Comparison of ordinal multinomial models with missing data: Application to length of stay in mental health healing community

Modeling length of stay (LOS) using ordered groups requires applying ordinal models due to ranking of data. When modeling LOS for individuals with persistent psychological health conditions at a live-in healing community in North Carolina which included missing values, there is a need for appropriate models of ordinal data with missing observations. It is important to predict length of stay to allocate appropriate funding to this community. 

Ordinal logistic regression models have been applied in recent years in analyzing data with ranked multiple response outcomes. Ordered information has been increasingly used in health indicators but their use in the public health is still rare (Abreu et al., 2009).  This may be attributed to these models’ complexity, assumptions validation, and limitations of modeling options offered by statistical packages (Lall, 2002). Missing values add more complexity to ordinal models but not much research exists about their handling techniques.

Regardless of their complexity, ordinal hypothesis tests provide increased power and ordinal logistic models allow for interpretations based on inherent rankings; therefore, increased accessibility of these models is important, particularly choosing among link functions such as cumulative logits, adjacent-category logits, and continuation-ratio logits, and choosing between missing data approaches like listwise deletion and imputation methods.

Using the mental health data, this study compares different link functions within ordinal multinomial logistic models and evaluates the appropriateness of missing data methods using SAS and R. The variables affecting the length of stay in the healing community, such as race, gender, and health conditions, are also presented.