From Dr. Darling:
In developmental psychology, change occurs not at the individual level, but within a series of nested relationships, for example, within dyads and classrooms. When one person within the system changes, it affects all others within the system. All of these changes unfolds over time. This type of complex reciprocal change cannot be modeled using traditional statistical techniques.
In this series of illustrative models, the association of teacher discipline and student misbehavior is explored in a series of increasingly complex nested models. In the first model, a simple Lotka Volterra model is used to illustrate the reciprocal relationship of teacher discipline and student misbehavior: as teacher discipline increases, child misbehavior decreases. Unlike traditional statistical models, the floor and ceiling effects of both variable keep behaviors within the bounds of the model.
A second level of the model nests four teacher:student dyads within a single ‘classroom’. Teacher patience is a joint function of the behavior of the student:teacher dyad and of the misbehavior of the classroom as a whole. Thus as more students misbehave, teacher latency to discipline will be reduced. Such a nested model can be useful for exploring the differential experience of children in a special education classroom who differ in problem behavior in classrooms with other students high or low in mischief.
The final model becomes increasingly realistic, as it works with a larger classroom of 28 students. In this model, student misbehavior is affected both by nearby students and by the teacher. Thus the distribution of misbehavior within the classroom affects individual students both directly (I am more misbehave if my neighbors do) and indirectly (my teacher’s patience will be lower if more students misbehave).
Such models are useful in exploring the different patterns of behavior: particularly using a person-centered framework for classifying ecological niches of self-reinforcing developmental processes. The models are explored as illustrative of the ways collaborative teams of researchers can use Numerus (Darling, Salter, and Burns, in press) and the useful of modeling in understanding development (Darling & Burns, in press).
References:
Darling, N. & Burns, I.R.D. (in press). Matching Methods To Theory: Using Dynamic Systems Models To Understand Nested Systems of Adolescent Development. In. S. Kunnen (Eds.) Psychosocial Development in Adolescence: Insights from the Dynamic Systems Approach. Abington:Routledge Press.
Darling, N., Salter, R. M., & Burns, I.R.D. (in press). NOVA: A Novel Tool for Collaborative Agent-Based and Dynamic Systems Modeling. In W. F. Porter, J. Zhao, L. Schmitt Olabisi, & M. McNall (Eds.), Innovations in Collaborative Modeling. Lansing, MI:Michigan State University Press.
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