Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model
Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in th...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Tehran
2020-04-01
|
| Series: | Journal of Sciences, Islamic Republic of Iran |
| Subjects: | |
| Online Access: | https://jsciences.ut.ac.ir/article_76403_aed3c546a5439007a7f74f316ac99e14.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849730746865942528 |
|---|---|
| author | Anna Islamiyati |
| author_facet | Anna Islamiyati |
| author_sort | Anna Islamiyati |
| collection | DOAJ |
| description | Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in the non-parametric model will have two different non-parametric regression functions. Therefore, we propose the use of two smoothing parameters in the bi-variate predictor non-parametric regression model. We demonstrated its ability through longitudinal data simulation studies with a comparison of one smoothing parameter. It was done on several numbers of subjects with repeated measurements. The generalized cross validation value which is a measure of the model's ability is poured through the box plot. The results show that the use of two smoothing parameters is more optimal than one smoothing parameter. It was seen through a smaller generalized cross validation value on the use of two smoothing parameters. Application of blood sugar level data for patients with two smoothing parameters produced a penalized spline bi-variate predictor regression model with several segments of change patterns. There are five patterns at the time of treatment and blood pressure with the number of smoothing parameters is two, namely 0.39 and 0.73. |
| format | Article |
| id | doaj-art-c7dfc005db1a4988b4e79c4a4a75673a |
| institution | DOAJ |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2020-04-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-c7dfc005db1a4988b4e79c4a4a75673a2025-08-20T03:08:46ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142020-04-0131217518310.22059/jsciences.2020.286949.100743576403Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression ModelAnna Islamiyati0Department of Statistics Faculty of Mathematics and Natural Sciences Hasanuddin University, Makassar, Sulawesi Selatan, Indonesia.Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in the non-parametric model will have two different non-parametric regression functions. Therefore, we propose the use of two smoothing parameters in the bi-variate predictor non-parametric regression model. We demonstrated its ability through longitudinal data simulation studies with a comparison of one smoothing parameter. It was done on several numbers of subjects with repeated measurements. The generalized cross validation value which is a measure of the model's ability is poured through the box plot. The results show that the use of two smoothing parameters is more optimal than one smoothing parameter. It was seen through a smaller generalized cross validation value on the use of two smoothing parameters. Application of blood sugar level data for patients with two smoothing parameters produced a penalized spline bi-variate predictor regression model with several segments of change patterns. There are five patterns at the time of treatment and blood pressure with the number of smoothing parameters is two, namely 0.39 and 0.73.https://jsciences.ut.ac.ir/article_76403_aed3c546a5439007a7f74f316ac99e14.pdfbi-variatelongitudinal datapenalized splinesmoothing parameter |
| spellingShingle | Anna Islamiyati Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model Journal of Sciences, Islamic Republic of Iran bi-variate longitudinal data penalized spline smoothing parameter |
| title | Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model |
| title_full | Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model |
| title_fullStr | Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model |
| title_full_unstemmed | Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model |
| title_short | Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model |
| title_sort | use of two smoothing parameters in penalized spline estimator for bi variate predictor non parametric regression model |
| topic | bi-variate longitudinal data penalized spline smoothing parameter |
| url | https://jsciences.ut.ac.ir/article_76403_aed3c546a5439007a7f74f316ac99e14.pdf |
| work_keys_str_mv | AT annaislamiyati useoftwosmoothingparametersinpenalizedsplineestimatorforbivariatepredictornonparametricregressionmodel |