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Detecting underlying emotional sensitivity in bereaved children via a multivariate normal mixture distribution

Kelbick, Nicole DePriest
http://rave.ohiolink.edu/etdc/view?acc_num=osu1064331329

Abstract Details

2003, Doctor of Philosophy, Ohio State University, Biostatistics.
A common theme in finite mixture problems involves a random sample taken from a population consisting of an unknown mixture of distributions. The goal is to identify the component distributions using information from the sample. A medical example might entail clinical test results from patients whose true disease status is unknown. Another example pertains to latent class models which attempt to relate observed data to an unseen variable whose possible outcomes correspond to classes of a population. Although mixture models are conceptually appealing many obstacles arise during their application. Areas of difficulty include complicated likelihoods, lack of clearly defined hypotheses, cumbersome estimating equations and elusive asymptotic properties. Progress in the study of mixture models was hindered by these difficulties until the advent of adequate computational power and numerical methods. The topic of this thesis is motivated by a longitudinal study conducted at The Ohio State University that focused on the course of grief in children who experienced the loss of a parent. Researchers hypothesize parental loss will have a greater psychological impact on some of the children which will manifest itself over an extended period of time as an increase in the number of symptoms associated with behaviorial, anxiety, mood and other psychological disorders. A mixture model approach is used to determine whether or not such a latent group of grieving children exists. Under the null hypothesis, the bereaved children are a homogenous group and the data is assumed to have a multivariate normal distribution. The alternative hypothesis states the data follow a mixture of two multivariate normal distributions. Data patterns are exploited to develop simple models for the variance and correlation structures. Mean models are formulated to test the statistical hypotheses of interest. This approach has the benefit of reducing the number of model parameters resulting in a simplified fitting process. A consequence of the nonexclusive relationship between the mixing distribution and the model parameters is that both play a fundamental role in the development and outcome of the statistical inference procedure. Results of model fitting are reported and conclusions based on the likelihood ratio test are discussed.
Joseph Verducci (Advisor)
122 p.
Statistics
Mixture Models; Longitudinal Data; Moment Estimation

Recommended Citations

Citations

  • Kelbick, N. D. (2003). Detecting underlying emotional sensitivity in bereaved children via a multivariate normal mixture distribution [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1064331329

    APA Style (7th edition)

  • Kelbick, Nicole. Detecting underlying emotional sensitivity in bereaved children via a multivariate normal mixture distribution. 2003. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1064331329.

    MLA Style (8th edition)

  • Kelbick, Nicole. "Detecting underlying emotional sensitivity in bereaved children via a multivariate normal mixture distribution." Doctoral dissertation, Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1064331329

    Chicago Manual of Style (17th edition)

osu1064331329
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© 2003, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.