Language models prompted with a user description or persona can predict a user's preferences and opinions, but existing approaches to building personas -- based solely on a user's demographic attributes and/or prior judgments -- fail to capture the underlying reasoning behind said user judgments. We introduce PB&J (Psychology of Behavior and Judgments), a framework that improves LLM personas by incorporating rationales of why a user might make specific judgments. These rationales are LLM-generated, and aim to reason about a user's behavior on the basis of their experiences, personality traits or beliefs. This is done using psychological scaffolds -- structured frameworks grounded in theories such as the Big 5 Personality Traits and Primal World Beliefs -- that help provide structure to the generated rationales. Experiments on public opinion and movie preference prediction tasks demonstrate that LLM personas augmented with PB&J rationales consistently outperform methods using only a user's demographics and/or judgments. Additionally, LLM personas constructed using scaffolds describing user beliefs perform competitively with those using human-written rationales.