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.

One time series model developed to predict economic data is Spatial Vector Autoregressive with Exogenous Variables (SpVARX). This model can accommodate simultaneously the interrelationships between variables, the impact of exogenous variables, and Inter-regional linkages. However, this model has not adjusted the nonlinearity relationships between variables. The relationship between economic variables is usually not linear. Therefore, we introduce the Threshold Spatial Vector Autoregressive with exogenous variables (TSpVARX). This paper assesses the forecasting performance of TSpVARX and compares it with SpVARX models. We conducted a simulation study by generating 100 times the simulation data with twelve scenarios. We found that the forecasting performance of the TSpVARX model is better than SpVARX when there is a nonlinear relationship between variables. In addition, we find that the forecasting performance of TSpVARX models will improve as the sample size increases.