چکیده : 

We consider modeling spatio-temporally indexed relational data, motivated by analysis

of voting data for the United States House of Representatives over two decades. The

data are characterized by incomplete binary matrices, representing votes of legislators on

legislation over time. The spatial covariates correspond to the location of a legislator’s

district, and time corresponds to the year of a vote. We seek to infer latent features

associated with legislators and legislation, incorporating spatio-temporal structure. A

model of such data must impose a flexible representation of the space–time structure,

since the apportionment of House seats and the total number of legislators change over

time. There are 435 congressional districts, with one legislator at a time for each district;

however, the total number of legislators typically changes from year to year, for example

due to deaths. A matrix kernel stick-breaking process (MKSBP) is proposed, with the model

employed within a probit-regression construction. Theoretical properties of the model are

discussed and posterior inference is developed using Markov chain Monte Carlo methods.

Advantages over benchmark models are shown in terms of vote prediction and treatment

of missing data. Marked improvements in results are observed based on leveraging spatial

(geographical) information.