Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis

Apantaku Fadeke Sola.; Olayiwola Olaniyi Mathew; Adewara Amos Adedayo

doi:doi:10.11648/j.ajtas.20130205.14

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Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis

Apantaku Fadeke Sola., Olayiwola Olaniyi Mathew, Adewara Amos Adedayo

Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 5)

Received: 6 August 2013 Published: 10 September 2013

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Abstract

The problem of allocation with more than one characteristic in stratified sampling is conflicting in nature, as the best allocation for one characteristic will not in general be best for others. Some compromise must be reached to obtain an allocation that is efficient for all characteristics. In this study, the allocation of a sample to strata which minimizes cost of investigation, subject to a given condition about the sampling error was considered. The data on four socioeconomic characteristics of 400 heads of households in Abeokuta South and Ijebu North Local Government Areas (LGAs) of Ogun State, Nigeria were investigated. These comprised of 200 households from each LGA. The characteristics were occupation, income, household size and educational level. Optimal allocation in multi-item was developed as a multivariate optimization problem by finding the principal components. This was done by determining the overall linear combinations that concentrates the variability into few variables. From the principal component analysis, it was seen that for both Abeokuta and Ijebu data sets, the variance based on the four characteristics as multivariate is less than that of the variables when considered as a univariate. From the results, it was seen that there was no difference in the percentage of the total variance accounted for by the different components from the merged sample when compared with the individual sample. Optimum allocation was achieved when there was stratification

Published in	American Journal of Theoretical and Applied Statistics (Volume 2, Issue 5)
DOI	10.11648/j.ajtas.20130205.14
Page(s)	142-148
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), 2013. Published by Science Publishing Group

Keywords

Stratified Sampling, Optimum Allocation, Stratification, Optimization

References

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[2]	Cheang, C. 2011. Sampling strategies and their advantages and disadvantages. http://www.2.hawaii.edu/~cheang/Sampling%20Strategies%20Advantages%20and%20Disadvantages.htm (Accessed March 5, 2011).
[3]	Cochran, W. G. 1977. Sampling Techniques (3rd Edition), New York, Wiley.
[4]	Diaz-Garcia, J.A and Ramos-Quiroga, R. 2011. Multivariate Stratified Sampling by Stochastic Multi Objective Optimization. Xiv: 1106.0773VI. Statistical Methodology. XIV, 1116-1123.
[5]	Diaz-Garcia, J. A. and Cortez, L. U. 2006. Optimum allocation in multivariate stratified sampling: multi-objective programming. Communicacion Technica: Communicaciones Del CIMAT. 6(7), 28-33.
[6]	Hartley, H. O. 1962. Multiple frame surveys: Proceeding of the social statistics section of American Statistical Association, 205 – 215.
[7]	Hartley, H. O. 1964. A new estimation theory for sampling surveys. Biometrics, 55, 545 – 557.
[8]	Khan, M.G.M and Ahsan, M.J. 2003. A note on Optimum Allocation in Multivariate Stratified Sampling. South Pacific Journal Natural Science, 21, 91-95.
[9]	Kokan, A.R and Khan, S.U., 1967. Optimum allocation in mutivariate surveys. An analytical solution. Journal of Royal Statistical Society. Series B, 29, 115-125.
[10]	Lumley, T. 2004. Analysis of complex survey samples. Department of Biostatistics. University of Washington Press.
[11]	Miettinen, K. M. 1999. Non linear multi-objective optimization. Kluwer Academic Publishers, Boston.
[12]	Pirzada, S. and Maqbool, S. 2003. Optimal Allocation in Multivariate sampling Through Chebyshev’s Approximation. Bulletin of the Malaysian Mathematical Science Society, 2, (26), 221 – 230.
[13]	Saxens, J., Narain, M. U. and Srivastava, S. 1986. The maximum likelihood method for non-response in Surveys. Survey Methodology. 12, 50 – 62.
[14]	Sethna, B. N. and Groeneveld, L. 1984. Research Methods in Marketing and Management. Tata, Mcgraw-Hill, publishing, New-Delhi.
[15]	Steuer, R.E. 1986. Multiple criteria optimization: Theory, Computation and applications. John Wiley, New York.
[16]	Winship, C. and Radbill, L. 1994. Sampling weights and regression analysis. Sociological Methods and Research, 23, (2), 230 – 257.

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Apantaku Fadeke Sola., Olayiwola Olaniyi Mathew, Adewara Amos Adedayo. (2013). Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis. American Journal of Theoretical and Applied Statistics, 2(5), 142-148. https://doi.org/10.11648/j.ajtas.20130205.14

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ACS Style

Apantaku Fadeke Sola.; Olayiwola Olaniyi Mathew; Adewara Amos Adedayo. Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis. Am. J. Theor. Appl. Stat. 2013, 2(5), 142-148. doi: 10.11648/j.ajtas.20130205.14

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AMA Style

Apantaku Fadeke Sola., Olayiwola Olaniyi Mathew, Adewara Amos Adedayo. Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis. Am J Theor Appl Stat. 2013;2(5):142-148. doi: 10.11648/j.ajtas.20130205.14

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@article{10.11648/j.ajtas.20130205.14,
  author = {Apantaku Fadeke Sola. and Olayiwola Olaniyi Mathew and Adewara Amos Adedayo},
  title = {Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {5},
  pages = {142-148},
  doi = {10.11648/j.ajtas.20130205.14},
  url = {https://doi.org/10.11648/j.ajtas.20130205.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130205.14},
  abstract = {The problem of allocation with more than one characteristic in stratified sampling is conflicting in nature, as the best allocation for one characteristic will not in general be best for others. Some compromise must be reached to obtain an allocation that is efficient for all characteristics. In this study, the allocation of a sample to strata which minimizes cost of investigation, subject to a given condition about the sampling error was considered. The data on four socioeconomic characteristics of 400 heads of households in Abeokuta South and Ijebu North Local Government Areas (LGAs) of Ogun State, Nigeria were investigated. These comprised of 200 households from each LGA. The characteristics were occupation, income, household size and educational level. Optimal allocation in multi-item was developed as a multivariate optimization problem by finding the principal components. This was done by determining the overall linear combinations that concentrates the variability into few variables. From the principal component analysis, it was seen that for both Abeokuta and Ijebu data sets, the variance based on the four characteristics as multivariate is less than that of the variables when considered as a univariate. From the results, it was seen that there was no difference in the percentage of the total variance accounted for by the different components from the merged sample when compared with the individual sample. Optimum allocation was achieved when there was stratification},
 year = {2013}
}

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TY - JOUR
T1 - Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis
AU - Apantaku Fadeke Sola.
AU - Olayiwola Olaniyi Mathew
AU - Adewara Amos Adedayo
Y1 - 2013/09/10
PY - 2013
N1 - https://doi.org/10.11648/j.ajtas.20130205.14
DO - 10.11648/j.ajtas.20130205.14
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 - 142
EP - 148
PB - Science Publishing Group
SN - 2326-9006
UR - https://doi.org/10.11648/j.ajtas.20130205.14
AB - The problem of allocation with more than one characteristic in stratified sampling is conflicting in nature, as the best allocation for one characteristic will not in general be best for others. Some compromise must be reached to obtain an allocation that is efficient for all characteristics. In this study, the allocation of a sample to strata which minimizes cost of investigation, subject to a given condition about the sampling error was considered. The data on four socioeconomic characteristics of 400 heads of households in Abeokuta South and Ijebu North Local Government Areas (LGAs) of Ogun State, Nigeria were investigated. These comprised of 200 households from each LGA. The characteristics were occupation, income, household size and educational level. Optimal allocation in multi-item was developed as a multivariate optimization problem by finding the principal components. This was done by determining the overall linear combinations that concentrates the variability into few variables. From the principal component analysis, it was seen that for both Abeokuta and Ijebu data sets, the variance based on the four characteristics as multivariate is less than that of the variables when considered as a univariate. From the results, it was seen that there was no difference in the percentage of the total variance accounted for by the different components from the merged sample when compared with the individual sample. Optimum allocation was achieved when there was stratification
VL - 2
IS - 5
ER -

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Author Information

Apantaku Fadeke Sola.

Department of Statistics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
Olayiwola Olaniyi Mathew

Department of Statistics, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria
Adewara Amos Adedayo

Department of Statistics, University of Ilorin, Nigeria

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APA Style

Apantaku Fadeke Sola., Olayiwola Olaniyi Mathew, Adewara Amos Adedayo. (2013). Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis. American Journal of Theoretical and Applied Statistics, 2(5), 142-148. https://doi.org/10.11648/j.ajtas.20130205.14

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ACS Style

Apantaku Fadeke Sola.; Olayiwola Olaniyi Mathew; Adewara Amos Adedayo. Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis. Am. J. Theor. Appl. Stat. 2013, 2(5), 142-148. doi: 10.11648/j.ajtas.20130205.14

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AMA Style

Apantaku Fadeke Sola., Olayiwola Olaniyi Mathew, Adewara Amos Adedayo. Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis. Am J Theor Appl Stat. 2013;2(5):142-148. doi: 10.11648/j.ajtas.20130205.14

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@article{10.11648/j.ajtas.20130205.14,
  author = {Apantaku Fadeke Sola. and Olayiwola Olaniyi Mathew and Adewara Amos Adedayo},
  title = {Optimum Allocation of Multi-Items in Stratified Random Sampling Using Principal Component Analysis},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {5},
  pages = {142-148},
  doi = {10.11648/j.ajtas.20130205.14},
  url = {https://doi.org/10.11648/j.ajtas.20130205.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130205.14},
  abstract = {The problem of allocation with more than one characteristic in stratified sampling is conflicting in nature, as the best allocation for one characteristic will not in general be best for others. Some compromise must be reached to obtain an allocation that is efficient for all characteristics. In this study, the allocation of a sample to strata which minimizes cost of investigation, subject to a given condition about the sampling error was considered. The data on four socioeconomic characteristics of 400 heads of households in Abeokuta South and Ijebu North Local Government Areas (LGAs) of Ogun State, Nigeria were investigated. These comprised of 200 households from each LGA. The characteristics were occupation, income, household size and educational level. Optimal allocation in multi-item was developed as a multivariate optimization problem by finding the principal components. This was done by determining the overall linear combinations that concentrates the variability into few variables. From the principal component analysis, it was seen that for both Abeokuta and Ijebu data sets, the variance based on the four characteristics as multivariate is less than that of the variables when considered as a univariate. From the results, it was seen that there was no difference in the percentage of the total variance accounted for by the different components from the merged sample when compared with the individual sample. Optimum allocation was achieved when there was stratification},
 year = {2013}
}

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