Modeling public opinion over time: A simulation study of latent trend models

Analyzing trends in public opinion is important for monitoring social change and for testing theories aimed at explaining this change. With growing availability of multi-wave surveys, social scientists are increasingly turning to latent trend models applied to survey data for examining changes in social and political attitudes. With the aim of facilitating this research, our study compares different approaches to modeling latent trends of aggregate public opinion: splines, Gaussian processes, and discrete autoregressive models. We examine the ability of these models to recover latent trends with simulated data that vary with regard to the frequency and magnitude of changes in the true trend, model complexity and data availability. Overall, we find that all three latent trend models perform well in all scenarios, even the most difficult ones with frequent and weak changes of the latent trend and sparse data. The two main performance differences we find include the relatively higher squared errors of autoregressive models compared to the other models, and the under-coverage of posterior intervals in high-frequency low-amplitude trends with splines. For all models and across all scenarios performance improves with increased data availability, which emphasizes the need of supplying sufficient data for accurate estimation of latent trends.