Comparison Between The Maximum Likelihood Method And A Nonparametric Method For Estimating A Poisson Regression Model

Numerical models are those that deal with specific numbers in health research and studies, such as the number of hospitalized patients, the number of phone calls, the number of cases of a particular disease, and other counts. Among the models that deal with such numbers are the Poisson model, negative binomial regression model, logistic model, and Bernoulli . In this research, the Poisson regression model was used, and the model parameters were estimated using parametric methods (Maximum Likelihood) and non-parametric methods (Spline Regression Method). Due to the complexity of the assumptions in the Poisson regression model, which makes it unsuitable for the least squares method, an alternative method was used to estimate the model for its flexibility and simpler assumptions. A comparison was made between these methods according to specific criteria, relying on real data related to one of the most prevalent diseases today: COVID-19, which affects the human body and causes various inflammations, including respiratory, liver, and kidney inflammation, among others. The data was analyzed using SPSS and R software, leading to the conclusion that the estimation method using the non-parametric approach (cubic spline regression) was better than the parametric method (MLE) based on the results of the MSE