Spatial Cumulative Probit Model: An Application to Poverty Classification and Mapping
International Journal of Statistical Distributions and Applications
Volume 5, Issue 1, March 2019, Pages: 15-21
Received: Oct. 12, 2018; Accepted: Nov. 7, 2018; Published: Jun. 11, 2019
Views 655      Downloads 91
Richard Puurbalanta, University for Development Studies, Faculty of Mathematical Sciences, Department of Statistics, Navrongo Campus, Ghana
Article Tools
Follow on us
Previous studies on household poverty classification have commonly dichotomized the dependent variable into non-poor or poor, and used binary models. This way, the most extreme categories of poverty, which are usually the main targets of interventions, are not identified. Moreover, expenditure data used to describe poverty is typically collected at several locations over large geographical domains. Local disturbances introduce spatial correlation, implying that global parameters (obtained via independence assumptions of standard statistical methods) cannot adequately describe site-specific conditions of the data. The objective, therefore, is to describe an appropriate method for ordered categorical data collected at geo-referenced locations over large geographical space. To achieve this, a model named Spatial Cumulative Probit Model (SCPM) was proposed. This model classified household poverty in an ordinal spatial framework. Bayesian inference was performed on data sampled by Markov Chain Monte Carlo (MCMC) algorithms. A test of model adequacy show that the SCPM is unbiased and attains a lower misclassification rate of 14.43% than the simple Cumulative Probit (CP) model with misclassification rate of 16.5% that ignores spatial dependence in the data. Overall, ‘savannah ecological zone’, ‘polygamous marriage’ and ‘rural location’ were the most powerful predictors of extreme poverty in Ghana. The prediction map, created by this study, identified positive correlation with respect to ‘poor’ and ‘extremely poor’ categories. Results of the model in this study can be considered a category and site-specific report that identifies all levels and sites of poverty for easy targeting, thus, avoiding the blanket approach that prefers the one-fits-it-all solution to the problem of poverty. Analysis was based on the Ghana Living Standards Survey (GLSS 6) dataset.
Ordered Responses, Spatial Correlation, MCMC, Cumulative Probit, Poverty Classification
To cite this article
Richard Puurbalanta, Spatial Cumulative Probit Model: An Application to Poverty Classification and Mapping, International Journal of Statistical Distributions and Applications. Vol. 5, No. 1, 2019, pp. 15-21. doi: 10.11648/j.ijsd.20190501.14
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Nelder, J., Wedderburn R. W. M. (1972). Generalized linear models. J. Roy. Statist. Soc. Ser. A135: 370-384.
Greene W. H., Hensher D. A., (2009). Modelling Ordered Choices. Cambridge: Cambridge University Press, 2010 xv, 365 p.: ill.; 25 cm. ISBN: 9780521194204.
Agresti, A. (2007). An Introduction to Categorical Data Analysis. 2nd Ed., New York, John Wiley and Sons.
Terza, J. (1985). Ordered Probit: A Generalization, Communications in Statistics -A. Theory and Methods, 14, pp. 1-11.
Elena (Tomori), M., Zyka, E., Bici, R. (2014). Identifying Household Level Determinants of Poverty in Albania Using Logistic Regression Model (SSRN Scholarly Paper No. ID 2457441).
Dudek, H., Lisicka, I. (2013). Determinants of poverty–binary logit model with interaction terms approach. Ekonometria, (3 (41), 65–77.
Ennin C. C., Nyarko P. K., Agyeman A., Mettle F. O., Nortey E. N. N., (2011). Trend Analysis of Determinants of Poverty in Ghana: Logit Approach. Research Journal of Mathematics and Statistics 3 (1): 20-27, 2011, ISSN: 2040-7505.
BARTOŠOVÁ, Jitka a Marie FORBELSKÁ (2013). Poverty Rate in Czech Households Depending on the Age, Sex and Educational Level. In LÖSTER, T. -- PAVELKA, T. International Days of Statistics and Economics. 7th ed. Slaný: Melandrium, 2013. s. 70-78, 9 s. ISBN 978-80-86175-87-4.
Saidatulakmal and Madiha Riaz (2012). Demographic Analysis of Poverty, Rural-Urban Nexus. Research on Humanities and Social Sciences. Vol. 2, No. 6, 2012.
Adebanji, A., Achia, T., Ngetich, R., Owino, J., Wangombe A. (2008). Spatial Durbin Model for Poverty Mapping and Analysis, European Journal of Social Sciences – Volume 5, Number 4.
Thomas N. O., Achia, A. W., Nancy K. (2010). A Logistic Regression Model to Identify Key Determinants of Poverty Using Demographic and Health Survey Data. European Journal of Social Sciences – Volume 13, Number 1 (2010).
Rusnak Z. (2012). Logistic regression model in poverty analyses. ekonometria econometrics 1 (35)• 2012; issn 1507-3866.
Williams, D. A. (1982). Extra-binomial variation in logistic linear models. Appl. Statist. 31: 144-148.
Gelman A., Carlin J. B., Stern H. S., Dunson D. B., Vehtari A., Rubin D. B. (2014). Bayesian Data Analysis. Third Edition. CRC Press, Taylor and Francis Group, 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742.
Neal, P. and Kypraios, T. (2015). Exact Bayesian inference via data augmentation. 25: 333., Springer US.
Bayes (1763). An Essay towards solving a Problem in the Doctrine of Chances. By the late Rev. Mr. Bayes, communicated by Mr. Price, in a letter to John Canton, M. A. and F. R. S.
De Oliveira, V. (2000). Bayesian prediction of clipped Gaussian random fields. Computational Statistics and Data Analysis, 34, 299–314.
R Development Core Team, (2015). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0.
Diggle PJ, Ribeiro PJ, Christensen OF (2003). An introduction to model-based geostatistics. In: Moller J, editor. Spatial statistics and computational methods Lecture notes in statistics. New York: Springer. 43–86.
Ghana Statistical Service (GSS) (2014). Ghana Living Standards Survey Round 6 (GLSS6): Poverty Profile in Ghana (2005-2013), Main Report, Accra, Ghana.
Cook E., Hague S., Mckay A. (2016). The Ghana Poverty and Inequality Report: Using the 6th Ghana Living Standards Survey. Accra, Ghana.
The International Fund for Agricultural Development (2015). IFAD Annual Report 2014. International Fund for Agricultural Development Via Paolo di Dono, 44 - 00142 Rome, Italy.
Jalan, J., Ravallion M. (1997). Spatial poverty traps? World Bank Policy Research Working Paper 1862.
Bigman, D., Fofack, H. (2000). Geographical Targeting for Poverty Alleviation: An Introduction to the Special Issue. The World Bank Economic Review, VOL. 14, NO. li 129-45.
The World Bank (2015). Global Monitoring Report 2015/2016: Development Goals in an Era of Demographic Change. The World Bank.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186