Cusp Catastrophe Regression and Its Application in Public Health and Behavioral Research

The effect of school size and class size on school preparedness

The purpose of the present study was to understand students' school readiness as a function of student and teacher behaviors but also school size and class size using both linear and non-linear analytical approaches. Data came from 21,903 schools distributed across 80 countries as per the 2018 cohort of the PISA database. Results pointed to a preference for the Cusp model in that the relationship between school and class sizes with achievement proved to be best described by the non-linearity of the Cusp catastrophe model. The critical benchmarks were a school size of 801 students and a class size of 27 students for which increases beyond those thresholds were linked to nonlinearity and unpredictability in school readiness. For this reason, we suggest using the cusp catastrophe model from Nonlinear Dynamical Systems Theory (NDST) to understand more fully such complex phenomena.

The detrimental effects of student-disordered behavior at school: evidence from using the cusp catastrophe

Introduction

The purpose of the present study is to examine the potentially complex relationship between disordered behavior at school and students' engagement with reading activities given that they enjoy reading. Of particular interest is the role of disordered behavior which we believe moderated the relationship between liking reading and reading engagement.

Methods

Participants were 2,420 fourth graders who participated in the 2021 PIRLS study from Saudi Arabia and were selected using stratified random sampling from 117 schools in the Kingdom. Data were analyzed using linear and nonlinear means such as the linear model, the logistic model, and the cusp catastrophe.

Results

Results pointed to the superiority of the cusp catastrophe towards predicting student engagement in reading by highlighting the splitting role of students' disruptive classroom behavior.

Discussion

It was evident that exceeding a critical upward level in disruptive classroom behavior was associated with unpredictable and sudden changes in reading engagement. It is concluded that the application of non-linear means may be conducive to understanding complex educational phenomena.

Self-Regulation Shift Theory: A Dynamic Personal Agency Approach to Recovery Capital and Methodological Suggestions

Recovery capital highlights person and environmental resources associated with overcoming significant life challenges. This paper utilizes social cognitive theory as a framework for understanding how recovery capital functions in trauma adaptation. This theory outlines the bidirectional, dynamic interactions among person (e.g., cognitive and affective), behavioral (e.g., problem focused coping), and environmental variables (i.e., triadic reciprocal determinism). The value of this approach to understanding human adaptation to trauma is that it targets the self-regulatory processes that unfold for trauma survivors as they attempt to put their lives back together. Self-regulation shift theory (SRST), as an extension to social cognitive theory, is offered to explain how self-regulation is involved in both positive and negative adjustment. The theory uses a dynamical systems approach and highlights the mechanisms related to non-linear shifts in both positive and negative trauma recovery. According to SRST, trauma recovery may not be linear with threshold shifts (i.e., bifurcations) from one organized state (broken self) to another (empowered self). Coping self-efficacy perceptions are a critical factor influencing these threshold shifts. This paper concludes with a brief review of study designs and analytic procedures that can facilitate the application of non-linear dynamic research in this area.