Each day humans generate massive volumes of data in a variety of different forms (Lazer et al., 2009). For example, digitized texts provide a rich source of political content through standard media sources such as newspapers, as well as newer forms of political discourse such as tweets and blog posts. In this chapter we analyze a corpus of 13,246 posts that were written for six political blogs during the course of the 2008 U.S. presidential election. But this is just one small example. An aggregator of nearly every document produced by the U.S. federal government, voxgov.com, has collected more than eight million documents from 2010–2014, including over a million tweets from members of Congress. These data open new possibilities for studies of all aspect of political life from public opinion (Hopkins and King, 2010) to political control (King, Pan, and Roberts, 2013) to political representation (Grimmer, 2013).
The explosion of new sources of political data has been met by the rapid development of new statistical tools for meeting the challenges of analyzing “big data.” (National Research Council, 2013; Grimmer and Stewart, 2013; Fan, Han, and Liu, 2014). A prominent example in the field of text analysis is latent Dirichlet allocation (LDA) (Blei, Ng, and Jordan, 2003; Blei, 2012), a topic model that uses patterns of word co-occurrences to discover latent themes across documents. Topic models can help us deal with the reality that large data sets of text are also typically unstructured. In this chapter we focus on a particular variant of LDA, the structural topic model (STM) (Roberts et al., 2014), which provides a framework to relate the corpus structure we do have (in the form of document-level metadata) with the inferred topical structure of the model.
Techniques for automated text analysis have been thoroughly reviewed elsewhere (Grimmer and Stewart, 2013).We instead focus on a less often discussed feature of topic models and of latent variable models more broadly: multimodality. That is, the models discussed here give rise to optimization problems that are nonconvex. Thus, unlike workhorse tools such as linear regression, the solution we find can be sensitive to our starting values (in technical parlance, the function we are optimizing has multiple modes). We engage directly with this issue of multimodality, helping the reader understand why it arises and what can be done about it.