IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i12p3336-3347.html
   My bibliography  Save this article

Frequentist Model Averaging with missing observations

Author

Listed:
  • 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.

Suggested Citation

  • Schomaker, Michael & Wan, Alan T.K. & Heumann, Christian, 2010. "Frequentist Model Averaging with missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3336-3347, December.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3336-3347
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00266-7
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yan, Jun, 2007. "Enjoy the Joy of Copulas: With a Package copula," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i04).
    2. 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.
    3. Agostinelli, Claudio, 2002. "Robust model selection in regression via weighted likelihood methodology," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 289-300, February.
    4. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    5. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
    6. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
    7. King, Gary & Honaker, James & Joseph, Anne & Scheve, Kenneth, 2001. "Analyzing Incomplete Political Science Data: An Alternative Algorithm for Multiple Imputation," American Political Science Review, Cambridge University Press, vol. 95(1), pages 49-69, March.
    8. Gerda Claeskens & Fabrizio Consentino, 2008. "Variable Selection with Incomplete Covariate Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1062-1069, December.
    9. Leeb, Hannes & Pötscher, Benedikt M., 2008. "Can One Estimate The Unconditional Distribution Of Post-Model-Selection Estimators?," Econometric Theory, Cambridge University Press, vol. 24(2), pages 338-376, April.
    10. Yang Y., 2001. "Adaptive Regression by Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 574-588, June.
    11. Buchholz, Anika & Hollander, Norbert & Sauerbrei, Willi, 2008. "On properties of predictors derived with a two-step bootstrap model averaging approach--A simulation study in the linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2778-2793, January.
    12. Honaker, James & King, Gary & Blackwell, Matthew, 2011. "Amelia II: A Program for Missing Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i07).
    13. Claeskens, Gerda & Hjort, Nils Lid, 2008. "Minimizing Average Risk In Regression Models," Econometric Theory, Cambridge University Press, vol. 24(2), pages 493-527, April.
    14. 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.
    15. Leeb, Hannes & Pötscher, Benedikt M., 2003. "The Finite-Sample Distribution Of Post-Model-Selection Estimators And Uniform Versus Nonuniform Approximations," Econometric Theory, Cambridge University Press, vol. 19(1), pages 100-142, February.
    16. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shangwei Zhao & Jun Liao & Dalei Yu, 2020. "Model averaging estimator in ridge regression and its large sample properties," Statistical Papers, Springer, vol. 61(4), pages 1719-1739, August.
    2. Zhao, Shangwei & Zhou, Jianhong & Li, Hongjun, 2016. "Model averaging with high-dimensional dependent data," Economics Letters, Elsevier, vol. 148(C), pages 68-71.
    3. Hai Wang & Xinjie Chen & Nancy Flournoy, 2016. "The focused information criterion for varying-coefficient partially linear measurement error models," Statistical Papers, Springer, vol. 57(1), pages 99-113, March.
    4. Zhimeng Sun & Zhi Su & Jingyi Ma, 2014. "Focused vector information criterion model selection and model averaging regression with missing response," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(3), pages 415-432, April.
    5. Nitzan Cohen & Yakir Berchenko, 2021. "Normalized Information Criteria and Model Selection in the Presence of Missing Data," Mathematics, MDPI, vol. 9(19), pages 1-23, October.
    6. Schomaker, Michael & Heumann, Christian, 2014. "Model selection and model averaging after multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 758-770.
    7. Jiming Jiang & Thuan Nguyen & J. Sunil Rao, 2015. "The E-MS Algorithm: Model Selection With Incomplete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1136-1147, September.
    8. Yuting Wei & Qihua Wang & Wei Liu, 2021. "Model averaging for linear models with responses missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 535-553, June.
    9. Xinyu Zhang & Alan T. K. Wan & Sherry Z. Zhou, 2011. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142, June.
    10. 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.
    11. Zhang, Xinyu, 2013. "Model averaging with covariates that are missing completely at random," Economics Letters, Elsevier, vol. 121(3), pages 360-363.
    12. Schomaker Michael & Heumann Christian, 2011. "Model Averaging in Factor Analysis: An Analysis of Olympic Decathlon Data," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(1), pages 1-15, January.
    13. 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.
    14. Yuan, Chaoxia & Fang, Fang & Ni, Lyu, 2022. "Mallows model averaging with effective model size in fragmentary data prediction," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    15. Michael Schomaker, 2012. "Shrinkage averaging estimation," Statistical Papers, Springer, vol. 53(4), pages 1015-1034, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    3. Xinyu Zhang & Alan T. K. Wan & Sherry Z. Zhou, 2011. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142, June.
    4. Wan, Alan T.K. & Zhang, Xinyu & Wang, Shouyang, 2014. "Frequentist model averaging for multinomial and ordered logit models," International Journal of Forecasting, Elsevier, vol. 30(1), pages 118-128.
    5. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    6. Aman Ullah & Huansha Wang, 2013. "Parametric and Nonparametric Frequentist Model Selection and Model Averaging," Econometrics, MDPI, vol. 1(2), pages 1-23, September.
    7. Schomaker, Michael & Heumann, Christian, 2014. "Model selection and model averaging after multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 758-770.
    8. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    9. Sun, Yuying & Hong, Yongmiao & Lee, Tae-Hwy & Wang, Shouyang & Zhang, Xinyu, 2021. "Time-varying model averaging," Journal of Econometrics, Elsevier, vol. 222(2), pages 974-992.
    10. Liu, Chu-An, 2012. "A plug-in averaging estimator for regressions with heteroskedastic errors," MPRA Paper 41414, University Library of Munich, Germany.
    11. 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.
    12. Cheng, Xu & Hansen, Bruce E., 2015. "Forecasting with factor-augmented regression: A frequentist model averaging approach," Journal of Econometrics, Elsevier, vol. 186(2), pages 280-293.
    13. Xu Cheng & Bruce E. Hansen, 2012. "Forecasting with Factor-Augmented Regression: A Frequentist Model Averaging Approach, Second Version," PIER Working Paper Archive 13-061, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 03 Sep 2013.
    14. Yuting Wei & Qihua Wang & Wei Liu, 2021. "Model averaging for linear models with responses missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 535-553, June.
    15. Michael Schomaker & Christian Heumann, 2020. "When and when not to use optimal model averaging," Statistical Papers, Springer, vol. 61(5), pages 2221-2240, October.
    16. Zhang, Xiaomeng & Zhang, Xinyu, 2023. "Optimal model averaging based on forward-validation," Journal of Econometrics, Elsevier, vol. 237(2).
    17. Alena Skolkova, 2023. "Model Averaging with Ridge Regularization," CERGE-EI Working Papers wp758, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    18. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    19. Shou-Yung Yin & Chu-An Liu & Chang-Ching Lin, 2021. "Focused Information Criterion and Model Averaging for Large Panels With a Multifactor Error Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 54-68, January.
    20. Yan Gao & Xinyu Zhang & Shouyang Wang & Terence Tai-leung Chong & Guohua Zou, 2019. "Frequentist model averaging for threshold models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 275-306, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3336-3347. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.