Hybrid Fourier series and smoothing spline path non-parametrics estimation model

Pathway analysis is one way to determine whether there is a causal relationship between extrinsic and intrinsic factors. The linearity assumption is something that can change the model. The shape of the model is subject to linearity assumptions. Path analysis is parametric when the linearity assumption is true, whereas non-parametric path analysis is used when the non-linear shape is unknown and there is no knowledge of the data pattern. Non-linear path analysis is used when the non-linear shape and data pattern are unknown. This work aimed to combine the smoothing spline method and the Fourier series method to compute non-parametric path function and it is believed that they would be able to produce more flexible function estimations for data patterns since both have the benefit of being accurate or close to the real data pattern. As a result, we found that Fourier series and smoothing splines can be used in non-parametric path analysis only if the linearity assumption is violated. Non-parametric regression-based path analysis estimators were then obtained using the ordinary least squares (OLS) approach. It uses a non-parametric approach and therefore gives non-unique estimation results.