ABSTRACT
So far, this book has focused on estimating spatial models and producing point estimates of latent quantities, such as ideal points. The importance of estimating uncertainty has been stressed, and we have discussed methods for displaying uncertainty bounds. But in this chapter, we transition to a richer discussion of incorporating uncertainty when using latent quantities as variables-either as independent or dependent variables. When unobserved variables are used on both sides of a model, this constitutes a full probability model. In this case, uncertainty is allowed to flow both ways in the estimation of the parameters. We discuss full probability models as well as MIMIC (Multiple Indicators and Multiple Causes) models in Section 7.1. MIMIC models allow latent variables to be functions of multiple observed variables. For instance, we have thus far considered only roll call votes as indicators of legislators’ ideological positions, but we could also use constituency and member characteristics (e.g., district partisanship and legislator gender and religion) to estimate ideology. MIMIC models allow us to do just that.
