Regression With Missing X's: A Review

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association.http://www.jstor.org Regression With Missing X's: A Review RODERICK J. A. LITTLE* The literature of regression analysis with missing values of the independent variables is reviewed. Six classes of procedures are distinguished: complete case analysis, available case methods, least squares on imputed data, maximum likelihood, Bayesian methods, and multiple imputation. Methods are compared and illustrated when missing data are confined to one independent variable, and extensions to more general patterns are indicated. Attention is paid to the performance of methods when the missing data are not missing completely at random. Least squares methods that fill in missing X's using only data on the X's are contrasted with likelihoodbased methods that use data on the X's and Y. The latter approach is preferred and provides methods for elaboration of the basic normal linear regression model. It is suggested that more widely distributed software is needed that advances beyond complete-case analysis, available-case analysis, and naive imputation methods. Bayesian simulation methods and multiple imputation are reviewed; these provide fruitful avenues for future research.

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