Missing data and multidimensional analysis with the Alkire-Foster method: A literature review
DOI:
https://doi.org/10.23881/idupbo.025.2-3eKeywords:
Alkire and Foster, Missing data, Multidimensional poverty, Multiple imputation, Data ethics, Bayesian neuronal networksAbstract
This article addresses the problem of missing data in measuring multidimensional poverty, with particular attention to its impact on the axiomatic validity of the Alkire-Foster method, regularly used to measure this broad concept of poverty. It argues that the absence of data is not purely a technical problem prone to generating bias, but can also compromise the identification of deprivation and violate some of the fundamental axioms of the method: monotonicity, decomposition by subgroups, and dimensional decomposition. Based on a critical review of the literature, four imputation approaches are compared: complete case analysis, multiple imputation by chained equations (MICE), matrix decomposition techniques (such as Soft-Impute), and Bayesian neural networks. Their strengths and limitations in relation to the preservation of the aforementioned axiomatic properties are discussed. In addition, arguments are presented in favor of a hybrid methodology that combines imputation algorithms with normative validation criteria to ensure ethical consistency and inferential robustness. The article concludes that the choice of imputation methods in social contexts should consider not only statistical efficiency but also structural compatibility with the theoretical model underlying the poverty measurement exercise. Future lines of research are proposed for the development of integrative frameworks that articulate imputation methods, respect for axioms, and use in public policy.Downloads
References
S. Alkire y J. Foster, “Counting and multidimensional poverty measurement,” J. Public Econ., vol. 95, no. 7-8, pp. 476–487, 2011, doi: 10.1016/j.jpubeco.2010.11.006.
S. Alkire, J. M. Roche, P. Ballon, J. Foster, M. E. Santos, y S. Seth, Multidimensional Poverty Measurement and Analysis. Oxford, UK: Oxford Univ. Press, 2015. [En línea]. Disponible: https://ophi.org.uk/multidimensional-poverty-measurement- and-analysis/
S. Alkire y M. E. Santos, “Measuring acute poverty in the developing world: Robustness and scope of the multidimensional poverty index,” World Dev., vol. 59, pp. 251–274, 2014, doi: 10.1016/j.worlddev.2014.01.026.
P. D. Allison, Missing Data. Thousand Oaks, CA, USA: Sage Publications, 2001. [En línea]. Disponible: https://us.sagepub. com/en-us/nam/missing-data/book9438
M. J. Azur, E. A. Stuart, C. Frangakis, y P. J. Leaf, “Multiple imputation by chained equations: What is it and how does it work?” Int. J. Methods Psychiatr. Res., vol. 20, no. 1, pp. 40–49, 2011, doi: 10.1002/mpr.329.
J. Bound, C. Brown, y N. Mathiowetz, “Measurement error in survey data,” en Handbook of Econometrics, vol. 5, J. J. Heckman y E. Leamer, Eds. Amsterdam, Netherlands: Elsevier, 2001, pp. 3705–3843, doi: 10.1016/S1573-4412(01)05012-7.
S. van Buuren, Flexible Imputation of Missing Data. Boca Raton, FL, USA: CRC Press, 2018. [En línea]. Disponible: https:// stefvanbuuren.name/fimd/
E. Chen, M. S. Andersen, y R. Chandra, “Deep learning framework with Bayesian data imputation for modelling and forecasting groundwater levels,” Environ. Model. Softw., vol. 178, Art. no. 106072, 2024, doi: 10.1016/j.envsoft.2024.106072.
J.-Y. Duclos, D. E. Sahn, y S. D. Younger, “Robust multidimensional poverty comparisons,” Econ. J., vol. 116, no. 514, pp. 943–968, 2006, doi: 10.1111/j.1468-0297.2006.01118.x.
I. Dutta, R. Nogales, y G. Yalonetzky, “Endogenous weights and multidimensional poverty: A cautionary tale,” J. Dev. Econ., vol. 151, Art. no. 102649, 2021, doi: 10.1016/j.jdeveco. 2021.102649.
F. H. G. Ferreira y M. A. Lugo, “Multidimensional poverty analysis: Looking for a middle ground,” World Bank Res. Obs., vol. 28, no. 2, pp. 220–235, 2013, doi: 10.1093/wbro/lks013.
D. Filmer y L. H. Pritchett, “Estimating wealth effects without expenditure data—or tears: An application to educational enrollments in states of India,” Demography, vol. 38, no. 1, pp. 115–132, 2001, doi: 10.1353/dem.2001.0003.
J. Foster, J. Greer, y E. Thorbecke, “A class of decomposable poverty measures,” Econometrica, vol. 52, no. 3, pp. 761–766, 1984, doi: 10.2307/1913475.
Y. Gal y Z. Ghahramani, “Dropout as a Bayesian approximation: Representing model uncertainty in deep learning,” en Proc. 33rd Int. Conf. Mach. Learn. (ICML), New York, NY, USA, 2016, pp. 1050–1059. [En línea]. Disponible: http://proceedings.mlr.press/v48/gal16.html
L. Gondara y K. Wang, “MIDA: Multiple imputation using denoising autoencoders,” en Advances in Knowledge Discovery and Data Mining (PAKDD), Melbourne, VIC, Australia, 2018, pp. 260–272, doi: 10.1007/978-3-319-93040- 4_21.
T. Hastie, R. Mazumder, J. D. Lee, y R. Zadeh, “Matrix completion and low-rank SVD via fast alternating least squares,” J. Mach. Learn. Res., vol. 16, no. 1, pp. 3367–3402, 2015. [En línea]. Disponible: https://jmlr.org/papers/v16/hastie15a.html
J. M. Hernández-Lobato y R. Adams, “Probabilistic backpropagation for scalable learning of Bayesian neural networks,” en Proc. 32nd Int. Conf. Mach. Learn. (ICML), Lille, France, 2015, pp. 1861–1869. [En línea]. Disponible: http://proceedings.mlr.press/v37/hernandez-lobato15.html
E. R. Hruschka, E. R. Hruschka, y N. F. F. Ebecken, “Bayesian networks for imputation in classification problems,” J. Intell. Inf. Syst., vol. 29, no. 3, pp. 231–252, 2007, doi: 10.1007/s10844-006-0004-5.
J. Krishnakumar y P. Ballon, “Estimating basic capabilities: A structural equation model applied to Bolivia,” World Dev., vol. 36, no. 6, pp. 992–1010, 2008, doi: 10.1016/j.worlddev. 2007.10.008.
R. J. A. Little y D. B. Rubin, Statistical Analysis with Missing Data, 3ra ed. Hoboken, NJ, USA: Wiley, 2019, doi: 10.1002/9781119482260.
E. Maasoumi, “The measurement and decomposition of multi-dimensional inequality,” Econometrica, vol. 54, no. 4, pp. 991–997, 1986, doi: 10.2307/1912845.
R. Mazumder, T. Hastie, y R. Tibshirani, “Spectral regularization algorithms for learning large incomplete matrices,” J. Mach. Learn. Res., vol. 11, pp. 2287–2322, 2010. [En línea]. Disponible: https://www.jmlr.org/papers/v11/mazumder10a.html
R. C. Pereira, P. H. Abreu, P. P. Rodrigues, y M. A. T. Figueiredo, “Imputation of data missing not at random: Artificial generation and benchmark analysis,” Expert Syst. Appl., vol. 249, Art. no. 123654, 2024, doi: 10.1016/j.eswa.2024.123654.
D. B. Rubin, “Inference and missing data,” Biometrika, vol. 63, no. 3, pp. 581–592, 1976, doi: 10.1093/biomet/63.3.581.
J. L. Schafer y J. W. Graham, “Missing data: Our view of the state of the art,” Psychol. Methods, vol. 7, no. 2, pp. 147–
D.A. Revilla Cabrera Investigación & Desarrollo, Vol. 25, No. 2: 5 – 16 (2025) - ISSN 1814-6333 15 177, 2002, doi: 10.1037/1082-989X.7.2.147.
A. Sportisse, C. Boyer, y J. Josse, “Imputation and lowrank estimation with missing not at random data,” Stat. Comput., vol. 30, no. 6, pp. 1629–1643, 2020, doi: 10.1007/s11222- 020-09963-5.
K. Tsui, “Multidimensional poverty indices,” Soc. Choice Welf., vol. 19, no. 1, pp. 69–93, 2002, doi: 10.1007/s003550100155.
S. van Buuren y K. Groothuis-Oudshoorn, “mice: Multivariate imputation by chained equations in R,” J. Stat. Softw., vol. 45, no. 3, pp. 1–67, 2011, doi: 10.18637/jss.v045.i03.
G. Vink, L. E. Frank, J. Pannekoek, y S. van Buuren, “Predictive mean matching imputation of semicontinuous variables,” Stat. Neerl., vol. 68, no. 1, pp. 61–90, 2014, doi: 10.1111/stan.12023.
S. Vyas y L. Kumaranayake, “Constructing socio-economic status indices: How to use principal components analysis,” Health Policy Plan., vol. 21, no. 6, pp. 459–468, 2006, doi: 10.1093/heapol/czl029.
J. N. Wulff y L. Ejlskov, “Multiple imputation by chained equations in praxis: Guidelines and review,” Electron. J. Bus. Res. Methods, vol. 15, no. 1, pp. 41–56, 2017. [En línea]. Disponible: https://academic-publishing.org/index.php/ejbrm/article/view/1344
J. Xiao y O. Bulut, “Evaluating the performances of missing data handling methods in ability estimation from sparse data,” Educ. Psychol. Meas., vol. 80, no. 5, pp. 932–954, 2020, doi: 10.1177/0013164420911136.
Downloads
Additional Files
Published
Issue
Section
License
Copyright (c) 2026 Daniel Alejandro Revilla Cabrera
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Creative Commons Attribution-Noncommercial-Share Alike
CC BY-NC-SA
This license lets others remix, tweak, and build upon your work for non-commercial purposes, as long as they credit the author(s) and license their new creations under the identical terms.
The authors can enter additional separate contract agreements for non-exclusive distribution of the version of the article published in the magazine (for instance, they may publish it in an institutional repository or a book), subject to an acknowledgement of its initial publication in this magazine.