Robust spatial Durbin modelling on tuberculosis data using the MM-estimator method

Ummul Auliyah Syam; Siswanto Siswanto; Nurtiti Sunusi

doi:https://doi.org/10.59170/stattrans-2024-013

Robust spatial Durbin modelling on tuberculosis data using the MM-estimator method

Ummul Auliyah Syam Department of Statistics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Indonesia ORCID:https://orcid.org/0009-0006-5254-3527 , Siswanto Siswanto Corresponding author, Department of Statistics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Indonesia ORCID:https://orcid.org/0000-0003-1934-5343 , Nurtiti Sunusi Department of Statistics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Indonesia ORCID:https://orcid.org/0000-0002-6436-831X Statistics in Transition new series, vol. 25, 2024, 2, pages: 23-38 Published online: 5 June 2024 https://doi.org/10.59170/stattrans-2024-013 Citation: Syam, U. A., Siswanto, S., Sunusi, N., 2024. Robust spatial Durbin modelling on tuberculosis data using the MM-estimator method. Statistics in Transition new series, 25(2), pp. 23-38. https://doi.org/10.59170/stattrans-2024-013

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ARTICLE

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ABSTRACT

The spatial Durbin model (SDM) is a spatial regression model which shows the existence of spatial dependency on the response variable and predictor variables. However, SDM modelling may sometimes involve problems associated with e.g. the existence of spatial outliers. One way to overcome outliers in the SDM model is to use robust regression in the form of the robust spatial Durbin model (RSDM). This study aims to estimate the parameters of RSDM based on data on tuberculosis (TB) cases recorded in 2020 in the South Sulawesi Province in Indonesia and to identify the factors that affect the number of TB cases in the region. The MM-Estimator robust regression estimation method was used. It is a combination of a method involving a high breakdown value for the S-estimator and a high efficiency of the M-estimator. The results of the analysis show that RSDM can overcome outliers in spatial regression models. This is reflected in the value of the mean square error (MSE) of the RSDM, which is 6,461.734, i.e. smaller than the value of the SDM model, and the adjusted R^2 value of 99.52%, which is greater than that of the SDM model. The factors that influence the number of TB cases in the South Sulawesi Province are population density, the percentage of households leading a healthy lifestyle, the percentage of residents with Bacillus Calmette-Guérin (BCG) immunisation, and the percentage of those suffering from malnutrition.

KEYWORDS

spatial regression, RSDM, MM-Estimator, tuberculosis.

REFERENCES

Anderson, R. M., May, R. M., (1991). Infectious Disease of Humans: Dynamic and Control. Oxford University Press.

Anselin, L., (1988). Spatial Econometrics: Methods and Models. Kluwer Academic Publishers.

Barnett, V., Lewis, T., (1994). Outlier In Statistical Data (3rd ed.). Jhon Wiley & Sons, Inc.

Chasnov, J. R., (2022). Infectious Disease Modeling. In: Mathematical Biology. LibreTexts.

Chowell G., Rothenberg R. (2018). Spatial infectious disease epidemiology: on the cusp. BMC Medicine, Vol. 16, pp. 1-5.

Feng, Y., Wang, X., Du, W., and Liu, J., (2018). Effects of Air Pollution Control on Urban Development Quality in Chinese Cities Based on Spatial Durbin Model. International Journal of Environmental Research and Public Health, Vol. 15, pp. 1–21.

Fox, J., Weisberg, S., (2010). Robust Regression in R: An Appendix to An R to Applied Regression (2nd ed.).

Gestal, M. C., Dedloff, M. R., and Torres-Sangiao, E., (2019). Computational Health Engineering Applied to Model Infectious Diseases and Antimicrobial Resistance Spread. Applied Sciences, Vol. 9, pp. 1–19.

Gong, Z., Kong, Q., and Tan, J., (2020). Analysis on Multidimensional Poverty Reduction of Industrial Structure Upgrading Based on Provincial Panel Data and Spatial Durbin Model. International Journal of Sustainable Development and Planning, Vol. 15, pp. 1197–1204.

Hakim, A. R., Warsito, B., and Yasin, H., (2020). Live Expectancy Modelling using Spatial Durbin Robust Model. Journal of Physics: Conference Series, Vol. 1655, pp. 1–11.

Johnson, M., Jones, K., (2019). Variables in Infections Disease Modeling. Journal of Epidemiology and Public Health, Vol. 7, pp. 98–105.

Ministry of Health of the Republic of Indonesia, (2021). Profil Kesehatan Indonesia 2021. Kementrian Kesehatan Republik Indonesia.

Khofifah, H. N., (2022). Robust Spatial Durbin Model (RSDM) untuk Pemodelan Tingkat Pengangguran Terbuka (TPT) di Provinsi Jawa Barat. Jurnal Riset Statistika, Vol. 1, pp. 135–142.

Kim, J. J., Cho, M. J., and Lee, M. H., (2022). An Analysis of the Price Determinants of Multiplex Houses through Spatial Regression Analysis. Sustainability, Vol. 14, pp. 1–14.

Lee, J., Wong, D. W. S., (2001). Statistical Analysis with Arcview GIS. John Wiley & Sons, Inc.

LeSage, J., Pace, R. K., (2009). Introduction to Spatial Econometrics. Taylor & Francis Group.

Prahutama, A., Rusgiyono, A., (2021). Robust Regression with MM-Estimator for Modelling The Number Maternal Mortality of Pregnancy in Central Java, Indonesia. Journal of Physics: Conference Series, Vol. 1943, pp. 1–7.

Rahman, M. B., Widodo, E., (2018). Perbandingan Metode Regresi Robust Estimasi Least Trimmed Square, Estimasi Scale, dan Estimasi Method Of Moment. Prosiding Seminar Nasional Matematika, pp. 426–433.

Ramadhani, E., Salwa, N., and Mazaya, M. S., (2020). Identifikasi Faktor-Faktor yang Memengaruhi Angka Harapan Hidup di Sumatera Tahun 2018 Menggunakan Analisis Regresi Spasial Pendekatan Area. Journal of Data Analysis, Vol. 3, pp. 62–75.

Ren, L., Matsumoto, K., (2020). Effects of Socioeconomic and Natural Factors on Air Pollution in China: A Spatial Panel Data Analysis. Science of the Total Environment, Vol. 740, pp. 1–10.

Shaweno D., Karmakar M., Alene K.A., Ragonnet R., Clements A. C. A., Trauer J. M., Denholm J. T., and McBryde, E. S., (2018). Methods used in the spatial analysis of tuberculosis epidemiology: a systematic review. BMC Medicine. Vol. 16, pp. 1–18.

Shekhar, S., Lu, C.-T., and Zhang, P., (2003). A Unified Approach to Detecting Spatial Outliers. GeoInformatica, Vol. 7, pp. 139–166.

Smith, J., Brown, L., and Green, D. (2018). Computer Modeling in Disease Prevention. Journal of Health Informatics, Vol. 12, pp. 201-210.

Smith, T. E. (2008). Encyclopedia of GIS (S. Shekhar & H. Xiong, Eds.), Springer US.

Sun, Y., Du, M., Wu, L., Li, C., and Chen, Y., (2022). Evaluating the Effects of Renewable Energy Consumption on Carbon Emissions of China’s Provinces: Based on Spatial Durbin Model. Land, Vol. 11, pp. 1–17.

Varatharajan, R., Manogaran, G., Priyan, M. K., Balaş, V. E., and Barna, C., (2018). Visual Analysis of Geospatial Habitat Suitability Model Based on Inverse Distance Weighting with Paired Comparison Analysis. Multimedia Tools and Applications, Vol. 77, pp. 17573–17593.

WHO, (2021, October 14). Tuberculosis. https://www.who.int/news-room/fact-sheets/detail/tuberculosis.

Xiao, G., Hu, Y., Li, N., and Yang, D., (2018). Spatial Autocorrelation Analysis of Monitoring Data of Heavy Metals in Rice in China. Food Control, Vol. 89, pp. 32–37.

Yasin, H., Hakim, A. R., and Warsito, B., (2020). Development Life Expectancy Model in Central Java Using Robust Spatial Regression With M-Estimators. Communications in Mathematical Biology and Neuroscience, Vol. 2020, pp. 1–16.

Yohai, V. J., (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. The Annals of Statistic, Vol. 15, pp. 642–656.