Defense Date


Document Type


Degree Name

Doctor of Philosophy



First Advisor

Dr. Viswanathan Ramakrishnan

Second Advisor

Dr. Al M. Best


In many applications of random-effects models to longitudinal data, such as heart rate variability (HRV) data, a normal-mixture distribution seems to be more appropriate than the normal distribution assumption. While the random-effects methodology is well developed for several distributions in the exponential family, the case of the normal-mixture has not been dealt with adequately in the literature. The models and the estimation methods that have been proposed in the past assume the conditional model (fixing the random-effects) to be normal and allow a mixture distribution for the random effects (Xu and Hedeker, 2001, Xu, 1995). The methods proposed in this dissertation assume the conditional model to be a normal-mixture while the random-effects are assumed to be normal. This is primarily to fit the HRV data, which seems to follow a normal-mixture within subjects. Another advantage of this model is that the estimation becomes much simpler through the use of an EM-algorithm. Existing methods and software such as the PROC MIXED in SAS are exploited to facilitate the estimation procedure.A simulation study is performed to examine the properties of the random-effects model with normal-mixture distribution and the estimation of the parameters using the EM-algorithm. The study shows that the estimates have similar properties to the usual normal random-effects models. The between subject variance parameter seems to require larger numbers of subjects to achieve reasonable accuracy, which is typical in all random-effects models.The HRV data is used to illustrate the random-effects normal-mixture method. These data consist of 9 subjects who completed a series of five speech tasks (Cacioppo et al., 2002). For each of the tasks, a series of RR-intervals was collected during baseline, preparation, and delivery periods. Information about their age and gender were also available. The random-effects mixture model presented in this dissertation treats the subjects as random and models age, gender, task, type, and task × type as fixed-effects. The analysis leads to the conclusion that all the fixed effects are statistically significant. The model further indicates a two-component normal-mixture with the same mixture proportion across individuals fit the data adequately.


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Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

June 2008

Included in

Biostatistics Commons