Structural Topic Model

LDA assumes every document draws its topic proportions from a single shared Dirichlet prior and treats topics as independent, ignoring any metadata. STM replaces that fixed prior with a logistic-normal distribution whose mean depends on document-level covariates, lets topics correlate, and can additionally make a topic's vocabulary depend on covariates. So where LDA gives you topics and then leaves you to compare them across groups by hand afterward, STM estimates the topics and the covariate relationships jointly and reports those relationships with uncertainty. When you have no covariates, STM reduces to a correlated topic model close to LDA in spirit; see lda-topic-model and topic-modeling for the unconditioned versions.

Prevalence covariates affect how much each document is about each topic — they shift the expected topic proportions, answering questions like 'do Republicans talk about this topic more than Democrats?' Content covariates affect the words used to express a topic — they let the same topic be discussed with different vocabulary across groups, answering 'do the two parties use different language when discussing the same topic?' You can specify either, both, or neither; content covariates are more demanding to estimate and are used more sparingly.

There is no single correct K. The stm package provides searchK to compare candidate values on diagnostics such as held-out likelihood, semantic coherence, and exclusivity, but these are aids, not arbiters. Best practice is to combine the diagnostics with substantive reading of the top words and representative documents at several K values, choosing a model whose topics are coherent, distinct, and useful for the research question. K is a modeling choice to be justified and checked, not a parameter the data fixes on their own.