Parameter Estimation of Geographically and Temporally Weighted Elastic Net Ordinal Logistic Regression

Geographically and Temporally Weighted Elastic Net Ordinal Logistic Regression is a parsimonious ordinal logistic regression with consideration of the existence of spatial and temporal effects. This model has been developed with the following three considerations: the spatial effect, the temporal effect, and predictor selection. The last point prompted the use of Elastic Net regularization in choosing predictors while handling multicollinearity, which often arises when there are many predictors involved. The Elastic Net penalty combines ridge and LASSO penalties, leading to the determination of the appropriate λEN and αEN. Therefore, the objective of this study is to determine the parameter estimator using Maximum Likelihood Estimation. The estimation process comprises defining the likelihood function, determining the natural logarithm of the likelihood function, and maximizing the function using Berndt–Hall–Hall–Hausman. These steps continue until the estimator converges on the values that maximize the likelihood function. This study contributes by developing an estimation framework that integrates spatial and temporal effects with Elastic Net regularization, allowing for improved model interpretation and stability. The findings provide an advanced methodological approach for ordinal logistic regression models that incorporate spatial and temporal dependencies. This framework is particularly useful for applications in fields such as economic forecasting, epidemiology, and environmental studies, where ordinal responses exhibit spatial and temporal patterns.