The application of Gaussian copula marginal regression for exploring the effect of weather to Covid-19 in Jakarta

On data that are not normally distributed, classical linear regression is developed into the Generalized Linear Model (GLM). One of them is logistic regression which is used for binary discrete data. A different strategy is to consider all variables (response and predictors) to be random observations from the joint probability distribution. A model with dependencies should be used because some factors are dependent. The copula model, one of which is the Gaussian copula, is a popular technique for creating multivariate models with dependencies. The Gaussian copula regression model (GCMR) is a general structure that can be used to model any form of dependent response. The Gaussian copula blends the ease of interpretation of marginal modeling with the flexibility of the dependency structure specification. In this case, the estimated parameter is the regression coefficient and the error is expressed in the dependency structure. The model estimation uses the maximum likelihood method. This paper aims to apply the GCMR model to time series data where the dependent variable is discrete with a binomial distribution. A case study was conducted to see the effect of weather factors on Covid cases in DKI Jakarta. The regression model used is binomial data logistic regression with the dependency structure expressed in the correlation matrix with the assumption that the error is obtained from the ARMA(p,q) process. The dependent variable is the number of Covid-19 cases and the independent variable is the maximum temperature, average temperature and humidity. The data are a daily time series with a range of March 1, 2020 to April 30, 2022. Based on the GCMR model, Maximum temperature, average temperature and Humidity have a significant influence on the number of Covid-19 cases in Jakarta. For this case study, the results show that the GCMR model is better than logistic regression analysis.