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Bayesian Inference on a Mixed-Effects Location-Scale Model with Normal and Skewed Error Distributions

McGill, Brian (2017) Bayesian Inference on a Mixed-Effects Location-Scale Model with Normal and Skewed Error Distributions. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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In handling dependent data, mixed-effects models are commonly used. These models allow for
each individual in the population to vary randomly about an overall population location. Most
methods focus on modeling the mean structure and treat the resulting between- and within-subject
variances as nuisance parameters. Hedeker has extended these models to allow for simultaneous
modeling of both the mean and variance components, each with appropriate random effects. His
work has focused on data with large amounts of repeated observations (30-50) from a one-week
period. His Marginal Maximum Likelihood estimation approach provides unbiased estimates in
those situations, but oftentimes fails to provide feasible results for these mixed-effects locationscale
models in other situations. By implementing a Bayesian Markov chain Monte-Carlo I am
able to fit these models in a more general setting that can include repeat observations collected
over a two-year span. I have also adapted this model to utilize the skew-normal distribution which
allows for skewed-error distributions. In applying these techniques to data from a bipolar clinical
trial, I am able to explain how different treatments impact the resulting scores for depression and
mania in both their mean and variance. These techniques lend themselves to addressing many
research questions that would focus on stabilizing the mood in their subjects.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
McGill, Brianbsm36@pitt.edubsm36
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairIyengar, Satishssi@pitt.edussi
Committee MemberCheng, Yuyucheng@pitt.eduyucheng
Committee MemberRen, Zhaozren@pitt.eduzren
Committee MemberAnderson, Stewartsja@pitt.edusja
Committee MemberWallace, Meredithmel20@pitt.edumel20
Date: 28 September 2017
Date Type: Publication
Defense Date: 12 June 2017
Approval Date: 28 September 2017
Submission Date: 12 June 2017
Access Restriction: 2 year -- Restrict access to University of Pittsburgh for a period of 2 years.
Number of Pages: 127
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Statistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Bayesian Location-Scale Mixed-Effects Skew-Normal
Date Deposited: 28 Sep 2017 21:38
Last Modified: 29 Sep 2019 05:15


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