Modelling Scholastic Aptitude Test of State Islamic Colleges in Indonesia using Least Square Spline Estimator in Longitudinal Semiparametric Regression

Scholastic aptitude test is one of tests used to select student candidates who want to enroll to the state Islamic colleges (SIC) in Indonesia. This test is affected by some factors for instances percentage of student candidates who pass to enroll in that enrolment year (t), and place of these colleges (SIC) where the student candidates enroll (X). Association between t and scholastic aptitude test score (Y) have no certain pattern (as nonparametric component). One of estimator in nonparametric regression is least square spline that include knots which can accommodate locally properties and give good flexibility. Place of SIC is dummy variable, so we can use parametric regression approach. To investigate Y from year to year we can use longitudinal data. Therefore, in this research model Y affected by t (as nonparametric component) and X (as parametric component) use longitudinal semiparametric regression based on least square spline estimator. The results give an estimated order one semiparametric regression model of scholastic aptitude test scores with three knots of 70.64; 80.32, and 90.67, and minimum generalized cross validation value of 204.42. Also, the results show that average of Y in western Indonesia is greater than in eastern Indonesia with difference of 20.45.