Most statistical analyses are at least implicitly based on the linear (or log-linear) relationship between research variables. If a suspicion on the nonlinearity is legitimate and theoretically supported, you can consider quantile regression whereby the significance, magnitude, and even direction (+/−) of the relationship can vary within the sample. The following paper employed quantile regression and confirmed the variation of the impacts of the built environment/land use.
Gim, Tae-Hyoung Tommy. Quantile regression on the nonlinear relationship between land use and trip time. Papers in Regional Science. (Accepted)
For a full list of journal publications, go to 연구업적(PUBLICATIONS) > 학술지논문(Journal Articles).