A hybrid model of spatial autoregressive-multivariate adaptive generalized Poisson regression spline

Abstract

Several Multivariate Adaptive Regression Spline (MARS) approaches are available to model categorical and numerical (especially continuous) data. Currently, there are other numerical data types—discrete or count data—that call for specific consideration in modeling. Additionally, spatially correlated count data is frequently observed. This has been seen in the case of health data, for example, the number of newborn fatalities, tuberculosis patients, hospital visitors, etc. However, currently no structurally consistent nonparametric regression and MARS model for count data incorporating spatial lag autocorrelation. The SAR-MAGPRS estimator (Spatial Autoregressive - Multivariate Adaptive Generalized Poisson Regression Spline) is developed to fill this gap. Although it can be applied to different count distributions, the estimator was developed in this study under the assumption of a Generalized Poisson distribution. This paper provides an information-theoretic framework for incorporating knowledge of the spatial structure and non-parametric regression models, especially MARS for the count data types. Moreover, the proposed method can assist in modeling the number of diseases while health policies are being developed. The framework presents an application of the Penalized Least Square (PLS) method to estimate the SAR – MAGPRS model.