At the microlevel, comparative public opinion data are abundant. But at the macrolevel—the level where many prominent hypotheses in political behavior are believed to operate—data are scarce. In response, this paper develops a Bayesian dynamic latent trait modeling framework for measuring smooth country–year panels of public opinion even when data are fragmented across time, space, and survey item. Six models are derived from this framework, applied to opinion data on support for democracy, and validated using tests of internal, external, construct, and convergent validity. The best model is reasonably accurate, with predicted responses that deviate from the true response proportions in a held-out test dataset by 6 percentage points. In addition, the smoothed country–year estimates of support for democracy have both construct and convergent validity, with spatiotemporal patterns and associations with other covariates that are consistent with previous research.