No abstract

This study developed a new method of hypothesis testing of model conformity between truncated spline nonparametric regression influenced by spatial heterogeneity and truncated spline nonparametric regression. This hypothesis test aims to determine the most appropriate model used in the analysis of spatial data. The test statistic for model conformity hypothesis testing was constructed based on the likelihood ratio of the parameter set under H0 whose components consisted of parameters that were not influenced by the geographical factor and the set under the population parameter whose components consisted of parameters influenced by the geographical factor. We have proven the distribution of test statistics V and verified that each of the numerators and denominators in the statistic test V followed a distribution of χ2. Since there was a symmetric and idempotent matrix S, it could be proved that Y~TS  Y~/σ2~χn-lm-12. Matrix Dui,vi was positive semidefinite and contained weighting matrix Wui,vi which had different values in every location; therefore matrix Dui,vi was not idempotent. If Y~TDui,viY~≥0 and Dui,vi was not idempotent and also Y~ was a N0,I distributed random vector, then there were constants k and r; hence Y~TDui,viY~~kχr2; therefore it was concluded that test statistic V followed an F distribution. The modeling is implemented to find factors that influence the unemployment rate in 38 areas in Java in Indonesia.

In this research, studied multivariable nonparametric geographically weighted regression use truncated spline approach. The model is an expansion of nonparametric truncated spline regression that takes into account geographical or spatial factors. The purpose of this study was to find statistics test and distribution for the simultaneous hypothesis test. This study obtains the statistic test used the maximum likelihood ratio test (MLRT) method. Results of the research obtained statistics test based on the ratio between the maximum of the likelihood function under the set of H_0  and the maximum of the set likelihood function below the population with each have a spatial factor. Distribution of statistical tests has been proven to have a distribution of F. The modeling application used the percentage of the death of Dengue Hemorrhagic Fever (DHF) in 38 districts/cities in East Java Province. The modeling resulted in the determination coefficient of 80.7% and SSE value that is 0.0043.

This article describes the application of spatial statistical epidemiological modeling and its inference and applies it to COVID-19 case data, looking at it from a spatial perspective, and considering time-series data. COVID-19 cases in Indonesia are increasing and spreading in all provinces, including Kalimantan. This study uses applied mathematics and spatiotemporal analysis to determine the factors affecting the constant rise of COVID-19 cases in Kalimantan. The spatiotemporal analysis uses the Geographically Temporally Weighted Regression (GTWR) model by developing a spatial and temporal interaction distance function. The GTWR model was applied to data on positive COVID-19 cases at a scale of 56 districts/cities in Kalimantan between the period of January 2020 and August 2021. The purpose of the study was to determine the factors affecting the cumulative increase in COVID-19 cases in Kalimantan and map the spatial distribution for 56 districts/cities based on the significant predictor variables. The results of the study show that the GTWR model with the development of a spatial and temporal interaction distance function using the kernel Gaussian fixed bandwidth function is a better model compared to the Ordinary Least Squares (OLS) model. According to the significant variables, there are various factors affecting the rise in cases of COVID-19 in the region of Kalimantan, including the number of doctors, the number of TB cases, the percentage of elderly population, GRDP, and the number of hospitals. The highest factors that affect COVID-19 cases are the high number of TB cases, population density, and the lack of health services. Furthermore, an area map was produced on the basis of the significant variables affected by the rise in COVID-19 cases. The results of the study provide local governments with decision-making recommendations to overcome COVID-19-related issues in their respective regions.

This article describes spatial-temporal analysis using the innovation of developing a Geographically Weighted Panel Regression model with a distance weighting function that includes the interaction between spatial and time aspects (GWPR-st). The method is a local regression technique that provides a parameter model that varies in each location through cross-sectional and time-series data observation units. This study develops a new model in spatial statistics and offers new methodologies in Geographic Models and Geographic Information Systems (GIS). This study aims to determine the factors that influence the increase in positive cases and map the spread of COVID-19 on the Kalimantan Regency/City Scale. The model applied in this study involves geographic weighting functions, including the Gaussian kernel, Bisquare kernel, and tricube kernel, which spatial interactions and time series have modified. This study uses national COVID-19 data from 56 regencies/cities until August 2021. According to the research results, the developed model with the geographic weighting of the Bisquare kernel function was considered the most acceptable method. The developed model, which is deemed capable of information the most substantial influence on the number of COVID-19 cases in Kalimantan, is health services, such as a shortage of doctors, number of hospitals, number of community health centers, and number of tuberculosis cases. The study results provide the local governments with decision-making recommendations for overcoming the COVID-19 problems in their regions.