Quantifying factors that affect evacuation decision making remains a challenging task. Progress is crucial for developing predictive models of collective behavior and for designing effective policies to guide the action of populations during wildfires. We conduct a controlled behavioral experiment to probe factors influencing evacuation decision making in the face of an impending virtual wildfire. We consider competing factors that influence small groups and the community as a whole. Based on our data, we develop two distinct but complementary empirically-driven approaches to characterize individual and group evacuation decision making. Our first approach is a stochastic model that predicts evacuation of a population of individuals guided by the same decision-making strategy, which we define to be a continuous function of key experimental variables such as the likelihood of the disaster and the availability of resources. We extend this model to investigate strategy shifts leading to differences between individual and group behavior which manifest at the collective level. In our second approach, we characterize decision making of individuals and groups by incorporating variation in individual traits, group decision protocols, and time-dependent changes in experimental variables with logistic regression. By including personal identifying characteristics of each subject, we develop a model that can predict evacuation decision times with 85.0% accuracy. In parallel, we demonstrate that the social media activity of individual subjects, specifically their Facebook use, can be used to generate an alternative individual personality profile that leads to comparable prediction accuracy of 84.2%. Our results from both approaches demonstrate the importance of using a rate-based rather than threshold function to describe individual behavior, and of accounting for social influence and individual heterogeneity in modeling group decision making.