Examination of Covariance Structures for Experimental Design with Repeated Measure

Abraham Okolo; Saidu Sauta Abdulkadir; Ikeme John Dike; Abubakar Adamu

doi:doi:10.11648/j.ajtas.20200903.16

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Examination of Covariance Structures for Experimental Design with Repeated Measure

Abraham Okolo, Saidu Sauta Abdulkadir, Ikeme John Dike, Abubakar Adamu

Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 3)

Received: 3 April 2020 Accepted: 3 May 2020 Published: 27 May 2020

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Abstract

This research examine different covariance structures for experimental design with repeated measure data. Multiple responses taken sequentially from same experimental unit at different periods of time for quantitative data are referred as Repeated Measurement. Weight of 105 broilers in grams for six group obtained from jewel farm Gombe were used as research materials/data. Eleven different covariance structures including the modified one (UN, UNC, TOEP, TOEPH, ANTE(1), AR(1), ARH(1), CS, CSH, HF and ARFA(1)) were examined. AIC, AICC, BIC, HQIC, CAIC and the modified criteria ASIC were used to examine covariance structures and bring the best among them using the named information criteria. The result shows that sphericity assumptions was violated a such the best covariance structure was ARH(1) while the least structure was CSH. Also on the basis of goodness of fit criteria HQIC was found to be the best information criteria. When examined the best information criteria and covariance structure with the modified ones, the modified ASIC and ARFA(1) found to be the best. In conclusion examine different covariance structures with repeated measure data give a very good result defending on the kind of data.

Published in	American Journal of Theoretical and Applied Statistics (Volume 9, Issue 3)
DOI	10.11648/j.ajtas.20200903.16
Page(s)	63-73
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Covariance Structures. Experimental Design, Repeated Measures, Information Criteria, Sphericity Test

References

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[2]	N. K. Rauf, "Classification of Multivariate Repeated Measures data with Temporal Autocorrelation," Advances in Data Analysis and Classifiation, pp. 175-199, 2008.
[3]	L. A. Guttman, New Approach to Factor Analysis: The Radex in P. F. Lazarsfeld (Ed.), Mathematical thinking in the Social sciences, New York: Columbia University Press, 1954.
[4]	L. Brandon, Misspecification of the Covariance Matrix in the Linear Mixed Model: A Monte Carlo Simulation, MN, USA: University of Minnesota, 2013.
[5]	D. J. Yanosky II, Comparability of Covariance Structures and Accuracy of Information Criteria in Mixed Model Methods for Longitudinal Data Analysis., Athens, Georgia: University of Georgia Press, 2007.
[6]	J. Ferron, R. Dailey and Q. Yi, "Effect of Misspecifying the First Level error Structure in Two Level Models of Change," Multivariate Behav. Res., pp. 379-403, 2002.
[7]	S. D. Maxwell and H. D. Delaney, Designing Experiments and Analyzing Data: A Model Comparison Perspective, 2nd ed., Mahwah, NJ: Laurence Erlbaum Associated Publishers, 2004.
[8]	E. R. Girden, ANOVA: Repeated Measures, Sage: Newbury Park CA, 1992.
[9]	S. W. Greenhouse and S. Geisser, "On Methods in the Analysis of Profile Data," Psychometrika, pp. 95-112, 1959.
[10]	H. Huynh and L. S. Feldt, "Estimation of the Box Correction for Degrees of Freedom from Sample Data in the Randomized Block and Split Plot Design," Journal of Educational Statistics, pp. 15-51, 1976.
[11]	R. P. McDonald, Factor Analysis and Related Methods, Lawrence Erlbaum Associates, 1985.
[12]	S. A. Mulaik, The Foundation of Factor Analysis, New York: McGray Hill, 1972.
[13]	R. I. Jennrich and M. D. Schluchter, "Unbalanced Repeated Measures Models with Structured Covariance Matrix," Biometrics, pp. 805-820, 1986.
[14]	R. C. Littell, G. A. Milleken, W. W. Stroup and R. D. Wolfinger, SAS System for Mixed Models, Cary: NC; SAS Institute, 1996.

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APA Style

Abraham Okolo, Saidu Sauta Abdulkadir, Ikeme John Dike, Abubakar Adamu. (2020). Examination of Covariance Structures for Experimental Design with Repeated Measure. American Journal of Theoretical and Applied Statistics, 9(3), 63-73. https://doi.org/10.11648/j.ajtas.20200903.16

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ACS Style

Abraham Okolo; Saidu Sauta Abdulkadir; Ikeme John Dike; Abubakar Adamu. Examination of Covariance Structures for Experimental Design with Repeated Measure. Am. J. Theor. Appl. Stat. 2020, 9(3), 63-73. doi: 10.11648/j.ajtas.20200903.16

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AMA Style

Abraham Okolo, Saidu Sauta Abdulkadir, Ikeme John Dike, Abubakar Adamu. Examination of Covariance Structures for Experimental Design with Repeated Measure. Am J Theor Appl Stat. 2020;9(3):63-73. doi: 10.11648/j.ajtas.20200903.16

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@article{10.11648/j.ajtas.20200903.16,
  author = {Abraham Okolo and Saidu Sauta Abdulkadir and Ikeme John Dike and Abubakar Adamu},
  title = {Examination of Covariance Structures for Experimental Design with Repeated Measure},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {3},
  pages = {63-73},
  doi = {10.11648/j.ajtas.20200903.16},
  url = {https://doi.org/10.11648/j.ajtas.20200903.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200903.16},
  abstract = {This research examine different covariance structures for experimental design with repeated measure data. Multiple responses taken sequentially from same experimental unit at different periods of time for quantitative data are referred as Repeated Measurement. Weight of 105 broilers in grams for six group obtained from jewel farm Gombe were used as research materials/data. Eleven different covariance structures including the modified one (UN, UNC, TOEP, TOEPH, ANTE(1), AR(1), ARH(1), CS, CSH, HF and ARFA(1)) were examined. AIC, AICC, BIC, HQIC, CAIC and the modified criteria ASIC were used to examine covariance structures and bring the best among them using the named information criteria. The result shows that sphericity assumptions was violated a such the best covariance structure was ARH(1) while the least structure was CSH. Also on the basis of goodness of fit criteria HQIC was found to be the best information criteria. When examined the best information criteria and covariance structure with the modified ones, the modified ASIC and ARFA(1) found to be the best. In conclusion examine different covariance structures with repeated measure data give a very good result defending on the kind of data.},
 year = {2020}
}

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TY  - JOUR
T1  - Examination of Covariance Structures for Experimental Design with Repeated Measure
AU  - Abraham Okolo
AU  - Saidu Sauta Abdulkadir
AU  - Ikeme John Dike
AU  - Abubakar Adamu
Y1  - 2020/05/27
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200903.16
DO  - 10.11648/j.ajtas.20200903.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 63
EP  - 73
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200903.16
AB  - This research examine different covariance structures for experimental design with repeated measure data. Multiple responses taken sequentially from same experimental unit at different periods of time for quantitative data are referred as Repeated Measurement. Weight of 105 broilers in grams for six group obtained from jewel farm Gombe were used as research materials/data. Eleven different covariance structures including the modified one (UN, UNC, TOEP, TOEPH, ANTE(1), AR(1), ARH(1), CS, CSH, HF and ARFA(1)) were examined. AIC, AICC, BIC, HQIC, CAIC and the modified criteria ASIC were used to examine covariance structures and bring the best among them using the named information criteria. The result shows that sphericity assumptions was violated a such the best covariance structure was ARH(1) while the least structure was CSH. Also on the basis of goodness of fit criteria HQIC was found to be the best information criteria. When examined the best information criteria and covariance structure with the modified ones, the modified ASIC and ARFA(1) found to be the best. In conclusion examine different covariance structures with repeated measure data give a very good result defending on the kind of data.
VL  - 9
IS  - 3
ER  -

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Author Information

Abraham Okolo

Department of Statistics and Operations Research, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria
Saidu Sauta Abdulkadir

Department of Statistics and Operations Research, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria
Ikeme John Dike

Department of Statistics and Operations Research, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria
Abubakar Adamu

Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria

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APA Style

Abraham Okolo, Saidu Sauta Abdulkadir, Ikeme John Dike, Abubakar Adamu. (2020). Examination of Covariance Structures for Experimental Design with Repeated Measure. American Journal of Theoretical and Applied Statistics, 9(3), 63-73. https://doi.org/10.11648/j.ajtas.20200903.16

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ACS Style

Abraham Okolo; Saidu Sauta Abdulkadir; Ikeme John Dike; Abubakar Adamu. Examination of Covariance Structures for Experimental Design with Repeated Measure. Am. J. Theor. Appl. Stat. 2020, 9(3), 63-73. doi: 10.11648/j.ajtas.20200903.16

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AMA Style

Abraham Okolo, Saidu Sauta Abdulkadir, Ikeme John Dike, Abubakar Adamu. Examination of Covariance Structures for Experimental Design with Repeated Measure. Am J Theor Appl Stat. 2020;9(3):63-73. doi: 10.11648/j.ajtas.20200903.16

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@article{10.11648/j.ajtas.20200903.16,
  author = {Abraham Okolo and Saidu Sauta Abdulkadir and Ikeme John Dike and Abubakar Adamu},
  title = {Examination of Covariance Structures for Experimental Design with Repeated Measure},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {3},
  pages = {63-73},
  doi = {10.11648/j.ajtas.20200903.16},
  url = {https://doi.org/10.11648/j.ajtas.20200903.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200903.16},
  abstract = {This research examine different covariance structures for experimental design with repeated measure data. Multiple responses taken sequentially from same experimental unit at different periods of time for quantitative data are referred as Repeated Measurement. Weight of 105 broilers in grams for six group obtained from jewel farm Gombe were used as research materials/data. Eleven different covariance structures including the modified one (UN, UNC, TOEP, TOEPH, ANTE(1), AR(1), ARH(1), CS, CSH, HF and ARFA(1)) were examined. AIC, AICC, BIC, HQIC, CAIC and the modified criteria ASIC were used to examine covariance structures and bring the best among them using the named information criteria. The result shows that sphericity assumptions was violated a such the best covariance structure was ARH(1) while the least structure was CSH. Also on the basis of goodness of fit criteria HQIC was found to be the best information criteria. When examined the best information criteria and covariance structure with the modified ones, the modified ASIC and ARFA(1) found to be the best. In conclusion examine different covariance structures with repeated measure data give a very good result defending on the kind of data.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Examination of Covariance Structures for Experimental Design with Repeated Measure
AU  - Abraham Okolo
AU  - Saidu Sauta Abdulkadir
AU  - Ikeme John Dike
AU  - Abubakar Adamu
Y1  - 2020/05/27
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200903.16
DO  - 10.11648/j.ajtas.20200903.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 63
EP  - 73
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200903.16
AB  - This research examine different covariance structures for experimental design with repeated measure data. Multiple responses taken sequentially from same experimental unit at different periods of time for quantitative data are referred as Repeated Measurement. Weight of 105 broilers in grams for six group obtained from jewel farm Gombe were used as research materials/data. Eleven different covariance structures including the modified one (UN, UNC, TOEP, TOEPH, ANTE(1), AR(1), ARH(1), CS, CSH, HF and ARFA(1)) were examined. AIC, AICC, BIC, HQIC, CAIC and the modified criteria ASIC were used to examine covariance structures and bring the best among them using the named information criteria. The result shows that sphericity assumptions was violated a such the best covariance structure was ARH(1) while the least structure was CSH. Also on the basis of goodness of fit criteria HQIC was found to be the best information criteria. When examined the best information criteria and covariance structure with the modified ones, the modified ASIC and ARFA(1) found to be the best. In conclusion examine different covariance structures with repeated measure data give a very good result defending on the kind of data.
VL  - 9
IS  - 3
ER  -

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