Abstract
<p>Systematic studies of aggregate trends in public opinion hold great promise for the study of political behavior, representation, and comparative politics. Recently, several approaches have emerged to facilitate these studies. But how solid is the methodological footing of these approaches? While their methodological properties have been examined in a limited number of simulation studies, those have focused on isolated aspects of the data generating process. We conduct a comprehensive analysis of two key methodological frameworks, based on polytomous and dichotomized item response solutions, across several dimensions: richness of the data, number of countries, and the nature of differential item functioning (DIF). We find that the polytomous approach yields credible intervals that are too small, that both approaches have difficulties with severe DIF, and that dichotomization increases uncertainty relative to polytomous items. We show these results while paying attention to the full distribution of the latent variable of public opinion---both its center and its tails. Aside from showing the difficulties with extant approaches, we also show how they can be adapted to yield better estimates and comparisons of public opinion across countries.</p>