Smoothing parameters of penalized spline nonparametric regression model using linear mixed model

Nonparametric regression is method of regression approach for data patterns of which regression curve is unknown. Meanwhile, spline is a type of segmented polynomial piecewise. Such segmented nature gives more flexibility than common polynomial models so that spline can adapt more effectively to local characteristics of function or data. The use of spline focuses on presence of behavior and patterns of data which in certain area has different characteristics from other areas. Data matching can be done by observing points on data in which an extreme change occurs in an area and consequently data patterns in each area differ. One approach using nonparametric regression is spline regression with penalized spline (P-spline). It is defined as a regression determined using method of least squares and roughness penalty. The article examines smoothing parameters of penalized spline nonparametric regression model. P-spline can be represented in linear mixed model with components of variance to control nonlinearity level of estimators of smooth functions. P-spline using linear mixed model approach can be estimated using either maximum likelihood or residual maximum likelihood. The results of research show that smooth function of best linear unbiased predictor in linear mixed model is equivalent to estimators of penalized spline regression.