Auxiliary variables in multiple imputation in regression with missing X: a warning against including too many in small sample research

BMC Medical Research Methodology

Rainer Leonhart²  Max Herke¹  Jochen Hardt¹ 

[1] Medical Psychology and Medical Sociology, Clinic for Psychosomatic Medicine and Psychotherapy, University of Mainz, Duesbergweg 6, Mainz 55128, Germany;Social Psychology and Methods, University of Freiburg, Engelberger Straße 41, Freiburg, 79106, Germany

关键词: Small and medium size samples;    Simulation study;    Auxiliary variables;    Multiple imputation;   

Others  :  1126352
DOI  :  10.1186/1471-2288-12-184

 received in 2012-07-05, accepted in 2012-11-28,  发布年份 2012

【 摘 要 】

Background

Multiple imputation is becoming increasingly popular. Theoretical considerations as well as simulation studies have shown that the inclusion of auxiliary variables is generally of benefit.

Methods

A simulation study of a linear regression with a response Y and two predictors X₁ and X₂ was performed on data with n = 50, 100 and 200 using complete cases or multiple imputation with 0, 10, 20, 40 and 80 auxiliary variables. Mechanisms of missingness were either 100% MCAR or 50% MAR + 50% MCAR. Auxiliary variables had low (r=.10) vs. moderate correlations (r=.50) with X’s and Y.

Results

The inclusion of auxiliary variables can improve a multiple imputation model. However, inclusion of too many variables leads to downward bias of regression coefficients and decreases precision. When the correlations are low, inclusion of auxiliary variables is not useful.

Conclusion

More research on auxiliary variables in multiple imputation should be performed. A preliminary rule of thumb could be that the ratio of variables to cases with complete data should not go below 1 : 3.

【 授权许可】

   
2012 Hardt et al.; licensee BioMed Central Ltd.

【 图 表 】

Figure 1.

Figure 2.

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