Methods for modeling time-dependent covariates with non-continuous response found in community health data

Recently the United States homeless population has seen an increase in families with children (National Coalition for the Homeless, 2009). Consequently the homeless population has increased pressure on social service networks that provide services to children, elderly, and other vulnerable populations with an increased risk of health related problems (Aday, 2001). The Greeley Transitional House works to provide emergency and extended housing to homeless families of at least one adult caring for at least on dependent child, helping to minimize the public health risks to the community. A primary interest of the transitional house is the typical length of stay of guests, and also whether house-sponsored programs such as job training and social case management reduce the length of stay. Data are recorded by month at the family level. Families often stay for multiple months, but many characteristics, such as hours of job training, vary monthly. These time-dependent covariates must be addressed in the analysis of length of stay. In this paper three analyses of the data are performed. For the first analysis, the varying nature of covariates is ignored, and a Generalized Estimating Equations model is applied (Zeger and Liang, 1986). A second analysis is applied in which the raw averages of the varying covariates are used as values. Finally, an analysis that addresses the time-dependency of some predictors is applied using the Generalized Method of Moments technique (Lai and Small, 2007). The results of these three methods are compared with respect to parameter estimates and standard errors.