Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Rajib Paul

Second Advisor

Dr. Joshua Naranjo

Third Advisor

Dr. Georgiana Onicescu

Fourth Advisor

Dr. Amy Curtis


Weibull Regression, MCMC Algorithm, CAR Model, Ordinal Logit Model, Spatial analysis, Survival analysis


Foster care youth is a medically vulnerable population. Poor dental health and irregular well-child visits may cause serious health-related issues, such as mental disorder, nutrition imbalance, tooth damage, etc. Michigan requires all youth in foster care to receive annual dental and well-child visits. Usually, the study of foster care well-child and dental visits include two parts: time between two consecutive visits (gap time) and number of visits. For this study, a longitudinal-spatial model that has the flexibility to analyze the well-child/dental gap times and number of visits was developed. The longitudinal data (2009-2012) on Michigan foster care youth from 10 years old to 19 years old, with county of residence information was analyzed. The bivariate outcome variables were time between two consecutive dental and two consecutive well-child visits. Explanatory variables include gender, age, race, number of living arrangements, type of living arrangement, and the population in each county. The numbers of visits for each youth were characterized by Poisson distributions. For analyzing gap times, two strategies were used in this study.

In the first strategy, the gap times were modeled using a conditional Weibull distribution. The intensity function was modeled in terms of explanatory variables and spatial frailties that captured the county level spatial and cross-spatial dependencies. In the second strategy, gap times were divided into three types based on the length of the time: 1). Short gap time, if the gap time is less than or equal to 10 months (4 months) in well-child (dental) analysis; 2). Appropriate gap times, if the gap time is greater than 10 months (4 months) and less than or equal to 14 months (8 months) in well-child (dental) analysis; 3). Long gap time, if the gap time is greater than 14 months (8 months) in well-child (dental) analysis. After this data transformation, the gap times were transformed into categorical data, so that a multinomial logit model and an ordinal logit model were fitted in terms of the explanatory variables and spatial frailties. In addition, a data-augmentation Markov Chain Monte Carlo (MCMC) algorithm was developed for model fitting, and posterior predictive check was used for checking the fitness.

Some future work should be considered based on the results of this study. First, a more accurate classification may be developed for the type of gap times. Second, some other distribution, such as log-normal distribution, exponential distribution, or gamma distribution, could be used for modeling the continuous gap times. Third, a more effective technique for Bayesian model check could be developed.

Access Setting

Dissertation-Open Access