Geographically Weighted Logistic Regression Model on Binomial Data to Explore Weather Spatial Non-Stationarity in Covid-19 Cases

Geographically Weighted Logistic Regression (GWLR) creates a logistic regression model by incorporating spatial variation through geographical weighting in parameter estimation. GWLR can be employed for investigating the relationship among a variable and its independent variables when the dependent variable has a Bernoulli distribution. In some studies, not only a single individual or experimental unit is observed but also a group of binary samples that have all been treated in the same manner. As a result, data with n total obser-vations can be considered to have a binomial distribution, and the total availability also indicates that the data have a binomial distribution rather than a Poisson distribution or a negative binomial distribution. In the present research, the GWLR model is modified into Geographically Weighted Binomial Logistic Regression (GWBLR). Unlike the GWLR, which only observes one binary sample as the response variable, the GWBLR allows n binary samples as the response variable. The parameter estimations were calculated by maximum likelihood estimation (MLE), and the optimum bandwidth was determined by a fixed Gaussian function based on the least Cross Validation (CV) result. The likelihood ratio test and the Wald test were used to test hypotheses. We created the model using both simulation and real data. The simulation parameter estimations demonstrated high consistency with the generated data. The GWBLR model was applied to real data to investigate the spatial effects of temperature, sunshine, humidity and precipitation on the number of confirmed Covid-19 cases in Indonesia. Temperature, sunshine, humidity and precipitation all had an important effect on confirmed Covid-19 cases, according to the data.