Parameter Estimation and Statistical Test in Multivariate Adaptive Generalized Poisson Regression Splines

Poisson regression is a standard model for data counts that can be used to determine these factors. Equidispersion is assumptions that must be met in poisson regression. Equidispersion is a condition that the average of response variable is equal with the variance of the response variable. In real cases, there are overdispersion or underdispersion cases. Generalized Poisson Regression (GPR) is one of method that can handle cases of overdispersion or underdispersion. Multivariate Adaptive Regression Splines (MARS) is a nonparametric regression that can handle data whose behavior changes in sub-intervals, so that there is a knot point that indicates the occurence of changes in data behavior patterns. Multivariate Adaptive Generalized Poisson Regression Splines (MAGPRS) model is used as the development of the MARS and Generalized Poisson Regression. This research use Weighted Least Squares (WLS) with Berndt Hall Hall Husman (BHHH) algorithm to obtain parameter model estimator. Afterwards, get the test statistic on the model Multivariate Adaptive Generalized Poisson Regression Splines using Maximum Likelihood Ratio Test (MLRT). Finally, the application of MAGPRS model was carried out in the case of the number of Acute Respiratory Tract Infection in babies.