Modeling Public Opinion Over Time: a Simulation Study of Latent Trend Models

Abstract

Abstract With the growing availability of multi-wave surveys, social scientists are turning to latent trend models to examine changes in social and political attitudes. Aiming to facilitate this research, we propose a framework for estimating trends in public opinion consisting of three components: the measurement model that links the observed survey responses to the latent attitude, the latent trend model that estimates a trajectory based on aggregated individual latent scores, and representativeness adjustments. We use individual-level item response theory models as the measurement model that is tailored to analyzing public opinion based on pooled data from multi-wave surveys. The main part of our analysis focuses on the second component of our framework, the latent trend models, and compares four approaches: thin-plate splines, Gaussian processes, random walk (RW) models, and autoregressive (AR) models. We examine the ability of these models to recover latent trends with simulated data that vary the shape of the true trend, model complexity, and data availability. Overall, under the conditions of our simulation study, we find that all four latent trend models perform well. We find two main performance differences: the relatively higher squared errors of AR and RW models, and the under-coverage of posterior intervals in high-frequency low-amplitude trends with thin-plate 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. To further illustrate the differences between the four latent trend models, we present a case study with an analysis of trends in political trust in Hungary, Poland, and Spain between 1995 and 2019. We note the relatively weaker performance of splines compared to other models in this application and conclude by discussing factors to consider when choosing the latent trend model, and further opportunities in this line of research.