A New Semiparametric Regression Framework for Analyzing Non-Linear Data

This work introduces a straightforward framework for semiparametric non-linear models as an alternative to existing non-linear parametric models, whose interpretation primarily depends on biological or physical aspects that are not always available in every practical situation. The proposed methodology does not require intensive numerical methods to obtain estimates in non-linear contexts, which is attractive as such algorithms’ convergence strongly depends on assigning good initial values. Moreover, the proposed structure can be compared with standard polynomial approximations often used for explaining non-linear data behaviors. Approximate posterior inferences for the semiparametric model parameters were obtained from a fully Bayesian approach based on the Metropolis-within-Gibbs algorithm. The proposed structures were considered to analyze artificial and real datasets. Our results indicated that the semiparametric models outperform linear polynomial regression approximations to predict the behavior of response variables in non-linear settings.