Mixed estimator of spline truncated, Fourier series, and kernel in biresponse semiparametric regression model

Regression analysis is a method of analysis to determine the relationship between the response and the predictor variables. There are three approaches in regression analysis, namely the parametric, nonparametric, and semiparametric approaches. Biresponse Semiparametric regression model is a regression model that uses a combination approach between parametric and nonparametric components, where two response variables are correlated with each other. For data cases with several predictor variables, different estimation technique approaches can be used for each variable. In this study, the parametric component is assumed to be linear. At the same time, the nonparametric part is approached using a mixture of three estimation techniques, namely, spline truncated, Fourier series, and the kernel. The unknown data pattern is assumed to follow the criteria of each of these estimation techniques. The spline is used when the data pattern tends to change at certain time intervals, the Fourier series is used when the data pattern tends to repeat itself, and the kernel is used when the data does not have a specific way. This study aims to obtain parameter estimates for the mixed semiparametric regression model of spline truncated, Fourier series, and the kernel on the biresponse data using the Weighted Least Square (WLS) method. The formed model depends on the selection of knot points, oscillation parameters, and optimal bandwidth. The best model is based on the smallest Generalized Cross Validation (GCV).

Model Regresi Semiparametrik Spline untuk D ata Longitudinal pada Kasus Demam Berdarah Dengue di Kota Makassar

Abstrak. Regresi semiparametrik merupakan model regresi yang memuat komponen parametrik dan komponen nonparametrik dalam suatu model. Pada penelitian ini digunakan model regresi semiparametrik spline untuk data longitudinal dengan studi kasus penderita Demam Berdarah Dengue (DBD) di Rumah Sakit Universitas Hasanuddin Makassar periode bulan Januari sampai bulan Maret 2018. Estimasi model regresi terbaik didapat dari pemilihan titik knot optimal dengan melihat nilai Generalized Cross Validation (GCV) dan Mean Square Error (MSE) yang minimum. Komponen parametrik pada penelitian ini adalah hemoglobin (g/dL) dan umur (tahun), suhu tubuh ( ), trombosit ( ) sebagai komponen nonparametrik dengan nilai GCV minimum sebesar 221,67745153 dicapai pada titik knot yaitu 14,552; 14,987; dan 15,096; nilai MSE sebesar 199,1032; dan nilai koefisien determinasi sebesar 75,3% yang diperoleh dari model regresi semiparametrik spline linear dengan tiga titik knot..Kata Kunci: regresi semiparametrik, spline, knot, Generalized Cross Validation, Demam Berdarah Dengue.Abstract. Semiparametric regression is a regression model that includes parametric and nonparametric components in it. The regression model in this research is spline semiparametric regression with case studies of patients with Dengue Hemorrahagic Fever (DHF) at University of Hasanuddin Makassar Hospital during the period of January to March 2018. The best regression model estimation is obtained from the selection of optimal knot which has minimum Generalized Cross Validation (GCV) and Mean Square Error (MSE). Parametric component in this research is hemoglobin (g/dL) and age (years), body temperature ( ), platelets ( ) as a nonparametric components. The minimum value of GCV is 221,67745153 achieved at the point 14,552; 14,987; and 15,096 knot; MSE value of 199,1032; and the value of coefficient determination is 75,3% obtained from semiparametric regression model linear spline with third point of knots.Keywords: semiparametric regression, spline, knot, Generalized Cross Validation, Dengue Hemorrahagic Fever.