Abstract
Graphical models are a powerful tool to analyze multivariate data sets that allow to reveal direct and indirect relationships and to visualize the association structure in a graph. As with any statistical analysis, however, the obtained results partly reflect the uncertainty being inherent in any type of data and depend on the selected variables to be included in the analysis, the coding of these variables and the selection strategy used to fit the graphical models to the data. This paper suggests that these issues may be even more crucial for graphical models than for simple regression analyses due to the large number of variables considered which means that a fitted graphical model has to be interpreted with caution. Sensitivity analyses might be recommended to assess the stability of the obtained results. This will be illustrated using a data set on undernutrition in Benin.
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References
Blauth, A., Pigeot, I. & Bry, F. (2000). Interactive analysis of high–dimensional association structures with graphical models, Metrika 51: 53–65.
Caputo, A., Foraita, R., Klasen, S. & Pigeot, I. (2003). Undernutrition in Benin - An analysis based on graphical models, Social Science & Medicine 56: 1677–1697.
Cox, D. R. & Wermuth, N. (1993). Linear dependencies represented by chain graphs (with discussion), Statistical Science 8: 204–283.
Cox, D. R. & Wermuth, N. (1994). Tests of linearity, multivariate normality and the adequacy of linear scores, Journal of the Royal Statistical Society, Series C (Applied Statistics) 43: 347–355.
Cox, D. R. & Wermuth, N. (1996). Multivariate Dependencies, Chapman & Hall, London.
Edwards, D. (2000). Introduction to Graphical Modelling, 2 edn, Springer, New York.
Foraita, R., Klasen, S. & Pigeot, I. (2008). Using graphical chain models to analyze differences in structural correlates of undernutrition in Benin and Bangladesh, Economics and Human Biology 6: 398—-419.
Foraita, R. & Sobotka, F. (2008). gmvalid: Validation of graphical models. R package version 1.2.
Friedman, N., Goldszmidt, M. & Wyner, A. (1999a). Data analysis with bayesian networks: a bootstrap approach.
Friedman, N., Goldszmidt, M. & Wyner, A. (1999b). On the application of the bootstrap for computing confidence measures on features of induced bayesian networks.
Frydenberg, M. (1990). The chain graph markov property, Scandinavian Journal of Statistics 17: 333–353.
Gorstein, J., Sullivan, K., Yip, R., de Onis, M., Trowbridge, F., Fajans, P. & Clugston, G. (1994). Issues in the assessment of nutritional status using anthropometry., Bull World Health Organ 72: 273–283.
Green, P. J., Hjort, N. L. & Richardson, S. (eds) (2003). Highly Structured Stochastic Systems, Oxford University Press, Oxford.
Klasen, S. (2003). Malnourished and surviving in South Asia, better nourished and dying young in Africa: what can explain this puzzle?, Measurement and Assessment of Food Deprivation and Undernutrition, FAO, Rome, pp. 283–287.
Klasen, S. (2008). Poverty, undernutrition, and child mortality: Some inter-regional puzzles and their implications for research and policy, Journal of Economic Inequality 6: 89–115.
Lauritzen, S. L. (1996). Graphical Models., Clarendon Press, Oxford.
Lauritzen, S. L. & Wermuth, N. (1989). Graphical models for associations between variables, some of which are qualitative and some quantitative, Annals of Statistics 17: 31–57.
Macro (1996). MEASURE DHS datasets Bangladesh, Benin. www.measuredhs.com, last accessed: 10. Aug 2009.
Steck, H. & Jaakkola, T. S. (2004). Bias-corrected bootstrap and model uncertainty, in S. Thrun, L. Saul & B. Schölkopf (eds), Advances in Neural Information Processing Systems 16, MIT Press, Cambridge, MA.
UNICEF (1998). The State of the World’s Children: Focus on Nutrition., UNICEF, New York.
WHO (1995). Physical status: The use and interpretation of anthropometry, WHO Technical Report Series 854, WHO, Geneva.
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Pigeot, I., Klasen, S., Foraita, R. (2010). Graphical Chain Models and their Application. In: Kneib, T., Tutz, G. (eds) Statistical Modelling and Regression Structures. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2413-1_13
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DOI: https://doi.org/10.1007/978-3-7908-2413-1_13
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