Copula deep learning control chart for multivariate zero inflated count response variables

Abstract

With the increasing popularity of big data analysis, research on zero-inflated count data with the copula method has garnered significant attention because zero-inflated count data do not follow a normal distribution and have high correlation among variables. Within the domain of quality control, there has been limited emphasis on multivariate statistical process control (SPC) techniques that specifically address the challenge of multicollinearity within regression models for multivariate zero-inflated count responses. In this paper, we explain a computational challenge in handling big data with parametric generalized linear models, such as the zero-inflated Poisson model. This challenge motivates us to introduce a copula-based deep learning and neural network model involving multivariate zero-inflated count response variables with highly correlated explanatory variables. This approach builds upon existing deep learning and neural network models designed for univariate count responses, expanding them to encompass multivariate count response models through the integration of a copula regression framework. To evaluate the performance of our proposed methodology, we conduct a comparative analysis of accuracies using the zero-inflated Poisson model, univariate deep learning and neural network models, multivariate count response deep learning and neural network models, and our proposed copula deep learning and neural network models. This assessment involves employing metrics such as root mean square error (RMSE), weighted mean absolute percentage error (WMAPE), and mean absolute deviation (MAD). We include both copula-based asymmetrical zero-inflated simulated data and real-world data. We also propose a temporal dependence control chart for assessing the temporal dependence between bivariate zero-inflated count response variables. Our proposed copula deep learning and neural network temporal control charts can check time-varying dependence and outliers by leveraging the Shewhart statistical process control chart and t-copula ARMA-GARCH dynamic control correlation.

Keywords:

• Copula
• multivariate statistical process control chart
• multivariate count response model
• deep learning

Acknowledgments

We thank the two respected referees, Associated Editor and Editor for constructive and helpful suggestions which led to substantial improvement in the revised version. For the sake of transparency and reproducibility, the code and data used for this study can be found in the following GitHub repository: https://github.com/kjonomi/Rcode.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) (No. NRF-2021R1G1A1094116 and No. RS-2023-00240794).