical for changes in food intake in animals. The aims of the current study were to examine ovarian hormone interactions in the prediction of within-subject changes in emotional eating in the largest sample of women to date (N = 196). Participants provided daily ratings of emotional eating and saliva samples for hormone measurement for 45 consecutive days. Results confirmed that changes in ovarian hormones predict changes in emotional eating across the menstrual cycle, with a significant estradiol x progesterone interaction. Emotional eating scores were highest during the midluteal phase, when progesterone peaks and estradiol demonstrates a secondary peak. Findings extend previous work by highlighting significant interactions between estrogen and progesterone that explain midluteal increases in emotional eating. Future work should explore mechanisms (e.g., gene–hormone interactions) that contribute to both within- and between- subjects differences in emotional eating.

The full text of this article can be downloaded from APA Psycnet as a PDF.

Tags: Eating disorders, Ovarian hormones

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January 16th, 2013
Hu, Y., Boker, S. M., Neale, M. C. & Klump, K. (in press) Latent Differential Equations with Moderators: Simulation and Application. *Psychological Methods*

Latent Differential Equations (LDE) is an approach using differential equations to analyze time series data. Due to its recent development, some technique issues critical to performing an LDE model remain. This article provides solutions to some of these issues, and recommends a step-by-step procedure demonstrated on a set of empirical data, which models the interaction between ovarian hormone cycles and emotional eating. Results indicated that emotional eating is self-regulated. For instance, when people have more emotional eating behavior than normal, they will subsequently tend to decrease their emotional eating behavior. In addition, a sudden increase will produce a stronger tendency to decrease than a slow increase. We also found that emotional eating is coupled with the cycle of the ovarian hormone estradiol, and the peak of emotional eating occurs after the peak of estradiol. Self-reported average level of negative affect moderates the frequency of eating regulation and the coupling strength between eating and estradiol. Thus, people with a higher average level of negative affect tend to fluctuate faster in emotional eating, and their eating behavior is more strongly coupled with the hormone estradiol. Permutation tests on these empirical data supported the reliability of using LDE models to detect self-regulation and a coupling effect between two regulatory behaviors.

The full text of this article can be dowloaded from APA Psycnet as a PDF.

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

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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.

Tags: Dynamical Systems Analysis, Intraindividual variability, Ovarian hormones

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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.

Tags: Dynamical Systems Analysis, Structural Equation Modeling

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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.

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

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