American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2018, 6(3), 80-95
DOI: 10.12691/ajams-6-3-1
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Improving the Statistical Capacity Index: A Statistical Approach

Dharmaratne MA1, and Attygalle MDT1

1Department of Statistics, University of Colombo, Sri Lanka

Pub. Date: May 22, 2018

Cite this paper:
Dharmaratne MA and Attygalle MDT. Improving the Statistical Capacity Index: A Statistical Approach. American Journal of Applied Mathematics and Statistics. 2018; 6(3):80-95. doi: 10.12691/ajams-6-3-1


Good quality, timely and accurate statistics lie at the heart of a country's effort to improve development effectiveness. As a response to the challenge of measuring the institutional capacity of a country in producing timely and accurate statistics, the World Bank developed its framework for the Statistical Capacity Index (SCI). Although the World Bank's framework is acknowledged for its simplistic approach, it has received extensive critique for the ad-hoc allocation of weights. This research attempts to find a solution to this criticism using a statistical methodology. Country information used by the World Bank to create the SCI for the year 2014 was considered. The data consisted information on 25 categorical variables out of which 16 were binary variables and 9 were ordinal variables. Nonlinear Principal Component Analysis (NLPCA) was conducted on the categorical data to reduce the observed variables to uncorrelated principal components. Consequently, the optimally scaled variables were used as input for factor analysis with principal component extraction. The results of the factor analysis were used to weight the new SCI. The dimension, availability and periodicity of economic and financial indicators explained most of the variance in the data set. The research proposes a simpler version of the new SCI with only 23 variables. In the proposed new index, the variables enrolment reporting to UNESCO, gender equality in education and primary completion indicators were the three variables receiving the largest weight. These three indicators measure the periodicity of reporting data on educational statistics to UNESCO; periodicity of observing the gross enrolment rate of girls to boys in primary and secondary education; and periodicity of observing the PCR indicator which is the number of children reaching the last year of primary school net of repeaters respectively. This research represents the first attempt to create a SCI using multivariate statistical techniques and especially index construction with NLPCA. The research concluded with a comparison of the proposed new index and the index created by the World Bank, which justified that the proposed index be used as a solution for the arbitrary allocation of weights in creating the SCI.

nonlinear principal component analysis optimal scaling statistical capacity index

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[1]  Abeyasekera, S. (2006). Chapter 18: Multivariate methods for index construction. Household Surveys in Developing and Transition Countries: Design, Implementation and Analysis. Retrieved June 26, 2015, from ch18fin3.pdf.
[2]  Asselin, L. M. (2009). Analysis of Multidimensional Poverty: Theory and Case Studies. (Vol. 7). New York: Springer Science+Business Media.
[3]  Biswas, B., & Caliendo, F. (2002). A Multivariate Analysis of the Human Development Index. Economic Research Institute: Study Paper No. 244. Retrieved September 20, 2015, from
[4]  de Leeuw, J. (2013). History of nonlinear principal component analysis. Retrieved November 2, 2015 from /.../History%20of%20Nonlinear%20Principal%20Comp.
[5]  Fantom, N., & Watanabe, N. (2008). Improving the World Bank’s Database of Statistical Capacity. African Statistical Newsletter, 2(3), 21-22. Retrieved September 2015, from
[6]  Johnson, R. A., & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis. (6th ed.). New Jersey: Pearson, Prentice Hall.
[7]  Krishnan, V. (2010). Constructing an Area-based Socioeconomic Index: A Principal Components Analysis Approach. Early Child Development Mapping Project Alberta: Canada. Retrieved September 18, 2015 from
[8]  Ledesma, R. D., & Valero-Mora, P. (2007). Determining the Number of Factors to Retain in EFA: an easy-to use computer program for carrying out Parallel Analysis. Practical Assessment, Research & Evaluation, 12(2). Retrieved October 30, 2015 form
[9]  Linting, M., & van der Kooij, A. (2012). Nonlinear Principal Component Analysis With CATPCA: A Tutorial. Journal of Personality Assessment, 94(1), 12-25.
[10]  Mair, P., & de Leeuw, J. (2010). A General Framework for Multivariate Analysis with Optimal Scaling: The R Package aspect. Journal of Statistical Software, 32(9). Retrieved October 18, 2015 from
[11]  Manisera, M., van der Kooij, A. J., & Dusseldorp, E. (2010). Identifying the Component Structure of Satisfaction Scales by Nonlinear Principal Component Analysis. Quality Technology & Quantitative Management, 7(2), 97-115. Retrieved October, 2015.
[12]  Merola, G., & Baulch, B. (2014). Using Sparse Categorical Principal Components to Estimate Asset Indices New Methods with an Application to Rural South East Asia. Paper presented at conference ABSRC Conference, September 24-26, 2014. Rome. Retrieved October 30, 2015 from CATEGORICAL%20PRINCIPAL.pdf.
[13]  Ngaruko, F. (2008). The World Bank’s Framework for Statistical Capacity Measurement: Strengths, Weaknesses, and Options for Improvement. The African Statistical Journal, 7, 149-169. Retrieved June 12, 2015.
[14]  Organization for Economic Co-operation and Development (OECD). (2008). Handbook on Constructing Composite Indicators: Methodology And User Guide [online book]. Retrieved August 8, 2015, from
[15]  The African Capacity Building Foundation. (2007). Towards Reforming National Statistical Agencies and Systems: A Survey of Best-Practice Countries with Effective National Statistical Systems in Africa. Zimbabwe. Retrieved October, 2015 from,%20Sept%2020071.pdf.
[16]  World Bank. (2009). Note on the Statistical Capacity Indicator. Retrieved September 12, 2015 from
[17]  World Bank. (2015). Data on Statistical Capacity. Retrieved September 27, 2015 from The World Bank Web site: