Publication Date

Winter 11-21-2020


Hierarchical models are becoming increasingly common in epidemiological and psychological research. When analyzing data from such studies, the nested structure of the data must be taken into account. Mixed modeling in conjunction with hierarchical mixed modeling allows researchers to ask broad questions about the population of interest. Modeling under restricted maximum likelihood estimation (REML), as opposed to full maximum likelihood estimation (ML), increases the accuracy of estimates for the random effects in the model. We use hierarchical mixed modeling under REML estimation to analyze which factors increase “community integration”, a concept and a construct developed and used in the mental health service sector focusing on bettering the development of personal, social, and vocational competency of individuals experiencing homelessness enrolled in permanent supportive housing (PHS) programs. “Community integration” takes central importance because it has been shown to improve individual quality of life. From increasing their chances of finding employment to expanding their social networks in order to lessen the psychological trauma of homelessness, tracking community integration is critical to understanding the overall experience of homeless individuals. Combining organizational research theory and growth modeling theory into a 3-level model illustrates the hierarchy of variables affecting the Community Integration Scale (CIS) Psychological score. Individual growth trajectories, variation in client growth parameters at each site, and variation between sites are represented, respectively, within the first, second, and third levels of the model. For individuals experiencing homelessness, CIS Psychological scores increase most drastically between intake and 6 months, with few contextual variables affecting this change.

Degree Name


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

Erik Barry Erhardt

Second Committee Member

Ronald Christensen

Third Committee Member

Fletcher G. W. Christensen




hierarchical model, mixed effects, REML, CIS Psychological score, individual growth

Document Type