APPLICATION OF PENALIZED SPLINE-SPATIAL AUTOREGRESSIVE MODEL TO HIV CASE DATA IN INDONESIA
Abstract
Spatial regression analysis is a statistical method used to perform modeling by considering spatial effects. Spatial models generally use a parametric approach by assuming a linear relationship between explanatory and response variables. The nonparametric regression method is better suited for data with a nonlinear connection because it does not need linear assumptions. One of the nonparametric regression methods is penalized spline regression (P-Spline). The P-spline has a simple mathematical relationship with mixed linear model. The use of a mixed linear model allows the P-Spline to be combined with other statistical models. PS-SAR is a combination of the P-Spline and the SAR spatial model so that it can analyze spatial data with a semiparametric approach. Based on data from monitoring the development of the HIV situation in 2018, the number of HIV cases in Indonesia shows a clustered pattern that indicate spatial dependence. In addition, the relationship between the number of positive cases and the factors tends to be nonlinear. Therefore, this study aims to apply the PS-SAR model to HIV case data in Indonesia. The resulting model is evaluated based on the estimates of autoregressive spatial coefficient, MSE, MAPE, and Pseudo R2. Based on the results, the PS-SAR model has an autoregressive spatial coefficient similar to the SAR model and has smaller MSE and MAPE than the SAR model.
Downloads
References
L. Anselin, Spatial Econometrics: Method and Models. Dodrecht (NLD): Kluwer Academic Publishers, 1988.
S. Sukmawati, A. Djuraidah, and A. H. Wigena, “Spatial Clustered Regression Analysis of 2017 Getis Score Indonesian Malaria Prevalence Data,” J. Phys. Conf. Ser., vol. 1863, no. 1, 2021, doi: 10.1088/1742-6596/1863/1/012043.
A. Djuraidah, P. Silvianti, B. Djaafara, and S. N. Laila, “Modeling Annual Parasite Incidence of Malaria in Indonesia of 2017 using Spatial Regime,” Indones. J. Geogr., vol. 53, no. 2, pp. 185–191, 2021.
A. Djuraidah, A. Alamudi, and A. Fadila, Modeling the Number of Tuberculosis Patients in East Java with Geographically Weighted Negative Binomial Regression. Bachelor [Undergraduate Theses]. Bogor, ID: IPB Univeristy., 2021. [Online]. Available: IPB Repository.
A. Djuraidah, Z. Mar’ah, and R. Anisa, “a Bayesian Conditional Autoregressive With Inla: a Case Study of Tuberculosis in Java, Indonesia,” Commun. Math. Biol. Neurosci., vol. 2022, pp. 1–15, 2022, doi: 10.28919/cmbn/7709.
Z. D. R, A. Saefuddin, and A. Djuraidah, “Modelling the Number of Cases of Dengue Hemorragic Fever with Mixed Geographically Negative Binomial Regression in West Java Province,” Int. J. Sci. Res. Sci. Eng. Technol., vol. 18116, no. Kemenkes 2014, pp. 71–77, 2019, doi: 10.32628/ijsrset196124.
Z. Chen and J. Chen, “Bayesian analysis of partially linear additive spatial autoregressive models with free-knot splines,” Symmetry (Basel)., vol. 13, no. 9, pp. 1–20, 2021, doi: https://doi.org/10.3390/sym13091635.
P. H. C. Eilers and B. D. Marx, “Flexible smoothing with B-splines and penalties,” Stat. Sci., vol. 11, no. 2, pp. 89–102, 1996, doi: 10.1214/ss/1038425655.
D. Ruppert and R. J. Carroll, “Penalized regression splines,” 1997.
B. A. Brumback and J. A. Rice, “Smoothing spline models for the analysis of nested and crossed samples of curves,” J. Am. Stat. Assoc., vol. 93, no. 443, pp. 961–976, 1998, doi: https://doi.org/10.2307/2669837.
J. Montero, R. Mínguez, and M. Durbán, “SAR models with nonparametric spatial trends: A P-spline approach,” Estadística Española, vol. 54, no. 177, pp. 89–111, 2012.
K. H. dan H. R. Dirjen P2 & PL (Direktorat Jendral Pengendalian Penyakit dan Penyehatan Lingkungan), Kementerian Kesehatan RI, Direktorat Jendral Permasyarakatan, Pedoman Layanan Komprehensif HIV-AIDS & AIMS di Lapas, Rutan dan Bapas. Jakarta: Dirjen P2 & PL, 2012.
D. B. Lolong, O. S. Simarmata, Novianti, and F. P. Senewe, “Situasi Human Immunodeficiency Virus - Tuberkulosis di Kabupaten Merauke 2018: Ancaman pada umur produktif,” J. Kesehat. Reproduksi, vol. 10, no. 1, pp. 1–9, 2019, doi: 10.22435/kespro.v10i1.1711.1-9.
I. Bates et al., “Vulnerability to malaria, tuberculosis, and HIV/AIDS infection and disease. Part 1: Determinants operating at individual and household level,” Lancet Infect. Dis., vol. 4, no. 5, pp. 267–277, 2004, doi: 10.1016/S1473-3099(04)01002-3.
A. Djuraidah, Model aditif spatio-temporal untuk pencemar udara PM10 dan ozon di Kota Surabaya dengan pendekatan model linear campuran. PhD [Dissertation]. Bogor, ID: IPB Univeristy., 2007. [Online]. Available: IPB Repository.
C. R. Henderson, O. Kempthorne, S. R. Searle, and C. M. Krosigk, “The estimation of environmental and genetic trends from records subject to culling,” Biometrics, vol. 15, no. 2, pp. 192–218, 1959, [Online]. Available: http://www.jstor.org/stable/2527669.
R. Christensen, The Theory of Linear Models. New Mexico (USA), 1987.
S. R. Searle, G. Casella, and C. E. McCulloch, Variance Components. New Jersey (USA): John Wiley & Sons, Inc., 1992.
J. LeSage and R. K. Pace, Introduction to Spatial Econometrics. Boca Raton (USA): CRC Press, 2009.
M. B. El-Kautsar, A. Djuraidah, and Y. Angraini, Identifikasi faktor-faktor yang memengaruhi kasus HIV di Indonesia tahun 2018 menggunakan regresi terboboti geografis campuran. Bachelor [Undergraduate Theses]. Bogor, ID: IPB Univeristy., 2022. [Online]. Available: IPB Repository.
Copyright (c) 2023 Nindi Pigitha, Anik Djuraidah, Aji Hamim Wigena
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
