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| Spline Truncated Nonparametric Regression Models for Longitudinal Data and Implementation in Modeling Indonesia's Family Planning Program
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Dita Amelia, Sa'idah Zahrotul Jannah
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Abstract:
The most widely used nonparametric and semiparametric regression models in the last decade are spline regressions. Spline is a model that has a very special and very good statistical interpretation and visual interpretation. In regression analysis, the data that is often used is cross section data. But regression analysis can also be applied to longitudinal data. In its application in the social field, longitudinal data studies are also used involving research subjects in the form of regions. Several social issues that have been discussed a lot lately are regarding Indonesia's population growth which continues to increase. Through various Family Planning programs called "Keluarga Berencana (KB)" program, it is hoped that it can reduce the rate of population growth so that population growth remains balanced. Therefore, further analysis was carried out to estimate the success of KB Program through the percentage indicator Contraceptive Prevalence Rate (CPR) with poverty depth index, the average length of schooling for the population aged ? 15, and the proportion of women aged 20-24 years who are married or living together before the age of 18 as predictor variables. The model estimator was obtained by the WLS method. At the model application stage, longitudinal data is used with an analysis unit of 34 provinces in Indonesia in 2017 to 2021 which is divided into groups of Java Bali, Outer Java Bali I, and Outer Java Bali II. From the three groups, it was found that the optimum knots used were three knots with a GCV value of 1,11x10-26 for the Java-Bali group, 1,05x10-26 for the Outer Java-Bali I group, and 3,19x10-27 for the Outer Java-Bali II group. Each variable has a different effect on each subject. The number of knots in the nonparametric spline regression model has an influence in relating the behavior of the data in each sub-interval or segment. The optimal knot value is given by the smallest GCV value and the application of longitudinal data will provide a more accurate model for each observed subject.
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