A Completely Nonlinear Approach of Multilevel Regression for Detecting Turning Points: Developing an Alternative Platform With an Application of TIMSS Data

There have been various traditional methods to identify turning points to establish nonlinear relationships. These methods use a linear approach (i.e., traditional piecewise regression) to seek a nonlinear relationship. The present study aimed to introduce a completely nonlinear approach as an alternative platform to identify turning points. This alternative approach was also multilevel to work with data hierarchy for the identification of turning points. The United States sample (8776 students from 287 schools) in the 2019 TIMSS (Trends in International Mathematics and Science Study) was applied to this alternative approach to identify turning points in the relationship between mathematics achievement and mathematics enjoyment with control of student and school characteristics. This alternative approach performed well, successfully revealing positive but differential effects on mathematics achievement across different degrees of mathematics enjoyment.