Machine learning can predict human behavior well when substantial structured data and well-defined outcomes are available, but these models are typically limited to specific outcomes and cannot readily be applied to new domains. We test whether large language models (LLMs) can support a more general-purpose approach by building person-specific simulations (i.e., "generative agents") grounded in self-report data. Using data from a diverse national sample of 1,052 Americans, we build agents from (i) two-hour, semi-structured interviews (elicited using the American Voices Project interview schedule), (ii) structured surveys (the General Social Survey and Big Five personality inventory), or (iii) both sources combined. On held-out General Social Survey items, agent accuracy reached 83% (interview only), 82% (surveys only), and 86% (combined) of participants' two-week test-retest consistency, compared with agents prompted only with individuals' demographics (74%). Agents predicted personality traits and behaviors in experiments with similar accuracy, and reduced disparities in accuracy across racial and ideological groups relative to demographics-only baselines. Together, these results show that LLMs agents grounded in rich qualitative or quantitative self-report data can support general-purpose simulation of individuals across outcomes, without requiring task-specific training data.