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

The coefficient of determination, known also as the R2, is a common measure in regression analysis. Many scientists use the R2 and the adjusted R2 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 R2, a procedure that might lead to biased results. In this paper, I introduce the use of multiple imputation for the estimation of R2 and adjusted R2 in incomplete data sets. I illustrate my methodology using a biomedical example.