# How to choose which imputation to use to replace missing values

I am a psychologist (i.e. not a statistician or mathematician) and wish to replace missing values in my dataset. I have followed the steps here and they seem straightforward. But I really don't know how to decide upon the replacement values for the missing values to enter into my dataset. I have looked on these threads and some answers have come close but none exactly explain what I need to know.

The toy data provided here is very similar in structure to my own: blood pressure measurements taken at three time points; first is a baseline, second after abstinence, third after treatment.

set.seed(2345)
systolic1 <- rnorm(20, 120, 5)
diastolic1 <- rnorm(20, 90, 3)
systolic2 <- rnorm(20, 125, 5)
diastolic2 <- rnorm(20, 94, 3)
systolic3 <- rnorm(20, 120, 5)
diastolic3 <- rnorm(20, 90, 3)
df <- data.frame(systolic1, diastolic1, systolic2, diastolic2, systolic3, diastolic3)
df[c(1,4), 1:2] <- NA
df[1, 3:4] <- NA
df[15, 5:6] <- NA

So I run the mice package on the data.

tempdf <- mice(df, m=5, maxit=5, meth='pmm', seed=500)

This will yield five imputed values for each missing value, e.g.

tempdf$imp$systolic1

If I choose one of the imputations I can even obtain a complete dataset with missing values replaced.

completeData <- complete(tempdf, 3)

But how do I know which of the five imputations to choose (I chose number three here at random)? The link above and most of the relevant cross-validated threads suggest fitting a regression model for each variable with missing data. Now I can do this with:

modelFit1 <- with(tempdf, lm(systolic1 ~ diastolic1 + systolic2 + diastolic2 + systolic3 + diastolic3))

summary(pool(modelFit1))

This yields a table of coefficients. But what do the coefficients mean? How do they help me choose which of the imputed values above to choose? I'm sorry if this seems obvious to everyone, but I would greatly appreciate a simple explanation.

• An excellent resource that goes into much greater depth than the link you provided does is Paul Allison's book Missing Data. One metric for choosing between imputations is the extent to which they alter the original, pre-imputation marginals. Good imputations should have minimal impact on these values. – Mike Hunter Mar 29 '16 at 12:33
• Thank you @DJohnson that actually makes a lot of sense. Is that row-wise or column-wise marginals, or both? And is there a way in mice to determine each imputation's impact on the marginals? And can you tell me how to use the pooled regression coefficients in the summary table? – llewmills Mar 29 '16 at 12:41
• The choice of row vs column should be a function of how your imputations are applied. I don't know mice and can't make a recommendation. The coefficients are the betas or weights used to make or predict the imputation, based on your inputs. – Mike Hunter Mar 29 '16 at 12:47
• Thankyou @DJohnson for the recommended reading; however I could really use some specific advice using the example I provided. For example how do I use the coefficients in the summary table to arrive at the correct imputation to use? – llewmills Mar 29 '16 at 17:51
• For an experienced predictive modeler that would be a straightforward exercise that's not even complex. The problem is that it's a multistep process that exceeds my patience to write an abbreviated comment in this space. Read any number of books or papers about data mining and/or predictive modeling focusing on topics such as holdout validation, cross-validation and model comparison/selection. – Mike Hunter Mar 29 '16 at 18:51