Holighi, Khalil Shafie
Lalonde, Trent L.
College of Education and Behavioral Sciences; School of Educational Research Leadership and Technology, Department of Applied Statistics and Research Methods
University of Northern Colorado
Type of Resources
Place of Publication
University of Northern Colorado
Longitudinal studies are commonly encountered in a variety of research areas in which the scientific interest is in the pattern of change in a response variable over time. In longitudinal data analyses, a number of methods have been proposed. Most of the traditional longitudinal methods assume that the independent variables are the same across all subjects. It is commonly assumed that time intervals for collecting outcomes are predetermined and have no information regarding the measured variables. However, in practice, researchers might occasionally have irregular time intervals and informative time, which violate the above assumptions. Hence, if traditional statistical methods are used for this situation, the results would be biased. The joint models of longitudinal outcomes and informative time are used as a solution to the above violations by using joint probability distributions, incorporating the relationships between outcomes and time. The joint models are designed to handle outcome distributions from a normal distribution with informative time following an exponential distribution. Several studies used the maximum likelihood parameter estimates of the joint model. This study, however, presented an alternative method for parameters estimation, based on a Bayesian approach, with respect to joint models of longitudinal outcomes and informative time. Using a Bayesian approach permitted the inclusion of knowledge of the observed data within the analysis through the prior distribution of unknown parameters. In this dissertation, the prior distribution adopted three scenarios: (1) the prior distributions of all unknown parameters are noninformative prior, which will set to be vague but proper prior: Normal(0, 1e6). (2) The prior distributions of all unknown parameters are informative prior, which will be set to be normal for unrestricted parameters, and inverse gamma (IG) priors for positive parameters such as the variance σ2. (3) A combination of two above scenarios, so the prior distributions of some unknown parameters are noninformative, and the others are informative. The procedure for estimating the model parameters was developed via a Markov chain Monte Carlo method using the Metropolis-Hastings algorithm. The key idea was to construct the likelihood function, specify the prior information, and then calculate the posterior distribution. Simulated observations were generated by the MCMC technique from the posterior distribution. Thus, the primary purpose of this study was to find Bayesian estimates for the unknown parameters in the joint model, with the assumptions of a normal distribution for the outcome process and an exponential distribution for informative time. The properties and merits of the proposed procedure were illustrated employing a simulation study through a written R program and OpenBUGS.
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