Multiple imputation by chained equations

Handling Missing Data with Imputations in R

Michal Oleszak

Machine Learning Engineer

The MICE algorithm

¹ van Buuren, S., & Groothuis-Oudshoorn, C. G. M. (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of statistical software, 45(3).

MICE: pros & cons

Pros:

Requires fewer replications than the bootstrap.
Works for MAR and MCAR data.
Allows for sensitivity analysis towards MNAR data.

Cons:

Only works with selected imputation methods.
Requires more tuning effort (model selection, choosing predictors).

The mice flow: mice - with - pool

Impute nhanes 20 times:

library(mice)
nhanes_multiimp <- mice(nhanes, m = 20)

Fit a linear regression model to each imputed data set:

lm_multiimp <- with(nhanes_multiimp, lm(Weight ~ Height + TotChol + PhysActive))

Pool regression results:

lm_pooled <- pool(lm_multiimp)

Analyzing pooled results

summary(lm_pooled, conf.int = TRUE, conf.level = 0.95)

            estimate std.error statistic      df p.value    2.5 %   97.5 %
(Intercept) -122.964    10.933   -11.247 735.389   0.000 -144.428 -101.500
Height         1.086     0.060    18.158 796.106   0.000    0.968    1.203
TotChol        2.653     0.884     3.003 305.460   0.003    0.915    4.392
PhysActive    -1.746     1.422    -1.228 733.957   0.220   -4.536    1.045

MICE: available methods

A table from the paper by van Buuren et al. showing imputation models available in MICE. Each model is described by the name, keyword, variable type that it can be used for and whether it is the default option.

¹ van Buuren, S., & Groothuis-Oudshoorn, C. G. M. (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of statistical software, 45(3).

Choosing methods per variable type

mice() takes an argument defaultMethod: a vector of 4 strings, specifying methods for:

Continuous variables
Binary variables
Categorical variables (unordered factors)
Factor variables (ordered factors)

nhanes_multiimp <- mice(nhanes, m = 20, 
                        defaultMethod = c("pmm", "logreg", "polyreg", "polr"))

Predictor matrix

The predictorMatrix governs which variables are used to impute other variables.

nhanes_multiimp <- mice(nhanes, m = 20)
nhanes_multiimp$predictorMatrix

           Age Gender Weight Height Diabetes TotChol Pulse PhysActive
Age          0      1      1      1        1       1     1          1
Gender       1      0      1      1        1       1     1          1
Weight       1      1      0      1        1       1     1          1
Height       1      1      1      0        1       1     1          1
Diabetes     1      1      1      1        0       1     1          1
TotChol      1      1      1      1        1       0     1          1
Pulse        1      1      1      1        1       1     0          1
PhysActive   1      1      1      1        1       1     1          0

Choosing predictors for each variable

Ideally, a proper model selection should be performed.
A quick alternative: use variables correlated with the target.

pred_mat <- quickpred(nhanes, mincor = 0.25)
nhanes_multiimp <- mice(nhanes, m = 20, predictorMatrix = pred_mat)

print(pred_mat)

           Age Gender Weight Height Diabetes TotChol Pulse PhysActive
Age          0      0      0      0        0       0     0          0
Gender       0      0      0      0        0       0     0          0
Weight       1      1      0      0        0       0     1          0
...

Let's practice imputing with MICE!

Handling Missing Data with Imputations in R