# Imputation and linear regression analysis paradox

Missing values, especially in small datasets, can introduce biases into your model. There are several data imputation methods (MICE, Amelia II), which use EM algorithms to "fill in" the missing values. (Examples: http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2005.00317.x/abstract;jsessionid=E8761B782A07D5528348E853CA10FD71.f04t02, http://www.jstatsoft.org/v45/i03/paper). Most of these imputation methods use a form of linear regression to impute the data, then linear models are fitted to the newly imputed data.

However, isn't the logic for this method circular since you're imputing data using a linear model, then fitting the imputed data with another linear model? Wouldn't that inflate c-statistics for fitting methods that use similar techniques to the imputation method? If so, are there any other techniques for handling datasets with missing values?

• You can use any method you wish. – mandata Aug 13 '15 at 17:08
• I think if you are already using EM to fit the model, which can deal with missing values, there is no need to impute values and fit again. Just use the original EM fit to the incomplete data set, and use statistics appropriate to EM fit to evaluate the result. – A. Donda Aug 13 '15 at 18:12

An advantage of multiple imputations, as provided by MICE, is that there is a stochastic element to the imputations. The imputed values are drawn from distributions estimated from the data rather than deterministically. Several different sets of imputed data are generated. Differences among the imputed sets represent uncertainty in the imputation process. The linear modeling is then applied to each of the imputed data sets separately. Combining regression coefficients among the multiple imputed data sets thus includes information about the uncertainties introduced by imputation, avoiding the circularity that you fear (and that would have to be taken into account in deterministic single imputations). This page has links to further information.