Heteroskedastic Ordered Probit Models with an Artificial Neural Network for Predicting Potential Consumer Ratings on Amazon Software Reviews

The ordered probit model is widely used to make inferences about ordinal dependent variables in the social sciences, while neural network models have proven effective for classification tasks across various domains. Although other scholars have proposed ordinal classification models using neural networks, empirical studies combining ordered probit models with neural networks remain limited. To date, no studies have examined ordered probit models with neural networks under the assumption of heteroskedasticity. Accordingly, this paper demonstrates the predictive performance of an ordered probit model with an artificial neural network (OPANN) using different activation functions. In addition, it introduces a newly developed heteroskedastic ordered probit model with an artificial neural network (HOPANN). To evaluate the predictive performance of the HOPANN and OPANN models for ordinal dependent variables, this study designs counterfactual predictive experiments to forecast potential consumer ratings of Amazon software products. Given the predominance of imbalanced online product reviews, this paper constructs balanced and imbalanced datasets. The HOPANN and OPANN models consistently yield the best or second-best F1 scores across all imbalanced datasets. In contrast, the other models—excluding the HOPANN and OPANN—fail to correctly classify the minority class when applied to the imbalanced datasets. However, neither the HOPANN nor the OPANN demonstrates superior predictive accuracy with the balanced dataset. Overall, the HOPANN and OPANN are well suited for domains characterized by imbalanced data. These models can be applied to predict star ratings in online reviews across different product groups on various platforms, as well as ordinal responses in other domains.