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Frequentist Model Averaging with missing observations

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  • Schomaker, Michael
  • Wan, Alan T.K.
  • Heumann, Christian

Abstract

Model averaging or combining is often considered as an alternative to model selection. Frequentist Model Averaging (FMA) is considered extensively and strategies for the application of FMA methods in the presence of missing data based on two distinct approaches are presented. The first approach combines estimates from a set of appropriate models which are weighted by scores of a missing data adjusted criterion developed in the recent literature of model selection. The second approach averages over the estimates of a set of models with weights based on conventional model selection criteria but with the missing data replaced by imputed values prior to estimating the models. For this purpose three easy-to-use imputation methods that have been programmed in currently available statistical software are considered, and a simple recursive algorithm is further adapted to implement a generalized regression imputation in a way such that the missing values are predicted successively. The latter algorithm is found to be quite useful when one is confronted with two or more missing values simultaneously in a given row of observations. Focusing on a binary logistic regression model, the properties of the FMA estimators resulting from these strategies are explored by means of a Monte Carlo study. The results show that in many situations, averaging after imputation is preferred to averaging using weights that adjust for the missing data, and model average estimators often provide better estimates than those resulting from any single model. As an illustration, the proposed methods are applied to a dataset from a study of Duchenne muscular dystrophy detection.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 54 (2010)
Issue (Month): 12 (December)
Pages: 3336-3347

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Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3336-3347

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References

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  1. Hannes Leeb & Benedikt M. Potscher, 2003. "Can One Estimate the Conditional Distribution of Post-Model-Selection Estimators?," Cowles Foundation Discussion Papers 1444, Cowles Foundation for Research in Economics, Yale University.
  2. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
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  7. Yuan, Zheng & Yang, Yuhong, 2005. "Combining Linear Regression Models: When and How?," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1202-1214, December.
  8. Zhou, Yong & Wan, Alan T. K & Wang, Xiaojing, 2008. "Estimating Equations Inference With Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1187-1199.
  9. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
  10. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
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Cited by:
  1. Zhimeng Sun & Zhi Su & Jingyi Ma, 2014. "Focused vector information criterion model selection and model averaging regression with missing response," Metrika, Springer, vol. 77(3), pages 415-432, April.
  2. Zhang, Xinyu & Wan, Alan T.K. & Zou, Guohua, 2013. "Model averaging by jackknife criterion in models with dependent data," Journal of Econometrics, Elsevier, vol. 174(2), pages 82-94.
  3. Schomaker, Michael & Heumann, Christian, 2014. "Model selection and model averaging after multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 758-770.
  4. Michael Schomaker, 2012. "Shrinkage averaging estimation," Statistical Papers, Springer, vol. 53(4), pages 1015-1034, November.
  5. Zhang, Xinyu, 2013. "Model averaging with covariates that are missing completely at random," Economics Letters, Elsevier, vol. 121(3), pages 360-363.
  6. Magnus, Jan R. & Wan, Alan T.K. & Zhang, Xinyu, 2011. "Weighted average least squares estimation with nonspherical disturbances and an application to the Hong Kong housing market," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1331-1341, March.

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