Performance of AIC-Selected Spatial Covariance Structures for fMRI Data

81 Pages·2016·0.46 MB·English

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Theses and Dissertations
2005-07-28
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David A. Stromberg
Brigham Young University - Provo
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Stromberg, David A., "Performance of AIC-Selected Spatial Covariance Structures for fMRI Data" (2005).
Theses and Dissertations. 634.
https://scholarsarchive.byu.edu/etd/634
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PERFORMANCE OF AIC-SELECTED SPATIAL COVARIANCE
STRUCTURES FOR FMRI DATA
by
David A. Stromberg
A Project submitted to the faculty of
Brigham Young University
in partial fulfillment of the requirements for the degree of
Master of Science
Department of Statistics
Brigham Young University
July 2005

BRIGHAM YOUNG UNIVERSITY
GRADUATE COMMITTEE APPROVAL
of a Project submitted by
David A. Stromberg
This Project has been read by each member of the following graduate committee
and by majority vote has been found to be satisfactory.
Date William F. Christensen, Chair
Date Gilbert W. Fellingham
Date G. Bruce Schaalje

BRIGHAM YOUNG UNIVERSITY
As chair of the candidate’s graduate committee, I have read the Project of David
A. Stromberg in its final form and have found that (1) its format, citations, and
bibliographical style are consistent and acceptable and fulfill university and de-
partment style requirements; (2) its illustrative materials including figures, tables,
and charts are in place; and (3) the final manuscript is satisfactory to the graduate
committee and is ready for submission to the university library.
Date William F. Christensen
Chair, Graduate Committee
Accepted for the Department
G. Bruce Schaalje
Graduate Coordinator
Accepted for the College
G. Rex Bryce
Associate Dean, College of Physical and
Mathematical Sciences

ABSTRACT
PERFORMANCE OF AIC-SELECTED SPATIAL COVARIANCE
STRUCTURES FOR FMRI DATA
David A. Stromberg
Department of Statistics
Master of Science
FMRI datasets allow scientists to assess functionality of the brain by mea-
suring the response of blood flow to a stimulus. Since the responses from neigh-
boring locations within the brain are correlated, simple linear models that assume
independence of measurements across locations are inadequate. Mixed models can
be used to model the spatial correlation between observations, however selecting
the correct covariance structure is difficult. Information criteria, such as AIC are
often used to choose among covariance structures. Once the covariance structure
is selected, significance tests can be used to determine if a region of interest within
the brain is significantly active.
Through the use of simulations, this project explores the performance of
AIC in selecting the covariance structure. Type I error rates are presented for the
fixed effects using the the AIC chosen covariance structure. Power of the fixed
effects are also discussed.

Acknowledgements
IwanttoexpressmythankstoDr. WilliamChristensenforthemanyhours
ofworkandconsultationhe investedwithme onthisprojectwhichultimatelylead
to the attainment of my Master’s degree. I would also like to thank all those who
contributed to the progression of the project.
I want to thank my family for their constant support and reassurance. I
would have never made it thus far without the care and guidance of a loving
mother, and never succeeded in my Master’s program without a loving, and sup-
portive wife. Most of all I want to express my gratitude to my Heavenly Father
for His abundant goodness in allowing me so many wonderful opportunities such
as the privilege of studying and this university.