Comparison of Bayesian and Sample Theory Parametric and Semiparametric Binary Response Models

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Studies have broadly applied binary response models as the foundation for various models—such as tree analysis, survey analysis and risk assessment. This paper proposes a Bayesian semiparametric binary response model and compares it with sample theory semiparametric and other parametric binary response models.

For semiparametric models, studies that compare the impact of regular and optimal bandwidth in estimations of kernel density made through a Bayesian Markov Chain Monte Carlo algorithm are normally constrained. This is because computing the optimal bandwidth is extremely time consuming. Using a graphic processing unit, we improve the efficiency of the modelling by increasing the running speed, making it 600 times quicker than regular computing speeds. As a result, we achieve an efficient numerical Monte Carlo simulation to compare models.

Our results show that optimal bandwidth does not outperform regular bandwidth in binary semiparametric models. When data are balanced, various binary response models perform similarly. When data are extremely unbalanced, Bayesian semiparametric modelling surpasses estimations of maximum likelihood estimation in convergence. Finally, we test the robustness of the Bayesian semiparametric and other binary response models by using TransUnion data to estimate consumer bankruptcy rates.