Multivariate adaptive inverse Gaussian regression spline: Parameter estimation and statistical hypothesis testing

Multivariate Adaptive Regression Spline (MARS) is a popular nonparametric regression technique that permits both additive and interaction effects among predictor variables. Because of these advantages, the MARS model generates more accurate estimations of the regression curve from the relationship between the predictors and the response variable. The presence of knot point in MARS allows this method to model the data whose patterns change at sub-intervals. This method is designed for high-dimensional data. The response variable may occasionally continuous data with positive skewness. When the response variable is highly skewness, inverse Gaussian regression is more recommended than gamma regression. The MARS algorithm and inverse Gaussian regression are combined in the Multivariate Adaptive Inverse Gaussian Regression Spline (MAIGRS) model. This study examines the estimation of parameters and statistical testing of MAIGRS model. Estimation of the model parameters is obtained in two stages. First, find the optimal basis function matrix. Then, modeling that basis function matrix with response variable using Generalized Linear Model (GLM) which parameters are estimated using Maximum Likelihood Estimation (MLE) method. Because no analytical solution was obtained from MLE, then it was continued using Iteratively Reweighted Least Square (IRLS) method. Simultaneous statistical testing of model uses the Likelihood Ratio Test (LRT).