Why the Use of Segmented Regression Analysis to Explore Change in Relations Between Variables Is Problematic: A Simulation Study

Relations between variables can take different forms like linearity, piecewise linearity, or nonlinearity. Segmented regression analyses (SRA) are specialized statistical methods that detect breaks in the relationship between variables. They are commonly used in the social sciences for exploratory analyses. However, many relations may not be best described by a breakpoint and a resulting piecewise linear relation, but rather by a nonlinearity. In the present simulation study, we examined the application of SRA-specifically the Davies test-in the presence of various forms of nonlinearity. We found that moderate and strong degrees of nonlinearity led to a frequent identification of statistically significant breakpoints and that the identified breakpoints were widely distributed. The results clearly indicate that SRA cannot be used for exploratory analyses. We propose alternative statistical methods for exploratory analyses and outline the conditions for the legitimate use of SRA in the social sciences.

Automated summary

Relations between variables can have different forms, including linearity, piecewise linearity, and nonlinearity. Segmented regression analyses (SRA) are often used for exploratory analyses in the social sciences, but they may not be suitable for describing nonlinear relationships. In this simulation study, we found that SRA, specifically the Davies test, frequently identified statistically significant breakpoints when there were moderate to strong degrees of nonlinearity. However, the identified breakpoints were widely distributed, indicating the limitations of SRA for exploratory analyses. We propose alternative statistical methods and outline the conditions for the legitimate use of SRA in the social sciences.