Missing data treatments and multiple regression: An empirical investigation of stochastic imputation, deterministic imputation, and the deletion procedure

The purpose of this study was to investigate, within the context of two-predictor multiple regression analysis with randomly missing data, the effects of eight missing data treatments on the sample estimates of R$sp2$ and each standardized regression coefficient. The missing data treatments examined were listwise and pairwise deletion, mean substitution, simple and multiple regression, stochastic mean substitution, stochastic simple regression, and stochastic multiple regression. One thousand bootstrap samples of size 50, 100, and 200 were drawn with replacement from two sets of educational data. Six proportions of data were randomly deleted within each sample to represent cases with missing data.;The data were analyzed utilizing a repeated measures analysis of variance for each data set, sample size, and dependent variable. Significant interaction effects between percent of missing data and missing data treatment were obtained $(p<.0001)$ in each analysis. Pairwise contrasts were calculated between the complete sample condition and each missing data condition.;Listwise deletion yielded slightly fewer estimates of R$sp2$ that were significantly different from the complete sample estimates than either stochastic multiple regression or pairwise deletion. The other missing data treatments yielded estimates of R$sp2$ that were statistically significant from the complete sample estimates 100% of the time.;For each standardized regression coefficient, listwise deletion and stochastic multiple regression did not yield any estimates that were significantly different from the complete sample estimates. Pairwise deletion was almost as effective as listwise deletion and stochastic multiple regression. Mean substitution, stochastic mean substitution, and multiple regression yielded parameter estimates significantly different from the complete sample parameter estimates 100% of the time. Simple regression and stochastic simple regression showed inconsistent results across variables and across data sets.;Based on the results of this study, the use of listwise deletion, stochastic multiple regression, and pairwise deletion were recommended for the treatment of randomly missing data.