The estimation of R² and adjusted R² in incomplete data sets using multiple imputation

Abstract

The coefficient of determination, known also as the R ², is a common measure in regression analysis. Many scientists use the R ² and the adjusted R ² on a regular basis. In most cases, the researchers treat the coefficient of determination as an index of ‘usefulness’ or ‘goodness of fit,’ and in some cases, they even treat it as a model selection tool. In cases in which the data is incomplete, most researchers and common statistical software will use complete case analysis in order to estimate the R ², a procedure that might lead to biased results. In this paper, I introduce the use of multiple imputation for the estimation of R ² and adjusted R ² in incomplete data sets. I illustrate my methodology using a biomedical example.

Keywords:

• coefficient of determination
• incomplete data
• multiple imputation
• linear regression

Acknowledgements

I would like to thank K. Martin and A. Ferris for the use of their data. Thanks are also due to the editor and two referees for many helpful comments.