Multidimensional Analysis of Roll Call Data via Bayesian Simulation: Identification, Estimation, Inference, and Model Checking

Vote-specific parameters are often by-products of roll call analysis, the primary goal being the measurement of legislators’ ideal points. But these vote-specific parameters are more important in higher-dimensional settings: prior restrictions on vote parameters help identify the model, and researchers often have prior beliefs about the nature of the dimensions underlying the proposal space. Bayesian methods provide a straightforward and rigorous way for incorporating these prior beliefs into roll call analysis. I demonstrate this by exploiting the close connections among roll call analysis, item–response models, and “full-information” factor analysis. Vote-specific discrimination parameters are equivalent to factor loadings, and as in factor analysis, they (1) enable researchers to discern the substantive content of the recovered dimensions, (2) can be used for assessing dimensionality and model checking, and (3) are an obvious vehicle for introducing and testing researchers’ prior beliefs about the dimensions. Bayesian simulation facilitates these uses of discrimination parameters, by simplifying estimation and inference for the massive number of parameters generated by roll call analysis.