This paper uses survival analysis to model exits over time from two alternative notions of homelessness. We are unique in being able to account for time-invariant, unobserved heterogeneity. We find that duration dependence has an inverted U-shape with exit rates initially increasing (indicating positive duration dependence) and then falling. Like previous researchers, we find results consistent with negative duration dependence in models which ignore unobserved heterogeneity. Exit rates out of homelessness fall with age and with the education level of mothers. Women are more likely than men to exit homelessness when it is broadly conceived, but appear to be less likely to exit when it is narrowly defined. Finally, higher paternal education and exemptions from welfare-related activity requirements due to either mental or physical health conditions are all associated with higher exit rates.