Bayesian Gaussian Processes. Or: How I Learned to Stop Worrying and Love Nonlinear Social Science

Introduction

Nonlinearity is ubiquitous in the social sciences. In cross-sectional research, nonlinearity naturally follows from the fact that variables often depend on human perception. The tendency to share fake news, for example, depends in a complex nonlinear manner on people's personality and political preferences.

Longitudinal Research

In longitudinal research, nonlinearity follows from the fact that temporal social processes are nonstationary by nature. For instance, stressful life events (e.g., unemployment, pandemic) have a complex nonlinear impact on well-being over time.

Data Requirements

To study these nonlinear phenomena, much more data are needed than in linear analyses. Therefore, researchers increasingly rely on technological innovations to collect rich data, such as:

• Panel data via online surveys
• Experience sampling data via mobile apps
• Temporal social network data using digital communication (e.g., email)

Prior Information

In addition, prior information (e.g., from experts) is often available to inform us about plausible nonlinear shapes. A crucial problem is, however, that statistical approaches for learning nonlinearity still heavily rely on old-fashioned techniques which can only model simple (curvilinear) effects and are unable to include external prior information. Our understanding of nonlinear phenomena therefore remains limited.

Project Goals

This project aims to resolve these shortcomings by developing cutting-edge methods for nonlinear social science using Bayesian Gaussian processes. With this nonparametric methodology, we can:

1. Learn complex nonlinear shapes
2. Add prior knowledge
3. Test nonlinear theories

Implementation

Implementation in user-friendly software will ensure general utilization. Tailor-made extensions will be developed for:

• Cross-sectional data
• Panel data
• Experience sampling data
• Temporal social network data

Conclusion

After this project, we will be able to truly understand complex nonlinear mechanisms, to learn how these unfold over time, and to make accurate predictions (e.g., of well-being after life events).