Although data loss was modest during the first year, especially for a chronically homeless sample, we examined the extent to which changes in service use and outcomes described above may have been biased by the attrition rates presented in Table 6. For this analysis we used the "marginal statistical model method of Robbins et al., (2000, 1993) to create sampling weights equal to the inverse of the predicted probability for each client of completing a follow-up interview for each period of time. This probability was calculated using a logistic regression model in which seven basic eligibility characteristics (two homelessness categories and five disabling conditions, including dual mental health and substance abuse problem) and seven baseline socio-demographic characteristics (age, gender, education, race/ethnicity, marital status, veteran status, and duration of homelessness in lifetime) were entered as a single block of predictors.
We thus weighted observations from persons with similar socio-demographic and clinical profiles who were more likely to have missed a given follow-up interview more heavily. Mixed regression models using these weights were used to calculate the least square means presented in the non-weighted Table 7. Statistical significance test results changed for only 1 measure, illicit drug use. Although no difference in illicit drug use rates was found between non-weighted and weighted analyses, the later showed a small, but statistically significant decrease over time, whereas no significant change was found using unweighted analysis. (Table 8). Thus, attrition bias appears to be minimal, and subsequent analyses were run using the simpler and more straightforward non-weighted observations.