Title: Parameter Estimation of Binary Probit Regression for Panel Data with Random Effect Using Newton-Raphson Iteration Method
Authors: Pressylia Aluisina Putri Widyangga , Suliyanto , M. Fariz Fadillah Mardianto , Sediono
Volume: 8
Issue: 11
Pages: 197-202
Publication Date: 2024/11/28
Abstract:
Binary probit regression is a popular statistical method for modeling binary outcome variables, particularly suited for cases where the dependent variable represents two categories. When applied to panel data, binary probit regression accounts for individual-specific heterogeneity across time, making it valuable in fields such as economics, healthcare, and social sciences. In this context, the inclusion of random effects enables the model to capture both within-individual and between-individual variation and offers robust insights into the factors influencing binary outcomes over time. This study aims to improve parameter estimation in binary probit regression models for panel data with random effect by applying Newton-Raphson iteration, an iterative optimization technique. Given the computational complexity of the likelihood function which involves an integral over the distribution of random effects, the study integrates Gauss-Hermite quadrature to enhance the Newton-Raphson method's convergence and accuracy. Gauss-Hermite quadrature is particularly suited for this task due to its efficacy in approximating integrals with normal distributions. The research findings demonstrate that Newton-Raphson iteration when coupled with Gauss-Hermite quadrature yields more precise parameter estimates which thereby enhancing the reliability of the model. This method proves efficient in dealing with high-dimensional integrals and improves convergence speed and makes it feasible for large panel datasets. In conclusion, the study provides an effective computational framework for binary probit regression models with random effect in panel data, addressing limitations in traditional estimation methods. The proposed approach enhances the accuracy and robustness of the model and offers significant implications for studies requiring precise parameter estimation in binary outcome modeling.