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Unconventional Approach with the Likelihood of Correlation Matrices

Song, Myung Soon (2011) Unconventional Approach with the Likelihood of Correlation Matrices. Doctoral Dissertation, University of Pittsburgh.

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    Abstract

    Numerical approximations are important research areas for dealing with complicated functional forms. Techniques for developing accurate and efficient calculation of combined likelihood functions in meta-analysis are studied. The first part of the thesis introduces a B-spline approximation for making a parsimonious model in the simplest case(2-dimensional case) of correlation structure. Inference about the correlation between vitamin C intake & vitamin C serum level is developed by using likelihood intervals and the MLE, along with comparison with conventional methods. The second part studies a multivariate numerical integration method for developing a better approximation of the likelihood for correlation matrices. Analyses for (1) intercorrelations among Math, Spatial and Verbal scores in an SAT exam and (2) intercorrelations among Cognitive Anxiety, Somatic Anxiety and Self Confidence from Competitive State Anxiety Inventory (CSAI-2) are explored. Algorithms to evaluate likelihood and to find the MLE is developed. Comparison with two conventional methods (joint asymptotic weighted average method & marginal asymptotic weighted average method) is shown.

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    Details

    Item Type: University of Pittsburgh ETD
    ETD Committee:
    ETD Committee TypeCommittee MemberEmail
    Committee ChairGleser, Leon J.gleser@pitt.edu
    Committee MemberGreenhouse, Joeljoel@stat.cmu.edu
    Committee MemberIyengar, Satishssi@pitt.edu
    Committee MemberCheng, Yuyucheng@pitt.edu
    Title: Unconventional Approach with the Likelihood of Correlation Matrices
    Status: Unpublished
    Abstract: Numerical approximations are important research areas for dealing with complicated functional forms. Techniques for developing accurate and efficient calculation of combined likelihood functions in meta-analysis are studied. The first part of the thesis introduces a B-spline approximation for making a parsimonious model in the simplest case(2-dimensional case) of correlation structure. Inference about the correlation between vitamin C intake & vitamin C serum level is developed by using likelihood intervals and the MLE, along with comparison with conventional methods. The second part studies a multivariate numerical integration method for developing a better approximation of the likelihood for correlation matrices. Analyses for (1) intercorrelations among Math, Spatial and Verbal scores in an SAT exam and (2) intercorrelations among Cognitive Anxiety, Somatic Anxiety and Self Confidence from Competitive State Anxiety Inventory (CSAI-2) are explored. Algorithms to evaluate likelihood and to find the MLE is developed. Comparison with two conventional methods (joint asymptotic weighted average method & marginal asymptotic weighted average method) is shown.
    Date: 30 September 2011
    Date Type: Completion
    Defense Date: 19 May 2011
    Approval Date: 30 September 2011
    Submission Date: 31 May 2011
    Access Restriction: No restriction; Release the ETD for access worldwide immediately.
    Patent pending: No
    Institution: University of Pittsburgh
    Thesis Type: Doctoral Dissertation
    Refereed: Yes
    Degree: PhD - Doctor of Philosophy
    URN: etd-05312011-162131
    Uncontrolled Keywords: correlation matrix; likelihood; meta-analysis; numerical integration
    Schools and Programs: Dietrich School of Arts and Sciences > Statistics
    Date Deposited: 10 Nov 2011 14:46
    Last Modified: 06 Jan 2012 13:17
    Other ID: http://etd.library.pitt.edu/ETD/available/etd-05312011-162131/, etd-05312011-162131

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