Date of Degree
The present simulation study evaluated and compared the performance of piecewise regression to one of the more recognizable methods utilized to model nonlinear relationships within the confines of OLS, polynomial regression. This investigation examined (a) the comparative performance of piecewise and polynomial regression under various experimental conditions (e.g., fitting datasets with different underlying structure, different sample sizes, and varying number slope change-points), and (b) their utility and ease for empirically identifying the point(s) where a regression line changes trajectory. The research design, which followed a mixed factorial design, included four independent variables: sample size, underlying data-generating model type, type of regression analyses (i.e., polynomial, piecewise with known knots, piecewise with unknown knots) and number of significant change-points. Seven outcome variables were used to evaluate and compare model performance: the square root of the mean squared error (RMSE), RMSE omitting the 10% most extreme residuals, RMSE for only the 10% omitted, R-squared values, estimated change-point location(s), estimated Y-hat when x was at the change-point, and the empirical standard error. Findings indicated that under conditions of misspecification, polynomial and piecewise were incapable of correctly estimating the location of the true change-points and the Y-hats when x was at the estimated change-point locations. Misspecified models, in general, had inferior RMSE and R2 outcomes than their correctly specified counterparts. Sample size was a good discriminatory element, as larger ones helped better expose a misspecified model fit.
Zapata, A., "The Ability of Polynomial and Piecewise Regression Models to Fit Polynomial, Piecewise, and Hybrid Functional Forms" (2019). CUNY Academic Works.