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Rp-Construeting a semi parametric regression model using circular data.pdf

The study of phenomena represented by data of a circular nature (angular) is an important aspect nowadays, as there are many phenomena of a circular nature. Semi-parametric regression is one of the appropriate statistical methods for studying phenomena of a circular nature. The study included the construction of a semi-parametric regression model (circular – linear – circular) , The model was formulated by employing two types of circular regression models, namely (Linear + Circular) and (Circular + Circular), and combining them using the (Combin Parameter). A semi-parametric integrated regression model was built (the Combined semi parametric Circular -Linear- circulear regression). By comparing three types of semi-parametric models (circular – linear – circular) in two models, the combined semi-parametric regression model . The parametric part (linear-circular) was estimated by the maximum likelihood method, and the non-parametric part was estimated by the circular kernel function method using the Von Mises kernel function and the wrapped Cauchy kernel function . The parametric part (linear-circular) was estimated by the maximum likelihood method, and the non-parametric part was estimated by the circular kernel function method using the Von Mises kernel function and the wrapped Cauchy kernel function. Also, the semi-parametric regression model was estimated to use the partial least squares method and the Fourier Series representation of the non-parametric part. Monte Carlo simulation method was used, and MATLAB program was used to implement circular data programming. Four sample sizes were generated (100, 200, 300, 400). The estimated models were compared using information criteria (AIC, BIC), and the model performance was evaluated using the coefficient of determination (R^2) and the mean square error (MSE). In the applied aspect, the actual data of patients with refractive error of the eye including (myopia, hyperopia, astigmatism, and presbyopia) were used, which were obtained from (Al-Noor Specialized Center for Ophthalmology and Surgery) in Dhi Qar Governorate, using the (Auto Kerato – Refracto Tonometer TOPCON TRK. 2P) device.
Therefore, a study (400 cases) was created that represents the measurement data of the right eye (OD cyl axis), the dependent eye (OD cyl axis), and the patient’s age (patient’s age) for people with refractive error (refractive error)
The best semi-parametric circular-linear-circulear regression model was built, as the model achieved the lowest (AIC, BIC), highest (R^2) and lowest (MSE).
The study concluded that the results of the circular-linear-circular semi-parametric model are not stable in small samples, as we notice the fluctuation of the value of the coefficient of determination (R^2) as well as the mean square error (MSE) between high and low. This may be due to changing the smoothing parameter of the kernel function or due to changing the variance. The best semi-parametric model using circular data when representing the non-parametric part using Fourier series.
The researcher recommended conducting studies on the circular-linear-circular semi-parametric regression model, adopting large samples to improve the stability of the results, and studying other types of circular regression models.