This paper aims to use semi-parametric regression to balanced longitudinal data model, where the parametric regression models suffer from the problem of strict constraints, while non-parametric regression models, despite their flexibility, suffer from the problem of the curse of dimensionality. Consequently, semi-parametric regression is an ideal solution to get rid of the problems that parametric and non-parametric regression suffer from. The great advantage of this model is that it contains all the positive features included in the previous two models, such as containing strict restrictions in its parametric component, complete flexibility in its non-parametric component, and clarity of the interaction between its parametric and non-parametric components.

Based on the above, two methods were used to estimate a semi-parametric balanced longitudinal data model. The first is the Bayesian estimating method; the second is the Speckman method, which estimated the unknown nonparametric smoothing function by employing the kernel smoothing Nadaraya-Watson method. The Aim was to make a comparison between the Bayesian estimation method and the classical estimation method. Three different sample sizes were used in the simulation studies: 50, 100, and 200. The study results showed that the Bayesian estimating method is best at low variance levels (1,5), whereas the Speckman method is best at high variance level (10).

Paper type: A Research derived from Dissertation  Ph.D.