Comparing Some Adjacency Matrices to Estimate a Spatial Negative Binomial Regression Model

The spatial regression model is used to illustrate the extent of the influence of independent variables on the dependent variable with the presence of spatial effects of adjacent locations. In such models, the dependent variable usually follows the normal distribution. In this research, a different case was studied, which is when the dependent variable is distributed in a negative binomial distribution, which is considered one of the important discrete distributions, and the basis of statistical models for count data. This distribution is suitable for data with overdispersion characteristics. In this research, a spatial negative binomial regression model is estimated using the maximum likelihood method of estimation, and based on the Queen adjacency criteria and the proposed longitudes to form the modified weight matrix, and simulation study is conducted to choose the best matrix from among the two used matrices. The results showed that the modified proposed longitude matrix is the best, as it was used to estimate the parameters of the negative binomial regression model using traffic accident data for 14 Iraqi governorates for the year 2022 as a response variable and based on the explanatory variables (temperature, rainfall, and amount of falling dust). The results showed that there is an effect of temperature and rainfall on the number of traffic accidents with spatial dependence.