## 5 Discussion and Conclusions
In addition, when solving a more complex problem, an approach combining multiple synthesizing methods might be required [12; 13]. Moreover, given that the newly GAN-based approach of introducing a roundtrip method to the conditional GAN is proposed [43], applying it to tabular-formed data might be promising. Although the present study calculated the deep generative models using default parameters, the approach of automatically optimizing hyperparameters of the GAN-based model has been proposed [44]. The evolutionary architectural search GAN (EAS-GAN) enables the optimization of hyperparameters, including network architecture [45]. These automated methods do not require searching for optimized parameters through trial-and-error. Although those methods are not applied to the tabular data format, another finding could be brought to our study if the optimized parameters were adopted in this study. Thus, further research is required to facilitate the use of generative multimodal data for management science challenges. Concretely, first, although the experiment in the present study was conducted with a small participant sample, we need to perform a comparable experiment between the results of the augmented data based on a small participant sample and a large participant sample's results under the condition of sampling these participants from the same population in the next step. This experiment might enable us to confirm the reproducibility of the results of experiments with a large participant sample by using augmented data. Second, to confirm the robustness of our results concerning the other new multimodality data besides both EEG and questionnaire survey data, we need to experiment with adding other modalities, such as photo images, movies, texts, music, and other physiological data. Third, to validate generalizing our results, we should apply the approaches of the present study to a wide variety of management science fields, including digital marketing and decision-making systems for managing businesses. In conclusion, the present study provides a beneficial approach for applying multimodal data to management science issues as a first step. We demonstrated that with sufficient training in deep generative models, we could generate big data almost similar to real data, using small multimodal data as seed data, which included EEG signals and questionnaire survey data. Furthermore, our results could be extended to other issues in management science, such as marketing management and marketing research, since they overcome the restrictions of the limited sample size and privacy concerns when using multimodal data, including physiological data such as EEG signals. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app14010378/s1](https://www.mdpi.com/article/10.3390/app14010378/s1)]([https://www.mdpi.com/article/10.3390/app14010378/s1](https://www.mdpi.com/article/10.3390/app14010378/s1)), Table S1: The default parameters in each deep generative model. Table S2: Results of optimizing parameters. Table S3: Basic statistics. Table S4: Data qualities in each deep generative model. Table S5: Predictive performance in each deep generative model. Table S6: Computation time. Code S1(A): CTGAN, Code S1(B): CopulaGAN, Code S1(C): TVAE, Code S2(A): XGBoost(Validation: Setting the trained model), Code S2(B): XGBoost(Validation: Predicted results). Conceptualization, S.W. and K.E. ; methodology, S.W. ; software, S.W. ; validation, S.W. ; formal analysis, S.W. ; investigation, S.W. ; resources, K.F., J.O. and K.E. ; data curation, S.W., Y.N., Y.K. and M.K. ; writing--original draft preparation, S.W. ; writing--review and editing, S.W. ; visualization, S.W. ; supervision, S.W., J.O. and K.E. ; project administration, S.W., J.O. and K.E. ; funding acquisition, K.E. All authors have read and agreed to the published version of the manuscript. This work was supported by JSPS KAKENHI (Grant no. JP17K03992).